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EXPERIMENTAL STUDIES OF HARMONIC GENERATION

FROM SOLID-DENSI'N PLASMAS

PRODUCED BY PICBSECOND ULTRA-INTENSE LASER PULSES

Liang Zhao

A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy

Department of Physics University of Toronto

O Copyright by Liang Zhao 1998

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Experimental Studies of Harmonic Generation from Solid-Density Plasmas

Produced by Picosecond Ultra-Intense Laser Pulses

Doctor of Philosophy, 1998, Liang Zhao, Department of Physics, University of Toronto

Abstract

In this thesis, an experimental investigation of harmonic generation from high-

intensity laser-plasma interactions is presented. Harmonic experiments performed on the

1-terawatt FCM-CPA laser system at the University of Toronto, and on the 10-terawatt T3

laser system at the University of Michigan, are described.

Using the FCM-CPA laser, various aspects of second harmonic generation were

investigated systematicaily, with a focus on the effect of preformed plasma on harmonic

generation. Experiments comparing hamonics generated by high-contrast pulses and by

pulses containing weak prepulses show that the preformed plasma causes spatial and

spectral breakup of harmonics and diffuses harmonic emission into large solid angles.

On the T3 laser system, mid-order harmonic generation from various solid materials was

studied and both odd and even harmonics up to the 7th were observed. Important

features of harmonic generation, Le., the laser-polarization dependence and the angular

distribution of harmonic emission, were characterized. Purnp-probe expetiments were

carried out as well on both laser systems by adding a controlled prepulse, which

demonstrated a strong dependence of harmonic production efficiency on the gradient of

preformed plasma.

We also describe what we believe to be the first observation of regular satellite

features accompanying the mid-order harmonics. Their dependence on target materials

and on laser intensity was measured, and possible pbysical explanations are discussed.

Besides, the development of the Toronto FCM-CPA laser system is summarized.

Its original design and unique features are described in detail.

Acknowledgments

First, 1 would iike to thank my thesis supervisor, Professor Robin Marjoribanks,

for his guidance and support during the course of this research. 1 thank him for

introducing me to this fast developing, yet challenging research field and for providing

me the opportunity of working in his lab. His advice and careful reading of various drafts

of the manuscript have significantly improved the quality of this thesis.

The members of rny Ph.D. supe~isory committee, Professor John Sipe and

Professor Henry van Driel, have provided me a great amount of help in the past years. 1

am very grateful for the advice and assistance they have given to me. I would also like to

thank Professor Paul Drake, Professor Aephrairn Steinberg, and Professor Peter Smith for

their critical reading of my thesis and for their valuable suggestions. Constant help in

many aspects provided by Mrs. Marianne IUiwana was also greatly appreciated.

This work could not possibly have been completed without the support, help, and

encouragement from my fellow graduate students, Fred Budnik and Gabor Kulcsh.

During the past several years, it was their enthusiasm, Wendship, and optirnism that kept

my spirit up, helped me to overcome the difficulties, and made this lab a much pleasant

place to work and to study. 1 am also grateful to Professor Peter Heman, who kindly let

me share most of his lab tools, and suggested many good ideas for my experiments. The

assistance of other members in the group was also greatly appreciated. Among them are:

Michel Stanier, James Mihaychuk, Hideo Yamakoshi, Sherry Crossly, Bin Xiao,

Hiroyuki Higaki, Estelle Rouillon, and Adrian Vitcu.

I would like to thank the Center for Ultrafast Optical Science at the University of

Michigan for providing me the opportunity of working on their excellent facilities. In

particular, 1 would like to thank Dr. Anatoly Maksimchuk and Robert Wagner for

assisting the expeririients in many ways and for staying so many late nights running the

laser system. Thanks also go to Dr. Jonathan Workman for providing his target materials

to me, to Dr. Paul Le Blanc and Professor Michael Downer for allowing me to use their

prepulse setup, and to Professor Donald Umstadter and Professor Gérard Mourou for

their encouragement and generosity with laser time.

My thanks aIso go to the staff in this department and at Photonic Research

Ontario who constantly provided both excellent technicai support and necessary

equipment whenever 1 needed either. Financial support frorn the University of Toronto

Open Fellowship, from the Burton Scholarship at the Department of Physics, and from

the research funding provided by the Natural Science and Engineering Research Council

of Canada and Photonic Research Ontario, is also gratefully acknowledged.

1 am especially grateful to my parents. Through out these years, it was their

continuing support and encouragement that motivated me working towards this final

goal. Without their support I could not have reached this far. Lastly, and most

importantly, 1 am deeply h debt to my wife, Yuanyuan, who endured ail the late nights

and lost weekends with remarkable patience and understanding.

Table of Contents

Abstract

Acknowledgments

Table of Contents

Chapter 1

1.1

1.2

1.3

1.4

Chapter 2

2.1

2.2

Introduction

A Brief Historical Review of Harmonic Generation in Solids

Scope of this Thesis

Outline of the Dissertation

Role of the Author

Theoretid Background

Introduction to Laser-Plasma Interaction

2.1.1 Plasma Generated by Intense Laser Pulses on Solid

Target

2.1.2 Waves in Plasma

2-1.3 Some Basic Processes in Laser-Plasma Interaction

Mechanisms of Harmonic Generation in an Overdense Laser-

Produced Plasma

Table of Contents

Simple Hmonic-Generation Phenomenology

Second Harmonic Generation: a Perturbation Theory

Particle-in-Cell Simulation Results

The Linear Mode-Coupling Model

The Oscillating-~irror Model

Model Predictions: Harmonic Generation with Varying

Experimental Parameters

2.3 RoIe of Preformed PIasma

2.3.1 Laser Prepulses

2.3.2 Effects of Preplasma on Harmonic Generation

2.3.3 Modification of Plasma Density Profde by a Deliberate

Prepulse

2.4 Conclusions

Chapter 3 Development of the Toronto FCM-CPA Laser System

3.1 Introduction to the CPA Technology

3.2 The Feedback-Controlled Mode-Locked (FCM) Oscillator

3.2.1 Purpose of Feedback Control in the Oscillator

3.2.2 Pulse Development in the FCM Oscillator

3.2.3 High-Contrast Characterization of Pulses from the FCM

Osciliator

3 -3 The FCM-CPA Laser S ystem

3.3.1 TheLaserSetup

3.3.2 Characterization of Beam Focus in the Target Chamber

3.3.3 Compressed Pulse Characterization Using High-

Contrast Cross-cordation

3.3 -4 Single-S hot Autocorrelation

Table of Contents

3.4

3.5

Chapter 4

4.1

4.2

4.3

4.4

4.5

4.6

Chapter 5

5.1

5.2

5.3

A Novel Cross-correlation Technique

3 -4.1 Design of the W e i Cross-correlator

3 -4.2 Experimental Results

Conclusions

Experimental Results of Second Harmonie Generation

Experimental Setup

Laser Pulse Cleaning with Saturable Absorber

Second Harmonic Generation (SHG) and the Effect of Prepulse

4.3.1 Power Scaling of SHG

4.3.2 Anguiar Distribution of SHG

4.3.3 Imaging of the SHG Emission

SHG with Controiled Prepulses

4.4.1 Prepulse Setup

4.4.2 Experimental Results

Experiments Beyond SHG

Conclusions

Experimental Results of Mid-Order Harmonic Generation

The T3 Laser System

Experimental Setup for the Hannonic Measurement

5.2.1 The Target Chamber

5.2.2 TheVUVSpectrometer

Results of Mid-Order Hannonic Generation

5.3.1 Observation of the Third to Seventh Harmonics

5.3.2 Dependence on Laser Polarization

5.3.3 Angular Distribution of the Harmonics

vii

Table of Contents

5.4 Harmonic Generation with ControUed Prepulses


5 A.2 Experimental Results

5.5 Observation of Satellite Structure in the Mid-Harmonies

5.6 Conclusions

Chap ter 6 Discussion and Conclusions

6.1 Summary of the Experimental Results

Effects of Preplasma on Harmonic Generation

Plasma Scale-length Dependence

Mid-Order Warmonic Generation on Different Solid

Targets

Angular Distribution of Harmonic Emission

Laser Polarization Dependence

First Observations of Hannonic Satellite Structures

High-Contrast CPA Laser

6.2 Suggestions for Future Experiments

References

Chapter 1 Introduction

The development of the chirped-pulse-amplification (CPA) technique cl] in the

last decade has enabled high power lasers to produce multi-terawatt femtosecond and

picosecond laser pulses which c m be focused on target at intensities previously

inaccessible in the laboratory. Many new interesting physical phenomena have been

studied in this new regime [2-51.

The generation of optical harmonies of very high order is one example of the new

phenomena that occur when extremely intense ultrashort laser pulses interact with matter

[6]. High odd-order harmonic generation has been studied extensively in noble gases [7],

in molecular gases [8], in atomic clusters [9], and in ionized media [IO], and harmonic

orders as high as 135 [Il] and wavelengths as shoa as 6.7 nm [12] have been reported.

The observed hannonic spectra exhibit a characteristic non-perturbative behavior: with

increasing harmonic order, the harrnonic intensity decreases initially, then remains

approximately constant up to a rather sharp cutoff, beyond which no further emission is

observed. The physical mechanism for this type of harmonic generation is now weli

understood, thanks to a so-called two-step mode1 developed by Corkum [13] and

Kulander [14]. In this quasi-classical interpretation, an electron first tunnels through the

barrier formed by the Coulomb potential and the laser field. Once free, the electron

moves in the laser field to gain a maximum energy of 3.2Up, where Up is the quiver

energy of a free electron in an oscillating electromagnetic field, and then retums towards

the nucleus as the laser field reverses direction. Harmonic photons with energies up to

Chapter I Introduction

1, + 3.2UP, where Ip is the ionkation potential of the atom, can then be produced when

the electron recombines with its parent ion. This predicted cutofT energy agrees very well

with the experimentally observed value of Ip + 2Up, when taking into account the

propagation effects 1151. Further development of this type of hannonic generation using

higher laser intensities, however. has been limited by medium depletion through

ionization, and by the resulting free electrons that induce phase mismatch between the

pump pulse and the harmonic signal, degrading the harmonic conversion efficiency.

High-order harmonic generation also occurs in intense laser interaction with solid

media In fact, twenty years ago, long before the gas-interaction experiments, pXple had

observed high-order harmonics from laser-produced plasmas on solid targets, using high-

intensity nanosecond COz lasers [16-191. Unlike the gas case, both odd and even orders

of harmonics were observed in those experiments, indicating that the harmonic radiation

was not from the ions in the laser-produced plasma, but generated under physical

conditions lacking inversion symmetry-it is generally believed now that this type of

harmonic generation originates from the strong anharmonicity of the collective electron

motions across the vacuum-plasma boundary, where the restoring force is extremely non-

uniform. Harmonies generated by this mechanism are not subject to the same saturation

or phase-matching limitations that gas harmonics suffer, thereby offering a very

promising and efficient means of producing intense short-wavelength coherent radiation.

In some applications, such as deeply bored channels in fast-ignitor laser-fusion

experiments [ZO], h m o n i c emission together with a clear means of interpretation may

provide a valuable new diagnostic of the conditions of intense laser-matter interaction.

Xn this thesis, we present an experimental investigation of harmonic generation

from high-intensity laser-plasma interaction on solid targets. The general goals of this

research are to gain insight b to the harmonic generation mechanism by testing various

theoretical predictions, to provide new empirical information, and to find the optimum

conditions for efficient harmonic production.

1.1 A Brief Elistorical Review of Harmonic Generation in Soiids

High-order harmonic generation in dense, laser-produced plasma was first

reported two decades ago in a nanosecond CO2-laser-target expenment performed by

Bunien et al. [16] at the National Research Council of Canada. Up to 1 lth harmonic,

with yields falling off approximately hearly with the harmonic order, were observed in

the back-scattered beam direction for an incident laser intensity > 1014 Wlcm2. Similar

results were produced later with a 75-ps N&glass laser at a intensity - 10'6 Wkm2 [17].

In the early 80's. in a series of experiments on CO2-laser-produced plasmas,

Carman et al. 118, 191 reported the observation of up to the 46th harrnonics at laser

intensities greater tha . 1015 W/cm2. The harmonic spectra exhibited a nearly constant

conversion efficiency over the observed harmonic orders before an apparent sharp high-

frequency cutoff. Theoretical models developed by Beverides et al. [21] and Grebogi et

al. [22] suggested that the high-harmonies onginated from the strong anhannonic

electron motion dong a steep density gradient of the surface plasma produced by the laser

pulse. By assurning a step-like discontinuity of the density arising from the

ponderomotive force of the laser light, these models predicted a characteristic high-

frequency cut-off in the harmonic spectra given by the plasma frequency corresponding

to the upper level of the density profile, which seemed agree with Carman's experimental

observations.

In the go's, progress in the generation of extremely intense ultrashort laser pulses

has led to renewed interest in the harmonic generation from overdense, laser-produced

plasmas. Because of the limited time allowed for plasma to expand, the ultrafast laser-

solid interaction naturaily provides a plasma with a steep density gradient, which is

beiieved crucial for harmonic generation. Although efficient harmonic production from

solid target using picosecond or sub-picosecond laser pulses has been predicted

theoretically, experimental observation has been scarce, and has only corne recently. The

Chapter I Introduction

explanation for this lies in the fact that, compared with the earlier CO2 work, there are

disadvantages associated with the ultrafast lasers. One of the major differences is the

laser wavelength. The current ultrafast lasers work mostly in the spectrai regions of W,

visible or near IR, where the wavelength is at least ten times shorter than that of CO2

laser ( A = 10.6 pm). This means that one needs rnuch higher laser intensities I to

achieve the sarne value of IA*, a scaling factor associated directly with the oscillating

current strength in a plasma and therefore the efficiency of harmonic generation. The

shorter wavelength for the fundamental light also rneans that the harmonics generated

will be in the UV region, where plasma recombination-emission background is strong;

this makes the detection of the harmonics more mcult. Besides the wavelength factor,

the ultrashort interaction time also means the ponderomotive steepening of the plasma

density profile is less effective than with the nanosecond pulses of the CO2 laser.

Therefore the intrinsichy foxmed plasma density profile, which is determined mostiy by

the intensity contrast of the ultrashort laser pulse, becomes extremely important.

The e s t experimental demonstration of high-order harmonic generation from

sub-picosecond laser-solid interaction was made by Kohlweyer et al. [23]. Using a 150-

fs terawatt Ti:sapphire laser, the authors detected up to the 7th harmonic of 794-nm light

and up to the 4th harrnonic for 397-m light from Al targets at intensities of 1017 Wlcmz.

Time-resolved spectral measurement was used in this experiment to enhance the signal-

to-noise ratio of the sub-picosecond harmonic signais by isolating them from the

nanosecond plasma recombination background. This experiment also demonstrated, for

the first time, the significant influence of laser prepulses on harmonic generation; the

latter was shown only possible when the pulse-prepulse contrast was greater than 106.

Using a similar Ti:sapphUe laser, von der Linde et al. [24,25] observed up to the

18th harmonics at laser intensities of IOi7 - 1018 W/cm2. It was found that hannonic

generation only occurred for p-polarized laser pulses with contrast better than 106. Both

dielectric and metallic targets gave very similar harmonic spectra, which were

Chapter I Introduction 5

characterized by a relatively smooth exponential roll-off at high frequencies. The

conversion efficiencies were roughly estimated as l e and 5 x 1û-8 for the lûth and 15th

harmonics, respectively.

Harmonie generation fiom a more extended plasma has recently been studied in a

series of experiments [26-291 performed on the Nd:glass VüLCAN laser system, which

produces 2.5-ps pulses with intensities up to 1019 Wkm2 and a contrast better than 106.

Up to the 68th harmonics were observed with relatively high conversion efficiencies

estimated to be 10-4 (16th harmonic) to 1 û-6 (68th hannonic). However, the observation

of an isotropie harmonic emission over a 27~ solid angle, and the insensitivity of harmonic

efficiency to the laser polarization and to the introduction of Eurther prepulses, Iead the

authors to conclude that they were observing harmonic production at a rippled critical

density surface, rather than from a thin planar plasma at the solid surface.

On the theoretical side, harmonic generation from thin, near-solid-density plasmas

has also become a topic of keen interest in the last few years. Cornplementary to the

theories developed by Bezzerides and Grebogi for the CO2 experiments, new harmonic

generation mechanisms have been proposed. Among them are the oscillating-mirror

mode1 [30-321 which interprets the harmonic generation as a phase modulation

experienced by the light reflected from an oscillating critical surface; the vacuum heating

mode1 [33, 341 which represents the harmonics as being produced by those electrons

which undergo large-amplitude vacuum excursions; and the J x B mechunim [35] which

emphasizes the AC-ponderomotive contributions to harmonic generation at relativistic

laser intensities (> 10'8 WIcrn2).

1.2 Scope of this Thesis

Compared to the case of interaction with gas targets, experiments on harmonic

generation using solid targets are much more difficult to perform and to analyze.

Chapter 1 Introduction 6

Because of this, many fewer harmonic generation experiments have been carried out

using solid targets than using gas targets.

One aspect of the complexity of high-harmonic generation from laser-plasma

interaction is that nonlinear hydrodynamics is virtually always folded together with the

nonlinear optical conversion process. In nanosecond CO2 experiments, the DC-

ponderomotive force of the laser pulse steepens the plasma density profile significantly,

and the process of harmonic production therefore folds together two types of nonlinearity:

nonlinear optical conversion largely from the electron fluid, and hydrodynamic

nonlinearities of grossly 'preparing' the plasma. This makes the interpretation of

experimental results much more difficult.

What makes things even more complicated is a preformed plasma. Plasma

preformed by laser prepulses is a concem in ail experiments studying intense laser

interaction with near-solid-density matter. It has particular impact in ultrafast laser-target

experiments where ponderomotive density profile steepening is less effective. Although

the effect of preformed plasma on harrnonic generation from solids had been widely

discussed, its effect 011 harmonic generation had not been systematically tested until this

work.

These physics issues are of particular interest to us. To understand the physical

mechanisms for harmonic generation in laser-plasma interaction, it would be useful to

characterize the optical participation of electrons without at the same time grossly

modifjring the plasma density gradients during irradiation. Because in sub-picosecond

laser-plasma interactions, ponderomotive modification is less significant due to the short

interaction time, studies of harmonic generation using very short pulse-durations offer the

prospect of separating the nonlinear contributions. To avoid preformed plasma, a high

contrast laser pulse is also needed. This wfi ensure a clean laser-soiid interaction. With

this done, one can further study the dependence of harmonic generation on the plasma

density gradient, which is of great theoretical and practical interest.

Analytic models predict that there exists an optimum density gradient for which

the electron motions responsible for hannonic generation can be driven most effectively

by laser Light, and therefore can produce maximum harmonic efficiency and orders. This

prediction has been demonstrated in cornputer simulations performed by Delettrez et al.

1361 and by Lichters et al. [37], and is ready to be tested experirnentally.

In the experiments descnbed in this thesis, we have partly dissected the physical

issues discussed above. We have used picosecond and subpicosecond laser pulses of

contrast better than 101°-the highest puIse contrast to be used in such experiments-to

study harmonic generation under the condition of minimized preplasma formation.

Furthemore, by comparing harmonics generated with the ultra-clean pulse and with

pulses containing a weak prepulse, we have systernatically investigated the effect of

preformed plasma on harmonic conversion-efficiency and angular distribution, as well as

on spatial and spectral brightness. Using a purnp/probe technique, we have also

performed experiments in which the conversion efficiencies of the second and third

harmonics were measured from different prepared plasma-gradients.

1.3 Outline of the Dissertation

In Chapter 2, the basic theory of laser-plasma interaction on a solid is provided.

Various mechanisms of harmonic generation in overdense plasmas are discussed. The

dependence of harmonic generation on several experimental parameters is also given.

Chapter 3 is devoted to a description of the development of the FCM-CPA laser

system constructed here at the University of Toronto. Unlike the original fiber-expansion

and grating-compression scheme used in most of the CPA laser systems in the early go's,

the FCM-CPA laser is an dl-Nd:glass system based on grating-only expansion and

compression of high-contrast 1-ps seed pulses produced in a feedback-controlled

Nd:glass oscillator. One of the unique features of this system is that, without using

Chapter 1 Introduction 8

complicated pulse-cleaning techniques, it provides a 5 x 107 puise-to-pedestal contrast

ratio. the highest arnong the systems built at the time of its construction. The original

design and the characterization of this system are presented in detail. At the end of the

chapter, a novel cross-correlation technique capable of measuring the true pulse shape of

picosecond pulses is described.

Chapter 4 describes the experiments perforrned on the FCM-CPA laser system to

snidy the second harmonic generation from laser-plasma interaction. In this series of

experiments, we focus on the effect of pre-formed plasma, produced by small prepulses,

on the harmonic generation process. We present a systematic study of the influence of

preplasma on harmonic yield, angular distribution, and spatial and spectral distributions.

A pump-probe experiment using a deliberate and controlled prepulse is also described,

and the relation between the harmonic generation efficiency and the plasma density scale-

length is discussed. Experimental efforts on the FCM-CPA system searching for

harmonics higher than the second are sumrnarized at the end of the chapter.

in Chapter 5, the mid-harmonic experiments conducted on the T3 laser system at

the University of Michigan are covered. We describe the experimental observation of up

to 7th harrnonic from various solid targets and the results of their angular distribution and

dependence on laser polarization. In addition, an improved pump-probe experiment

together with a quantitative relation between the harmonic generation efficiency and the

scaie-Iength of the plasma are presented. The chapter concludes with what we believe to

be the first observation of a regular Stokes- and anti-Stokes-like satellite features

accompanying the mid-order harmonics. Measurement of their dependence on target

material and laser intensity are given, and possible physical explanations are discussed.

The final conclusions are drawn in Chapter 6, together with suggestions for future

directions of the work.

Chapter 1 IntroductSon

1.4 Role of the Author

This thesis contains experimental work performed jointly by researchers from

severai research groups. Due to the nature of this collaboration work, it is sometimes

difficult to pull out single threads from individual researh ers.

The FCM-CPA laser system described in Chapter 3 represents a team effort with

contributions from al1 the members in the Toronto group. The author's major

contributions were: building of the hg-design regenerative amplifier, high-dynamic-

range characterization of pulse contwst, meosvrement of pulse development in the FCM

oscillator, and construction and calibration of the single-shot autocorrelator. The noveI

cross-correlator described in 5 3.4 was originally built by Gabor Kulcsik, Michael

Woodside, and James Mihaychuk. The author's involvement in this project was

optirnizing the performance of the cross-correlator and using it to measure the real shape

of pulses from the FCM oscillator.

The second harrnonic experiments (Chapter 4) and mid-harmonic experiments

(Chapter 5) were performed and analyzed mainiy by the author. But this work could not

be compieted without the valuable suggestions and assistance from Fred Budnik, Ggbor

KulcsAr, and my research supervisor Robin Marjoribanks, as well as the staff on the T3

system, AnatoIy Maksimchuk and Robert Wagner.

Chapter 2 Theoretical Background

In this chapter, the theones of harmonic generation by the interaction of an ultra-

intense laser pulse with a solid target are described. The harmonic generating

mechanisms discussed here are diffèrent fiom those in relativistic harmonie-generation in

underdense plasmas [38, 391, or in surface harmonie-generation at moderate-intensities

[40,4 11. In order to understand the physics involved, a brief introduction is given fxst, in

which the basic properties of plasmas produced by laser-solid interaction, and processes

that are particularly important to the generation of harmonies, are discussed. As we will

see, preformed plasmas produced by laser prepulses play important role in laser-solid

interactions. Their influences on harmonic generation are discussed in the last section.

2.1 Introduction to Laser-Plasma Interaction

2.1.1 Plasma Generated by Intense Laser Puises on Solid Target

When a terawatt laser pulse is tightly focused, extremely high intensities between

1017 - 1019 Wlcrn2 c m be achieved in the focal spot. The corresponding electric field

amplitudes for such laser intensities are much higher than the magnitude of the atomic

field. For example, the Coulomb field acting on an electron in the f ~ s t Bohr orbit of the

hydrogen atom is E, = e/rb =5.1 x 109 V/cm. This high electric field amplitude can be

achieved in a linearly poiarized laser beam with intensity 1, = c ~ z / 8 a = 3.4 x 1016

W/cm2.

Chapter 2 Theoretical Background 11

When a solid target is exposed to such high intensities, its surface Iayer is

immediately ionized and tninsformed into a hot expanding plasma. It is interesting to

note that, under such high intensities, there is almost no difference in the behavior

between dielectric and conducting targets, since in the dielectric case the fmt electrons

are set free in a fraction of a laser cycle by field ionization. Plasmas produced in such a

fashion exhibit many features different from those in conventional laboratory plasmas,

such as very high electron density (near solid density) and temperature (a few keV, or

107 K), extreme non-uniformity, and ultrashort lifetime. In the case of a high-atomic

number (2) target, free electron densities of at least one order of magnitude higher than in

a metallic conductor c m be achieved. Thus, laser-produced plasma from solid targets

provides an ideal object supporthg fundamental studies of matter in extreme conditions

involving ultrahigh pressures, electric field, and temperatures.

After creating the plasma, the same laser pulse will further interact with the

plasma formed by its rising edge. The interaction between a laser pulse and plasma

depends cntically on the ratio of the pulse carrier fiequency CO to the medium's electron

plasma frequency a,,, (also called Langmuir frequency) defined as

where me is the electron mass and ne is the electron density in units of cm-3. The ratio

w /ape defines two different regimes of laser-plasma interactions. In an underdense

plasma, where w > ape, the plasma is transparent to the laser light. Physical processes

such as inverse bremsstrahlung, stimulated Raman scattering, stimulated Brillouin

scattering, and wake-field generation, etc., are generaIIy studied in this regime of laser-

plasma interaction. On the other hand, the overdense region of the plasma, where

o S wpe, acts much like a totally reflecting &or. Light incident at other than normal

incidence is reflected before reaching the underdense-overdense plasma boundary called

critical density sugace. The evanescent waves penetrating to the critical surface can be


coupled resonantly with the local plasma waves and produce resonance absorption.

harmonic generation, etc. The critical density of a plasma is given by

where hp is the laser wavelength in microns. Obviously, the temis of underdense and

overdense plasmas are relative, depending on the frequency of the incident laser. For

example, a plasma with an electron density ne = 1019 cm-3 is underdense for a YAG laser

(Â= 1.053 un, n,= 1 x 1 0 2 0 ~ 1 ~ 3 ) . but is slightly overdense for a COz laser

(A= 10.6 p, nc= 9.8 x 1018 cm-3).

Laser plasma produced from a solid is very non-unSom-the electron density

drops from near-solid density to vacuum in a distance around the order of laser

wavelength, As we will see in the following sections, much important physics in the

laser interaction with overdense plasmas is govemed by the shape of the plasma density

gradient in the coupling region. For example, plasmas with finite density gradients

usually absorb laser energy much more efficiently than plasmas with sharp vacuum

boundaries. The quantity which is often used to characterize the spatial extent of the

underdense plasma at the vacuum-plasma boundary is the dense scale-le@ defmed as

Foliowing its creation by the laser pulse, the plasma will expand into vacuum clriven by

the kinetic pressure of the hot electrons. As a result its density scaie-length will increase

with time at a rate set by the ion-sound speed c, = (Figure 2.1). Here Z is

the ionkation stage, Te is the electron temperature, and mi is the ion mas . Assuming the

incident laser has a pulse-width Ar and contains no prepulse, the scale-length of the

plasma which the laser will interact with c m be estimated as L = c,&. For a 300-eV

silicon plasma, c,- 10' c d s , or 0.1 W p s , which means that a 1-ps pulse wiil interact

with a plasma of L - 0.1 p.

Chpter 2 Theoretical Background

vacuum solid

Figure 2.1. A sketch illustrating the spatial profile of the electron density distribution. Scale-length L increctses as the plasma expmds.

Zn the discussion of ultra-intense laser-matter interactions, the laser field strength

is usually expressed by the unitless laser-strenm* parameter

where 4 is the peak amplitude of the laser vector potentid, III is the laser intensity in

units of 1018 W/crn2, and Ap is the laser wavelength in microns. The quantity 112 in

Eq. (2.4) is associated with many phenornena in laser-plasma interactions, implying that

the interaction depends not only on the laser intensity, but on the laser wavelength as

well. The value of a. describes how quickiy an electron oscillates in a laser field, i.e.,

oo,& = ao/dG, where vox is the quiver velocity of the electron. From Eq. (2.4)

we can see that for a laser with 1a2 abovel.4 x 1018 W ~ r n - ~ pmz, a. becomes greater

than one, sipiQing the quiver motion of the electron becomes highly relativistic and

2.1.2 Waves in Plasma

A characteristic feature of a plasma is its ability to support waves, or collective

modes of interaction [42,43]. These waves correspond to charge-density fluctuations at a

characteristic frequency determined by the electrons and/or the ions. In a plasma with no


large imposed magnetic fields (the electrostatic approximation), there are two such

densiîy waves: a high-frequency electron plasma wave and a low-frequency ion-plasma

wave. In addition, the propagation of electromagnetic waves in a plasma c m also be

modified by the response of electrons.

EZectron plasma waves

Electron plasma waves (also called Langmuir waves) are longitudinal electrostatic

waves associated with the high-fiequency density fluctuations of electrons, for which the

ions are practically immobile. They obey the following dispersion relation:

where vtk = ,/ksT,/m, = 4 x 107 cm/s is the electron thermal velocity at

electron temperatwe Te- One can see that the frequency of electron plasma waves is

essentially mpe, the electron plasma frequency (Eq. 2.1), with a srnall thermal coirection

depending on the wavenumber k .

The dispersion relation (2.6) is actually an approximation for long-wavelength

waves and has a limited range of validity. It is based on the assumption of adiabatic

compression [42], which is valid when vtk « o / k - wpe/k, or kjl , CC 1. Here

A, m vIhe/mpe is called the electron Debye length, a quantity we will discuss shortly.

Taking this approximation into account, Eq. (2.5) can be written in another useful form:

Ion plasma waves

In addition to the high-frequency electron plasma oscillations, a plasma also

supports ion oscillations, typically at a much lower frequency. These oscillations, which

generally involve longitudinal motions of both electrons and ions, are cailed ion plasma

waves. The general dispersion relation for ion plasma waves is given by


where AD, = 4- is the electron Debye length which we have just seen,

vthi = d m is the ion themai velocity at ion temperature Ti, and spi is the ion-

plasma frequency defined as

Here Z and A are the ionization state and atomic weight of the ions, mi is the ion mas,

and m, is the mass of a proton. Eq. (2.6) is valid when the second term on the right is

much less than the first. In the foliowing, we will consider the case when the second term

in Eq. (2.6) is ignored, Le., the hnit of Ti = 0.

The electron Debye length is the scde-length over which the eiectrons can shield

out the field of a test charge. In the long-wavelength b i t , where A = 2 n/k >> AD,, or

kaDe <C 1, the plasma stays quasi-neutral (ne = Eni), and the ion plasma wave reduces to

the familiar ion-acoustic mode, which has the foilowing dispersion relation

where c, = 4zkB~,/rni is the ion-sound speed which we discussed before. In this case,

the single-fluid oscillations of electrons and ions together are driven by the restoring

force of pressure gradients provided by changes in electron density, with the electrons

closely tied to the ions by their Debye shielding.

The quasi-neutrality assumption holds only for Long-wavelength waves. In the

short-wavelength limit, where kAD, >> 1, the electrons are no longer able to screen the

excess charge of ion density fluctuations, so quasi-neutraiity is no longer achieved and

the restoring force is augmented by charge differences. In this case, the ion plasma wave

becomes purely electrostatic, i.e., ions osciliate in a locally uniform background of

negative charge, in a fashion sirnilar to the electron plasma wave in which electrons

osciliate about a uniform ion background. An interesthg feature of this nonquasineutrd


mode of oscillations is that the wave kquency approaches an asymptotic value which

depends only on the plasma parameters. In this case, the electrostatic ion plasma wave

(often simply c d e d an ion plasma wave. in analogy to the electron plasma wave) simply

oscillates at the ion plasma frequency, Le.,

Uniike the ion-acoustic wave, which has been thoroughly investigated, much less

has been observed for the ion plasma wave, even though it was predicted 70 years ago

[44]. In fact, it was oniy recently that this wave was experimentdy observed for the f i t

tirne [45,46].

Electromagnetic waves

Besides the electrostatic density waves described above, the only other waves in

unmagnetized homogeneous plasma are electromagnetic waves, which have the foilowing

dispersion relation

where a,, is the electron plasma frequency, and c is the speed of light in vacuum.

Letting the plasma density approach zero we regain the free space light waves with

o = ck . Note that the dispersion relation for the electromagnetic waves is very similar to

that for the electron plasma waves (Eq. 2.5), where c2 is replaced by 3vk.

In optical theory, the propagation of light in a medium is usually described by the

medium's refractive index, nmf = c k / o . From Eq. 2.8 we can see that in a plasma the

refractive index is

According to Eq. 2.9, the refractive index of a plasma becomes imaginary when

w c mpe. This is why there is a minimum frequency for a propagating electromagnetic

wave in the plasma.


We have discussed very bnefly the properties of the electron plasma wave, the

ion-plasma wave (including the ion-acoustic wave), and the electromagnetic wave. They

represent the three possible linear modes of plasma oscillations in an unifonn

unmagnetized plasma. As a summary, the dispersion relations for these three waves are

shown qualitatively in Figure 2.2. The number of linear modes in a plasma wili be

greatiy increased with the addition of inhomogeneity or an extenid magnetic field [42].

e

-1 . , ,, , ,<, ,, ,, - ,, ,, , - , z : - - .- - - ---, - - .- - - - - 0 Z

4

1 4 0

/ C =-, Ion plasma waves

Figure 2.2. Dispersion diagrams for electromagnetic waves, electron plasma

waves and ion plasma waves in a homogenous unmagnetized plasma (Ti =O). The correspondhg asymptotic slopes are shown as the dashed Lines.

2.1.3 Some Basic Processes in Laser-Plasma Interaction

The interaction between laser and plasma involves many physical processes. A

full description of these processes is obviously out of the scope of this section. Here we

will discuss some basic processes in laser-plasma interaction, which are most closely

related to the generation of harmonics.


In an inhomogeneous plasma, the electromagnetic and the electron plasma waves

are coupled. For instance, electromagnetic radiation will be emitted if electron-plasma

waves are present in a plasma. Similady, an electromagnetic wave incident on a plasma

c m excite electron-plasma waves. As we will see, these wave-coupling phenomena play

a crucial role in the generation of harmonies.

One of the wave coupling

mechanisms is resonance absorption.

When a electromagnetic wave is incident

on a plasma gradient at an oblique

incident angle 8 , it will be reflected at a X

position called classical turning point, t 1

2 I I

where electron density ne = n, cos 0 (b) ewave t~ I l

I l

I I [47]. The subsequent evanescent wave I l I I I

beyond this point behaves quite

differently depending on its polarization I ' 1 '

* X I I

(Figure 2.3). The s-polarized wave (c) pwave

simply decays exponentially as i t

propagates further into the plasma; the p-

polarized wave, on the other hand, when )X

reaching the critical density surface

x = x,, will become resonant with the Figure 2.3. A sketch of the plasma local electron plasma wave, and wiii act density profile and the qualitative field

as a resoaant driver for the electron distributions. (a) plasma density profile.

The light is refiected at the classical turning plasma oscillations. Consequently, part point. (b) Amplitude of the parailel of the energy of the p-polarized incident component of the E-field. (c) Amplitude of

laser is converted into the form of the normal component of the E-field.


electrostatic oscillations, which eventually become thermalized through various wave-

dumping mechanisms. The absorption by this mode-conversion process is termed

resonance absorption [48].

Resonance absorption is characterized by its strong sensitivity to the polarization

and incident angie of the incident light. It only occurs with p-polarized light at an

intermediate angle of incidence. At normal incidence, or with s-polarized light, there is

no electric field component dong the plasma gradient; while at grazing incidence, the

turning point is so far from the cntical surface that no evanescent field reaches it. For a

p-polarized plane wave of wavelength A incident into a plasma with a linear density

profile (scale-length of L), the optimum incident angle for maximum resonance

absorption has been shown to be [49]

O,, = sin-' [o. 4 4 ( ~ /a )-'/3].

Resonance absorption is one of the most important collisionless mechanisms for

laser-plasma coupling. It is associated with many physical phenomena in laser-plasma

interaction, such as the steepening of plasma density profile near n, and the generation of

supra-thermal electrons. As we will see later, one of the most important mechanisms of

harmonic generation in plasma is through currents driven in resonance absorption.

Nonlinear excitation of plasma waves through inslabilities

As discussed above, an electron plasma wave (aep, kep) can be resonantly excited

at the critical surface by the incident laser light (a, k) through resonance absorption. This

Iinear mode-conversion process involves two waves and occurs when w = mep, k = kp-

As a laser of sufficientiy high intensity passes through a plasma, plasma waves c m also

be excited through a family of three-wave interactions in which the incoming laser Light

decays into two daughter-waves. The daughter wave can be the high-fiequency electron-

plasma waves (EP), the low-frequency ion-acoustic waves (IA), or the scattered


electromagnetic waves. Since the beating between one of the daughter waves and the

incident laser can normally enhance the other daughter wave, these three-wave processes

are unstable and c m cause exponentid plasma-wave growth (instabilities) [SOI. Some of

the welI known instabilities in plasma and their corresponding coupling conditions are

listed in Table 2.1.

Table 2.1. Laser induced instabilities in plasma.

Instability Couphg condition Coupling density

Stirnulated Raman scattering a = + mep9 k = kcat + kp < 1/4 n,

S timulated BRLlo~in scattering = oxat + Qa9 k = kat + kia I Q,

Two-plasmon decay 63 = me, + sep, k = kep + kep - 1/4 n,

Ion-acoustic decay - o = c o ~ ~ + o ~ ~ , k = k i a + b p -&

We note that many of the instabilities occur at densities significantly less than the

critical density. Aiso, the thresholds and efficiencies of these instabilities depend mainly

on the spatial inhomogeneity of the underdense plasma. It has k e n shown [43] that the

instabiiity thresholds IIh generally scale as Ith = L-l, where L is the density scale-length

of the plasma. Therefore. most of the instabilities are not important in Our current

discussion of the harmonic generation in short-scaie-length plasmas, aithough they can be

effective and hence are of particular concem in long-scale-length plasmas. However,

these processes can be important if the incident laser contains a substantial amount of

energy in prepulse; in this case the peak of the laser pulse will interact with a large

volume of underdense plasma before arriving at the overdense region.

The ion-acoustic decay (also called parametric decay) instability is of special

interest to us, since, Like resonance absorption, it a h occurs at the critical surface and

excites an electron plasma wave. Its relation with harmonic generation will be discussed

in several places in this thesis.


Ponderomotive force and density profüe rnodifiatiun by a b e r pulse

When a laser beam is incident on a plasma, the momentum it carries can be

transferred directly to the plasma by means of the ponderomotive force. In contrast to the

rapidly changing oscillating force of an electric wave which causes the quiver motion of

the electrons, the ponderomotive force is a secular force, i.e., a force which acts in the

same direction over the whole duration of the laser puise. The ponderomotive force has

been recognized as an entity of centrai importance in many phenornena in laser-produced

plasmas, including the harmonic generation process.

The ponderomotive force oiiginates from the nonlinearity of the momentum

equation of a charged particle in an electromagnetic field (48, 511, To see this, we

consider an electron in an electromagnetic wave whose amplitude is spatially dependent,

i.e., E = E, ( r ) cos ut. The force exerted on the electron is given by the Lorentz equation:

Using perturbation analysis, to first order in an expansion in IEl, the electron only

responds to the electric field (the effect of the magnetic field is O(v/c)), and simply

oscillates about its rest position at v = v,,,sinmt, where vos, = e E o / m p is the

oscillation velocity (or quiver velocity) of an electron in an electromagnetic wave. To

this order, the electron is not subject to a tirne-averaged force. It is oniy to second order

that wave inhomogeneity and the magnetic field enter the problem, where Eq. (2.11) has

a form

e 2 F = -el&-, ( r ) cos wt - 2 VIE, (r )f (1 + COS 2 ~ t ) . (2.1 1-1)

4m,w

We can see that besides the first-order oscillating force -eEo cosot, the electron also

experiences an additional force which effectively pushes it away from regions of high

field pressure. This second force is proportional to the gradient of I E 1 and is called the

ponderomotive force. Notice that the ponderomotive force contains two parts, a tirne-

Chupter 2 nieoretical Background 22

averaged DC-component Fp = - ( e 2 / 4 m e o 2 ) ~ ( ~ 0 1 2 and an oscillating AC-component

F F = Fp cos2mt. Conventionally, the term 'ponderomotive force' only refers to the

DC-component Fp, because it is this force that actuaLiy transfers net momentum from the

laser pulse to electrons. In an equivalent form, the ponderomotive force can also be

written as F, = -VUp, where LIp is the ponderomotive potential which equals to the

averaged kinetic energy of the electron in the electromagnetic field, 1/2 r n , ~ ? ~ ~ .

One of the ponderomotive effects in laser-plasma interactions is density-profile

steepening. As a laser pulse reflects at the critical surface, twice its momentum is taken

up by the plasma near the reflecting point. This local momentum deposition retards the

plasma expansion [52] and steepens the density profile near the cntical surface [53].

With obliquely incident p-polarized light. the density-profile steepening can be further

enhanced by resonance absorption because of the pressure from the resonantly-generated

electrostatic field near the cntical surface [54]. At relativistic intensities, the pondero-

motive force becomes so strong that it can even bore a hole into solid matter [55,56].

Besides causing density-profile steepening near the critical surface, the

ponderomotive force can also give rise to oscillation of the critical surface at twice the

laser fiequency. This is done through the AC-component F F , which drives electrons in

and out across the plasma-vacuum boundary and effectively causes the cntical surface to

oscillate at 201. As we will see in the next section, both the density-profile steepening and

the critical-surface oscillation play crucial roles in the generation of harmonies from

laser-plasma interactions.

2.2 Mechanisms of Harmonic Generation in an Overdense Laser-Produced

Plasma

A laser-produced plasma is a very complex and extremely nonlinear medium.

One of the nonlinear responses of such a medium to incident laser light is the generation

of very high order harmonics of the fundamentai light. Generally speaking, there are

numerous mechanisms and processes involved in the generation of hannonics of different

types, under different conditions, but it seems likely that the host of mid- and high-order

harmonics are al1 generated by the same basic mechanism, under any particular

irradiation. To date, no analytical theory of mid- and high-order h m o n i c generation

gives satisfactory quantitative agreement with expiment. PIC code simulation has been

quite successfûl in descnbing general characteristics, although it is clear that few, if any,

suitable experimental series, producing well-defined conditions, have been conducted

before this work. Although satisfactory a prion anaiytical theory does not really exist,

some physical models of harmonic generation have been suggested to create simple

physicai pictures of possible mechanisms. In this chapter, we describe some of these

models and their predictions. We will limit our discussion to a 1-D problem by assuming

a plane laser wave and a Bat plasma density surface.

23.1 Simple Harmonie-GenerrUun Phenomenology

At their sirnplest, free electrons driven by a harmonic forcing-term respond

harmonically themselves, and radiate at the same frequency but with a phase delay

associated with their back-reaction. Electrons in quadratic (harmonic) potentiais will also

respond harmonically, and at the driving frequency, but with a power resonance and with

relative phase which depends on the relation between their natural (resonant) frequency,

as a simple harmonic oscillator, and the frequency of the driving force.

The simplest mode1 of nonlinear response then follows when this potential is not

quite harmonic. An electron in any non-quadratic potential will respond to a harmonic

forcing term in a more cornplex way; for a non-pathological potential (e.g., with positive

curvature) the response will typicaily be periodic, but it may be Fourier-analyzed to show

anharmonic content at sub-multiples of the period. Thus, fairly generally, if plasma

electrons reside in an anharmonic potential, strong laser fields wiil lead to currents with


sub-multiple periods, and harmonic radiation via Larmor radiation [57].

In another simple example, very strong optical fields may lead to relativistic

quiver velocities. In this case, the force equation qE = ma for a charge in a strong

optical field is nonlinear because the mass is itself velocity dependent. This aiso leads to

harmonic content in the radiation field of the accelerating charge.

Much of the general nature of harmonics from laser-produced plasmas c m be

reproduced simply fiom this mode1 of a harmonicaliy forced anharmonic oscillator; this

includes the broad spectrum of odd- and even-order harmonics, and much of their

character, including a monotonie drop of conversion efficiency with order, and aspects of

their dependence on laser intensity. However, other aspects of harrnonic spectra are

dependent on plasma characteristics, and more detailed physical modelling is necessary.

2.2.2 Second Harmonic Generation: a Perturbation Theory

Second harmonic (SH) generation in a plasma c m be interpreted as a two-step

process. In the first step, electron density oscillations (electron plasma waves) at a

frequency equal or very close to the laser frequency o are produced. In the second step,

the incident laser is nonlinearly scattered from the electron plasma waves, or two electron

plasma waves interact to produce light around 2 0 .

As discussed in the last section, electron plasina waves can be excited by the

incident laser through two main processes: resonance absorption (a linear process) and

the parametric decay instabiiity (a nonlinear process), each occumng near the critical

surface of the plasma. SH generation involving parametric processes is typically

characterized by the existence of a certain threshold value and some non-specular

distributions of the SH emission [58]. In fact, the non-specular SH emission is often used

in experiments to detect and to identiQ parametric plasma processes. By contrast. a

distinctive feature of the resonance absorption mechanism is the generation of SH in the

specular direction. In the following, we will concentrate on this mechanism of SH


generation, since, as we will show in Chapter 4, it agrees with our expenmental

observations.

Like other nonlinear optical phenomena, SH generation in plasma c m be treated

by solving Maxwell's equations using the current density J and charge density p = -en,

as the source t e m s [59]. If J and ne induced by the applied electromagnetic fields are

small, the response of the plasma may be obtained using a perturbation approach. We

assume this is the case and expand the electron density and velocity a s ne = n(O) + dL)t - - and v = v(') + d2)+- -, where n(*) is the initia! electron density without perturbation and

n(') is the fust order electron density perturbation. The current density can be expanded

as:

(1) (2) J = - e n , v = J + J +-. (2.12)

where the linear cument density J(') = -en(o)~(') is responsible for the fust-order optical

properties such as propagation, reflection and absorption of the incident light, while the

second order current density f2) = -e(n(0)~(2) +n")dL)) gives rise to second-order

nonlinear optical effects, in particular, second harmonic generation.

Now we consider the case of an incident electrornagnetic wave of frequency o.

The SH is generated through the Zu>-component of the second-order current density ~$0, which can be readily related to the a-component of the local electrk field E, [57]:

To find the SH emission field E20r one needs to fust find the local electric field E,,

calculate ~ $ 2 using Eq. (2.13), and then solve the SH wave equation with ~ $ 2 as the

source term. However, as discussed by von der Linde in Ref. [59], important

characteristics of the SH emission can already be inferred sirnply by examining

Eq. (2.13). For convenience in the following discussion, the fust and second ternis in

Eq. (2.1 3) wiil be referred to ~ $ 2 and ~$2' . respectively .

Chupter 2 Theoretical Background 26

( 1 ) Angular dependence: S H G is rnost efficient at intermediate incident angles.

This is because at normal incidence, no SH is generated since ~ $ 2 ' vanishes

(E - ~ n ( * ) = 0 ) and ~ $ 2 is normal to the surface and thus unable to radiate; for large

angles of incidence, the SHG also decreases because of decreasing penetration of the

fiindamental Iight to the critical surface.

(2) Pola~zation: In the absence of a transverse gradient of the electric field, JI? always leads to current density polarized in the plane of incidence, thus p-polarized SH,

no matter what the polarization of the incident light. On the other hand, SH due to Ji?' always has the same polarization as that of the fundamental. Since ~ $ 2 ' vanishes for s-

polarized incidence, only p-polarized SH is produced by this tem. Based on these

discussions, the following can be concluded: (a) oniy p-polarized SH is generated when

the incident light is purely s- or p-polarized; (b) p-polarized laser is more efficient in

generating SH because in this case both tems in Eq. (2.13) contribute; (c) s-polarized

SH can be generated in the following situations: fundamental beam with mixed

polarization, existence of a transverse E-field gradient (due either to f d t e spot size or to

intensity nonuniformities in the focal spot), or electron density perturbations caused by

other than resonance absorption.

(3) Resonont enhancernenr: ~ 4 : ' demonstrates explicitly the dependence of the

SH generation on plasma density gradient. It also shows that when vn(O) # O , SH

generation is greatly enhanced at the resonant frequency o = w,,. In fact, this resonant

effect occurs in both terms of the current density (2.13). In the limit of vanishing density

scale-length (step profile), SH generation from a plasma is very much like that from

metal surfaces [60, 611, where the resonmt effect disappears [62]. The resonant effect

also becornes less significant in plasmas of large scale-lengths because of the increasing

distance between the classical turning point and the cntical surface. Therefore, one

expects the existence of an optimum scale-length for maximum resonant enhancernent of

SH generation.


Finally we notice that ~ $ 2 ' is proportional to (V - E,)E, a n z ) ~ ~ [59], where

ng) is the electron density perturbation associated with an electron plasma wave at

frequency o. It follows that in certain configurations electron plasma waves can be

detected by measuring the SH signal. This idea was indeed demonstrated by von der

Linde, in an experiment where SH generation was used to detect eIectron density

oscillations produced by a strong pump pulse [63].

The perturbation theory discussed above requires that the charge density

fluctuation n(') induced by the extemal field rnust be srnail compared to the critical

density n,. The ratio of n(') and n, can be estimated using the following expression [43]:

where x,,, is the oscillation amplitude of electrons, L is the density scale-length, and %

is the nomalized laser field strength defined by Eq. (2.4). For a plasma gradient of

L / n = O. 1, ratio (2.13) becornes greater than one when 1~~ > 1.4 x 1016 Wcm2 p 2 ,

indicating that this perturbation theory is no longer valid. One of the non-perturbation

effects in SH generation is the depletion of the harmonic conversion eficiency at strong

resonance due to wave-breaking of the excited electron plasma waves [64].

2.2.3 Particle-in-Ceil Simulation ResuIts

The perturbation approach discussed above becomes very tedious and

inconvenient when used to explain higher-order harmonic generation in plasma. It dso

fails at high laser intensities, where the induced charge- and current-densities become too

large. In this case, one has to rely on computer simulations in order to get reasonable

quantitative solutions. In laser-plasma studies, two commonly used types of computer

simulation codes are particle-in-ce11 (PIC) modelling, which treats plasma as a large

collection of charged particles, and hydrodynamic modeliing, which treats plasma as

fluids.


PIC simulations performed recently by severai authors have concluded that

efficient high-order hannonic generation is possible fiom the interactions of sufficiently-

intense laser pulses at solid surfaces. For a normal incidence laser beam with m? > 1018 Wcm-2 p* (% > l), Wilks predicted odd-order harmonics in both 1 -D and 2-D

PIC simulations, and weaker even-order harmonics when 2-D effects were taken into

account [35]. For oblique incidence, highly-resolved simulations of harmonic generation

(restricted to specular emission) also become possible by carrying out 1-D calculations in

the Lorentz-boosted b e , in which the electromagnetic wave appears to be normaily

incident [30]. Using this technique, Gibbon [34] and Lichters et al. [31] investigated

harmonic generation over a large parameter space with varying laser intensity, angle of

incidence, polarization, and plasma density. Their simulation results show that the high-

harmonic yield increases significantly when approaching the relativistic laser intensities

(q, 2 1). The harmonic output also increases with decreasing plasma density and is

particularly large for o, = 2 0 , when the AC-ponderomotive force F F ( 5 2.1.3) is at

resonance with the local pIasma frequency. For s-polarized incidence, the harmonic

output decreases monotonically with increasing incident angle; for p-polarized incidence,

the harmonic yield peaks at an optimal incident angle which depends on laser intensity

and plasma density. Based on the simulation results, a phenomenological expression for

the conversion efficiency of the nth-order harmonic (assuming p-polarized laser with a

large incident angle) was given by Gibbon [34]:

This shows that, for example, a conversion eficiency of 9 x 10-5 can be achieved for the

10th harmonic with an incident laser of I A ~ = 1018 Wcm-2 g m 2 (LQ = 0.85).

The dependence of harmonic conversion-efficiency on plasma density scale-

length was also studied theoretically using PIC-simulations, which showed the existence

of an optimum scale-length near L - A for maximum harmonic generation [36,37].


AIthough cornputer simulation is a very powerful tool and can usuaily deiiver

valuable quantitative information, it provides Little physical insight of the high-order

harmonic generation mechanism. In the efforts of presenting a physical picture of the

harmonic generation process, several models have been developed. In the following

sections, we will discuss two of these physical models which describe harmonic

generation in two different physical regimes.

2.2.4 The Linear Mode-Coupling Model

The mechanism of SH generation via resonance absorption can also be extended

to explain the multiple-harmonic generation process 161. As discussed before, resonance

absorption provides an efficient means of converting an electromagnetic wave (61) into a

localized electron plasma wave (upe). At the critical surface where o = mpe, these two

waves can mix to produce a second harmonic ( o2 = CO + wp, = 2 0 ) via the current ~ $ 2 . This wave is mainly reflected, but part of it can propagate up to the density profile to 4nc

where it excites an electron plasma wave at 20. This in tum couples with CU to generate a

third hamonic, which is resonant at 9nc, and so on (see Figure 2.4).

Shce only hannonics with frequencies up to the bulk plasma frequency find their

respective resonance layers, a spectral cutoff at the bulk plasma frequency is predicted.

Therefore, the highest order of harmonies which can be generated is m,, = ,/=, where n, is the upper plasma density (buik density). This simple mode-coupling pichue

was suggested by a number of early harmonic experiments using nanosecond CO2 lasers

[18, 191 for which a spectral cutoff was indeed claimed. (This cutoff was interpreted

from unreduced film densitometry; subsequent independent interpretation of this raw

data by Zepf [29] including plausible spectrograph resolution, strongly suggests that this

data does not in fact support the interpretation of a cutoff.) More-quantitative theories

based on this model were further developed by Bezzerides et al. 1213 and Grebogi et al.

W I -


Figure 2.4. Schematic picture of harmonic generation via linear mode-

coupling in a plasma density gradient.

As discussed in the SH generation (5 2.2.2), the linear mode-coupling picture

breaks down at high laser intensities or in very steep density gradients, where the electron

oscillation amplitude becomes comparable to the density scale-length, Le., x,,/L 2 1.

For a plasma of LIA. = 0.1, this breakdown condition is satisfied when ZA? is above

1.4 x 1016 Wcm-2 pm? In this regime, the oscillating-mirror mode1 discussed below

becomes a good picture for harmonic generation.

2.2.5 The OsciUating-Mirror Mode1

As discussed previously, an electromagnetic wave incident on a plasma density

profile couples strongly with the electron motions near the critical surface, where the

electromagnetic forces push and pull electrons back and forth across the plasma-vacuum

boundary. These collective motions of electrons represent strong oscillations of the

cntical surface. With normally incident, or s-polarized obliquely incident light, the

cntical surface is driven solely by the AC-ponderomotive force F r , which osciliates at

Chapter 2 Theoretical Background 3 1

twice the laser frequency o. The purely Coulomb force -eE, in this case, has no

component dong the plasma gradient, and therefore is less effective in driving the cntical

surface. For obliquely incident p-polarized light, since both Coulomb force (a) and the

AC-ponderomotive force (20) contribute to the driving force, the cntical surface is

expected to move as a superposition of two oscillation modes with frequencies w and 20.

These collective motions of electrons were demonstrated ciearly by Lichters et al. in their

PIC simulations 13 11.

Based on this analysis and the fact that hannonics are generated in a region very

close to the cntical surface, Bulanov 1301 suggested an oscillating-mirror model which

interprets the high-order hannonic generation from a plasma-vacuum interface as a phase

modulation expenenced by the light reflected from an oscillating boundary (Figure 2.5).

This mode1 was further developed by Lichters et al. [3 11 and von der Linde et al. [32].

The basic approximation made by this model is to neglect the details of the changes of

the electron density profile and to represent the collective electronic motion by the

periodic motion of the critical surface. Obviously, this picture of harmonic generation

ceases to be true when the plasma-vacuum boundary is spread out over a distance

comparable with the electron excursion ( x, / L < 1 ).

Figure 2.5. Schematic plot of electron-density surface

(dashed line) oscillating relative to the fixed ion density

(shade) .

Chapter 2 Theoretical B a c k g r o d 32

Let's consider a monochromatic plane-wave E = & eq(-iot) incident at angle 0

ont0 a mirror which oscillates sinusoidally at frequency a, dong the x-direction,

~ ( t ) = s0 sin a>,t. The phase-shift of the reflected wave from this oscillating mirror is

@(t ) = p i n o,t , (2.16)

where x = ( 2 ~ 0 s ~ cos 0) lc is the phase-modulation amplitude. Using the well-known

Jacobi expansion: exp(-i~ sin ~ , t ) = J, (X)exp(-inm,,$), one can easily see that the

reflected wave Er = Eo exp(-iot + i@(t)) contains a senes of sidebands at frequencies

on = o + no, with amplitudes given by J&), where Jn (x) is the Bessel function of

order n. The normalized strength of the nth sideband in the reflected wave can be

calculated as

Using this simple geometric model, and

assuming o, = 2w, spectra consisting of

odd-order harmonies are calculated for

different values of x (Figure 2.6).

The simple mode1 (2.17) is actually

valid o d y when the rnirror oscillates much

slower than the oscillating fiequency of the

incident wave (a , « a). When a, is

close to optical frequencies, relativistic

retardation effects corne into play which

lead to important modification of the simple

model presented above. When the relativis-

tic retardation effects are taken into account,

O 5 10 15 20

harrnonic order

Figure 2.6. Harmonic spectra calculated

based on the simple model (Eq. (2.17)). the harmonic conversion effkiencies are - -


found to be significantly enhanced. The detailed derivations are given in Ref. [3 1, 321.

Here we only summarize the main results.

For normal-incidence or s-polarized oblique-incidence light, we have w, = 2 0 ,

and the reflected light is cornposed of s-polarized odd harmonics whose intensity

distribution is given by

For p-polarized incident light, the mirror is driven with two frequencies. o and 2w. The

spectrum of the reflected Iight contains p-polarized odd and even harmonics. The

harmonic spectm produced by the CO mode done can be written as

I V . - O 5 1 O 15 20 O 5 10 15 20

harmonic order harrnonic order

Figure 2.7. Harmonie spectra generated by (a) s-polarized light and @) p-polarized

light for different values of x (Eq. (18) and (19)).


The normalized harmonic spectra generated by s-polarized and p-polarized light

with different phase-modulation amplitudes x are plotted in Figure 2.7. It shows that the

efficiency of high-order harmonic generation increases strongly with X . Cornparison of

Figures 2.7(a) and 2.7(b) also indicates that, for a given value of X , the harmonic

conversion efficiency for s-polarized incident Light is higher than that for p-polarized

light. This apparent disadvantage for p-polarized light in generating harmonies is

somewhat artificial: it is overwhelmed by the fact that, with the same laser intensity on

target, p-polarized light c m drive the osciiIating &or with much larger amplitude

(therefore a higher value of X ) than s-polarized light.

Using the oscillation amplitude as the only free parameter, Lichters et al.

demonstrated that the oscillating-rnirror model was able to quantitatively reproduce

harmonic spectra calculated with PIC simulations uader a large range of experimental

conditions [3 11. The model also works satisfactorily at relativistic intensities, where

a. io 1, by adding a few high-order oscillation modes (30 and 40) to take into account

the anharmonic mirror oscillations.

In principle, if the plasma restoring force f&) on the electron surface is known,

we should be able to calculate the motion of the critical surface s ( t ) , hence the oscillation

amplitude of the reflecting mirror. But f&) is very complicated and is strongly

asymmetric across the plasma-vacuum boundary. So, to describe the situation

satisfactorily, one has to rely on PIC simulations. Physically, the plasma restoring-force

is supplied by charge-separation in the medium, which c m be approximated as

f, = under the low driving fkequency limit ( rn << mpe ) Here mpe is the electron

plasma fkequency. Under this approximation, the oscillation amplitude for normal laser

incidence is approximately given by [32]

a a:[ )l dl(%)"' -=- - =- A x ope nt?

which shows the oscillation amplitude so decreases with plasma density ne.


Finally, the oscillating-mirror model c m also be used to explain another

mechanism of harmonic generation. PIC simulation shows that s-polarized Light at

obLique incidence is expected to produce not only s-polarized odd harmonics, but p-

polarized even harmonics as weU. The latter, however, cannot be interpreted in tems of

a phase-rnodulated reflected wave, because there is no incident light with p-polarization.

This harmonic emission cm be considered in the following way. Since the ions are

considered immobile, the forward and backward motion of the reflecting surface will

induce an oscillating electric-dipole sheet at the plasma-vacuum boundary. For obliquely

incident light, there is a penodic variation of the electric dipole moment dong the

direction parallel to the target surface, with a spatial frequency given by the parallel

component of the wave vector of the incident light. This dipole sheet oscillates at the

same frequency as the oscillating rnirror. It c m be shown that this osciilating dipole

sheet radiates a p-polarized wave composed of even harmonics [32]. Obviously, this

harmonic generation mechanism also exists with p-polarized incident light. It is hard,

however, to distinguish it from the phase-modulation mechanism because both

mechanisms produce p-polarized odd and even hamonics in this case.

2.2.6 Mode1 Predictions: Harmonie Generation with Varying Experimental

Parameters

Using the oscillating-rnirror model, the dependence of harmonic generation

efficiency on several experimental parameters can be discussed. These parameters

include the laser intensity, polarization and incident angle, target matenal (i.e., the initial

electron density) as wel1 as the initial plasma scale-length. In the following, we will

discuss how harmonic generation will be Ïnfluenced by these factors.

Laser intensiîy

Assume the reflecting surface oscillates with ampLitude so and frequency o. Since


the maximum surface velocity os0 must not exceed the speed of light, so is limited by

s,, < c / o = A / 27r = 0.16A. Similarly, the maximum amplitude of the 2w mode is

0.08 A,. At low incident intensity, the reflecting surface oscillates harmonically with

small amplitude so << 0.12, and the hannonic intensity falls off rapidly with increasing

order. At relativistic intensities ( a. 2 l), the surface starts to move very anharmonically

with speeds close to the speed of iight, and higher order surface modes (at 3 ~ ~ 4 0 , etc.)

are induced by relativistic effects in addition to the w and 2 0 modes driven by the electric

and the ponderomotive forces. Harmonic emissions, particularly of the higher-order

harmonics, are significantly enhanceci by these higher surface modes, which are of

genuinely relativistic origin. Meanwhile, the oscillation amplitudes of the low-order

surface modes (lm and 20) reach their limits at relativistic laser intensities, which result

in saturation of the low order hannonic emissions. So with increasing laser intensity, the

harmonic spectnim is expected to show both a slower growing (Le., saturation) of the low

harmonies and a slower frequency roll-off of the high harmonics.

Laser polarization

Harmonic generation depends strongly on the laser polarization because of the

different driving rnechanisms associated with s-polarized and p-polarized waves. This

has been discussed in the last section. The conclusion can be summarized in the

following polarization selection rules: at normal incidence, Linearly polarized light

generates only odd harmonics of the same polarization as the incident light; at oblique

incidence, s-polarized light generates s-polarized odd harmonics and p-polarized even

harmonics, while p-polarized light produces only p-polarized harmonics of both odd and

even orders (Table 2.2). It is woah to note that the selection rules denved for SHG

(8 2.2.2) using perturbation theory are consistent with these generalized d e s .

In practice, these selection rules may be violated by 2-D effects, e.g.

nonuniformities due to preformed plasma (see the following section), finite size of the

Chpter 2 Theoretical Background

focal spot, hole b d n g and surface rippling due to the Rayleigh-Taylor instability.

Table 2.2. Polarization selection d e s

Fundamental Odd harrnonics Even harmonies

Oblique incidence

S S P

P P P Normal incidence

linear linear

Angle of incidence

For s-polarized Light, the surface is driven only by the AC-ponderomotive force,

which falls off monotonicaily with angle of incidence 8. For p-polarized Iight, the

normal component of the electric field ( Ex = Eo sin O ) , which increases with 0, acts on

the surface in addition to the decreasing ponderomotive force. So we expect to see the

odd harmonics generated by a s-polarized laser fall off monotonically with 0, while

harmonics generated by a p-polarized laser increase with 0 first, and then vanish at

grazing incidence (8 = 90') because of the decreasing penetration of the electnc field, as

for resonance absorption. The even harmonics generated by s-polarized light should have

similar angle dependence as for p-polarized drive, but with much lower intensity. This

dependence on incident angle is shown schematically in Figure 2.8.

Plasma density and scale-length

The frequency factor w / mp, (or equivalently, n, /ne) in Eq. (2.20) signifies the

resistance of the medium to the perturbation of the electron density. It indicates that to

obtain large so and therefore high output of harmonics one should use a plasma with

relatively low density (Le., slightly overdense ne 2 n,). Furthemore, a considerable

enhancement of the oscillation amplitude is expected to occur for resonant excitations,

when the driving frequencies (w or 20) equals the electron plasma fiequency ope.


O 15 30 45 60 75 90

angle of incidence (degree)

Figure 2.8. Qualitative dependence of mid-order harmonic generation on angle

of incidence for s-polarized (dashed-lines) and p-polarized laser (solid-lines).

The harmonic emission depends also strongly on the plasma scale-length L.

Generally, the harmonic intensities increase with L, since then the laser pulse interacts

essentiaily with plasmas of lower density and drives larger surface oscillations due to the

weaker plasma restoring force. This trend eventually will stop at appreciably larger

scale-lengths (typically L - Â ), above which the harmonic efficiency decreases again.

This is because the distance between the classical tuming point and the critical surface

increases with L, so that the light amplitude driving oscillations at the critical density

decreases. This dependence has been verified by the PIC simulations perfomed by

Delettrez, et al. [36], and by Lichters, et al. [37j.

Chapter 2 ï7ieoretical Background

2.3 Role of Preformed Plasma

In discussions above, we have assumed an ideai physical picture in which short

laser pulses interact directly with solid targets. From an expenmental point of view, a

serious problem that can prevent this from happening may arisr from a laser prepulse. If

the prepulse intensity on target is higher than the threshold intensity for plasma

formation, a preformed plasma (preplasma) is formed which prevents the main pulse

from interacting directiy with the soiid. hdeed, the preplasma is a key issue in al1

experiments üsirig short-pulse intense lasers incident on solids [65].

2.3.1 Laser Prepulses

Laser prepulse refers to any laser energy deposit on target prior to the main laser

pulse. There are three kind of laser prepulses [65]. The first kind of prepulse is any laser

light which reaches the target at a time independent of the main pulse. It could be the

amplified spontaneous emission (ASE) from the laser amplifiers or the leak-through

pulses from imperfect optical gates in the system. This kind of prepulse normally extends

several nanoseconds or longer. As the intensiv of this prepulse exceeds 108 Wkm*, it

will evaporate the target surface, producing a cloud of vapor which expands at - 3 nm/ps.

Thus, a prepulse that occurs more than 1 ns before the main pulse will produce a gas

cloud of thickness > 3 pm in front of the target, which when ionized will f o m a plasma

that alters the interaction of the main laser pulse with the target.

The second kind of prepulse is the pedestal under the main laser pulse. For a CPA

laser, this pedestal is usuaily caused by uncompensated group velocity dispersion in the

laser system (see 5 3.3.4). Comparing to the fnst kind of prepulse, the duration of the

pedestal is usuaLly much shorter, and is typicaUy several times of the main pulse width.

The intensity levels of these two kind of prepulses are usuaily characterized by the

laser pulse contrast defined as b/lP , where Io and IF are the maximum laser and


prepulse intensities. Typically, preplasmas start to be produced by laser prepulses of

intensities greater than 1012 W/cm2. So in a laser-target experiment where peak laser

intensity Io = 1018 W/cm2, one needs a pulse contrast better than 1010 to avoid preplasma

production. Two commonly used pulse-cleaning tools are saturable absorbers and

frequency-doubling crystals. Both are effective in suppressing the fust kind of prepulse.

For pedestai suppression, only the doubling crystal will work because of the short

duration of the pedestal. In the harmonic experiments descnbed below, both pulse-

cleaning methods were enployed (see Chapters 4 and 5).

The thkd kind of prepulse refers to the laser energy on the leading edge of an

ideal main Iaser-pulse itself, which dependents very much on the pulse-width and shape.

To illustrate this, the iime distributions of two Gaussian pulses used in Our experiments,

together with a sech2 pulse, ail having the same peak intensity of 1018 W/cm2, are shown

in Figure 2.9. Obviously, shorter pulses tend to produce less plasma by this mechanism,

time (ps)

Figure 2.9. Intensity distributions of three pulses of different shapes and

durations, with a peak intensity of 1018 Wkm?


so long as they retain smalI pedestals. We can see from Figure 2.9 that the 1.2-ps

Gaussian pulse reaches the plasma-forming intensity of 1012 ~ l c r n 2 more than 2.5 ps

before the peak reaches the target. If the plasma could expand freely at the typical ion-

sound speed of - 0.1 W p s , it would approach 0.25 pn in extent by tirne the peak of the

laser pulse arrives. Sirnilarly, a clean 350-fs Gaussian pulse and sech2 pulse would

produce preplasmas of 0.08-p and 0.15-pm thick, respectively. Here we have ignored

the ponderomotive steepening by the laser pulse. If this effect is taken into account, the

actual preplasma might be thinner than we have estimated.

2.3.2 Effects of Preplasrna on Harmonic Generation

Preformed plasmas have been proven useful for the purpose of maximizing the

production of hot eiectrons [66] or x-rays [67,68], but they are hamiful if one's goal is to

obtain very clear evidence regarding laser interactions with overdense and soiid-density

plasmas. As we saw in the last section, harmonic emission generated from a flat cntical

surface should be dong the direction of specular reflection. This will no longer be true,

however, if a large extent of preplasma is present, because in this case the cntical surface

is not flat any more, the incident angle is no longer well defmed, and therefore harmonies

are expected to be emitted in a much broader solid angle. The polarization selection rule

for harmonic generation is wother powerful criterion to test the validity of harmonic

generation models. This selection rule may also be violated by the 2-D effects associated

with the preformed plasma, making it more diffIcult to interpret the experimental result.

Both of these effects (wide harmonic emission-angle and the polarization-insensitivity)

were noticed in a recent experirnent performed at the Rutherford Appleton Laboratory

where himnonics were generated by a laser containing of a substantial prepulse [26].

Hannonic conversion-efficiency can dso be strongly affected by a preplasma.

Because of their long expansion time, preplasmas generdly have much longer scale-

lengths, which make harmonic generation inefficient. The existence of a long scale-


length preplasma also means that the laser has to interact with a large amount of

underdense plasma before reaching the overdense region. By this, beam quality at critical

density is significantly altered through self-phase modulation and fdamentation in the

underdense region. This will also innuence the harmonic conversion-eff~ciency. For the

same reason, the spectral brightness of harmonic emission will also be reduced by the

preplasma. The reduced harmonic efficiency by preplasma has been reported in an

experiment in which harmonic emission was only observed when the prepulse was

removed [23].

The preplasma effect on harmonic generation c m be studied experimentally if one

can control the experimental conditions so that harmonies generated by a high-contrast

clean pulse and by a pulse containing known amount of prepulse can be directiy

compared. This idea is demonstrated experimentally in Chapter 4, in which preplasrna

effects on SHG are studied in a systematic fashion.

2.3.3 Modification of Plasma Density Profile by a Deliberate Prepulse

A laser prepulse is often an unwanted artifact in the study of laser-solid

interactions. Under certain conditions, however, it can be a useful expenmental

parameter, providing its intensity and timing are controllable. As discussed in § 2.2.6,

harmonic generation depends also on the plasma density scale-length. This dependence

can be studied experimentally in an expanding plasma produced by a prepulse

deliberately added at a controiled time in advance of the main pulse.

The scale-length of a ffeely evolving plasma, following a weak prepulse, can be

reasonably estimated by hydrodynarnic modeling. We used the one-dimensional

hydrocode MEDUSA [69, 701 to calculate the electron density distribution in a plasma

dong the direction of expansion, at various time d e r the Iaser shot. Figure 2.10 shows

two typical electron density profiles calculated for a 1 - p thick silicon target and a laser

pulse of I = 2.5 x 1016 Wkm2 and Â. = 0.526 p. The solid line represents the profile just

Chaprer 2 Theoretical B a c k g r d 43

before the laser pulse arrives (solid density) and the dashed line is the profile 3 ps after

the laser shot,

Using Eq. (2.3), we caiculated the plasma scale-length for each electron density

profile at different time delays. Based on the assumption that the laser-plasma interaction

occurs mainly at the cntical surface, the scale-length was calculated at the critical density

n,= 4.0 x 1021 cm3 (for A = 526 nm). The result is plotted in Figure 2.1 1, which shows

that the plasma scde-length increases with the time delay after the deiiberate prepulse,

roughly at a speed of 0.06 pxdps. Based on this modeling, we perfomed an expenment

in which the third-harmonic emission was measured at different delays of a controllable

prepulse (see Chapter 5).

x (crm) t (PSI Figure 2.10. Modification of electron Figure 2.11. Plasma scale-length caicu-

density profile by a prepulse of intensity lated at different time-delays after the

2.5 x 1016 W/cm2. The solid line is the prepulse. The solid line is for visual

profile just before the prepulse arrives; guidance ody.

the dashed line is the profde 3 ps after the

prepulse.

3

2

I I

- 1 1 solid - : ', boundary

- ,"t + -

1 L * - 1 '

\ \

- \ -

O - " " ' " ' ' b ,

O 0.5 1 1.5


2.4 Conclusions

We have briefly discussed the important physical issues involved in the harmonie

generation from intense laser interaction with solid targets. Cornputer simulations

demonstrate that efficient high-order harmonies (of both odd and even orders) can be

generated from soiid targets at Iaser intensities above 10'6 W/cm2. To get some insight

of this harmonic generating mechanism, two physical models were introduced: at iow

intensity and long scale-length plasma (x,,, /Le 1). the linear mode-coupling

mechanism presents a good picture for harmonic generation; at high intensity and short

scale-Iength plasma ( xosc /L 2 l), the oscillating-mirror mode1 provides satisfactory

explanations. Based on the physical understandings from these models, the dependence

of harmonic generation on several experimental parameters was given. Finally, the

importance of the laser prepulse issue for expenmental studies of harmonic generation

from solid targets was emphasized. Based on hydrodynamic modeling, an idea of using a

controllable prepulse to study the scale-length dependence of harmonic generation was

also developed.

Chapter 3 Development of the Toronto FCM-CPA Laser S ys tem

In this chapter, the FCM-CPA laser systern developed at the University of

Toronto is described. A systematic characterization of this system as well as a novel

cross-correlation technique are presented.

3.1 Introduction to the CPA Technology

Since the invention of the pulsed laser, peak laser power has increased by nearly

12 orders of magnitude in 37 years. After a relatively quick development in the 1960s,

thanks to the invention of Q-switching and mode-locking techniques, for more than 20

yem the peak power of compact solid-state laser systems had stagnated near the gigawatt

level. This was because in almost al1 gain media nonlinear optical effects that could

break up the laser beam irnposed a severe limit on the power one could get from a laser of

given aperture. So to obtain higher peak power, one had to increase the sizes of the

amplifiers, as well as the cost.

This situation changed dramaticaily in the mid-80s after the introduction of a new

type of amplification, die chirped-pulse amplification (CPA) technique [Il. The basic

scheme of this novel technique is Uustrated in Figure 3.1. Fist, picosecoii.: laser pulses

are generated from an oscillator. Instead of being amplified directly, these seed pulses

are sent to an optical expander where the pulse durations are stretched by, Say, 1000


Figure 3.1. The chirped-pulse amplification concept.

times. The chirped and temporaily stretched pulses, having their peak powers reduced by

1000 times, can then be amplified safely in the amplifiers. Afier ampiifïcation, the pulses

are compressed back to their original picosecond durations in a cornpressor. In this way,

one c m produce laser pulses which are 1000 times more powemil without darnaging the

optical elernents, and without having to increase the sizes of the amplifiers.

Nowadays, the CPA technique has become a standard solid-state-laser tool used

to produce terawatt-class optical pulses [71]. This technique has been applied to many

laser media which can be broadly divided into two groups: sub-100-fs systems based on

the broad-band laser materials, such as Ti:sapphire [72-751, Cr:LiSAF [76, 771 and

alexandrite [78], and roughly 1-ps systems based on the traditional high-power laser

material Nd:glass [79-821. The first group approaches high peak power by producing

pulses with extremely short pulse widths but of relatively low energies; terawatî-lasers

producing pulses as short as 54s at 1-kHz repetition rate have been demonstrated recently

[83,84]. In laser-produced plasma studies, one often needs not only high peak irradiance,

but also substantial energy per pulse. For these kinds of applications, Nd:glass systems

are still preferred; based on the best-developed, large-size, high-energy-storage Laser

medium, they currently produce the greatest energy per pulse [82].

Chapter 3 Development of the Toronto FCM-CPA Laser System 47

The major disadvantage of using the CPA technique in Nd:glass systems was the

lack of stable short-pulse oscillators. The onginal approach used puises from Nd:YLF or

Nd:YAG osciliators. Because of their narrow bandwidths, a combination of fiber and

grating expansion scheme had to be used, which led to a mismatch between the expansion

and compression stages and resulted in a pedestal on the recompressed pulses. The

intnnsic pulse contrast ratio obtained was limited to - 103. At terawatt power-levels this

pedestal can form a substantial prepulse which will pre-ionize the target matenals. Much

work had been done in an effort to solve this contrast issue by re-shaping the pulse

spectmm [85], by fast temporal-windowing [86], or by applying additional pulse cleaning

using saturable absorbers [87], plasma-shutters [88] or nonlinear birefringent fibers [89,

901. Contrast ratios of 105-107 had been achieved using these rnethods. In the last few

years, with the matunng of the Tksapphire technology, hybnd systems combining a

Ti:sapphire oscillator and regenerative amplifier with the well-developed Nd:glass power

amplifier chain have become more common configurations among the multi-terawatt

Nd:glass lasers [80-821 . Using direct grating expansion and compression, a contrast ratio

of 106 is nomally achieved in these hybrid systems.

At the University of Toronto, we have developed an improved dl-Nd:glass

terawatt laser system [9 1, 921 which employs high-contrast (109, pJ-level, 1 -2-ps pulses

produced frorn a feedback-controlled mode-locked oscillator as seed pulses. These

transform-limited seed puises are suitable for direct grating expansion and compression,

and because of their relatively high energy, require less subsequent amplification. The

system produces 14, 1.2-ps pulses with contrast better than 5 x 107 without additional

pulse cleaning measures. This compact, relatively simple terawatt laser system has

become a routine tool for the ongoing picosecond laser-plasma experiments in Our

laboratory [93].

Chaprer 3 Development of the Toronto FCM-CPA Loser System

3.2 The Feedback-ControUed Mode-Locked (FCM) Oscillator

The FCM Nd:glass oscillator [94,953 is the key element in the Toronto CPA laser

system. Compared to other mode-locked oscillators, it has two unique features: high

output level (- pJ) and high pulse-contrast (108). The design and charactenzation of this

oscillator are described in this section.

3.2.1 Purpose of Feedback Control in the Oscillator

Figure 3.2(a) shows a schematic diagram of the FCM oscillator. It is a hybrid

mode-locked Nd:gIass oscillator (Kigre 498 athermal phosphate glass, 6-mm @,2 1.2-nm

gain-bandwidth). An acousto-optic modulator driven at 66.7 MHz provides active mode-

locking. For passive mde-locking, a tramlatable thin dye ce11 is placed inside an

intracavity telescope at Brewster's angle, in which Kodak Q-switch II (dye 9860) in 1,2-

dichioroethane is used as the saturable absorber [96]. The dye concentration is adjusted

such that the saturable absorber provides a round-trip transmission of - 65% for smdl

signals. A photodiode, a fast high-voltage amplifier (- 500 V), a Pockels ceil and a thin-

film polarizer together provide a negative feedback control of the intracavity laser pulse

energy.

The purpose of the feedback control is twofold. First, it maintains pulse energy at

the optimum level for effective pulse shortening in the saturable absorber, preventing it

from bleaching the dye and causing passive Q-switching. Second, it iimits the shot-to-

shot variation intrinsic to passive mode-locking, and stabilizes the laser output. The

feedback signal is provided by Fresnel reflection from one uncoated face of the laser rod;

the circulating power in the cavity cm be continuously adjusted by attenuation of the

optical feedback signal. Voltage pulses of up to 500 V can be generated from the

negative-feedback control circuit and applied to the Pockels ce11 which is electrically

biased at 1200 V, increasing the cavity coupling loss and Iowering the circulating pulse


- - -- -

1-4 1 ps (133 round trips)

Figure 3.2. (a) Schernatic diagram of the FCM oscillator. Ml (r = 5 m), M2 (r = .a), high reflectivity mirrors; LI, L2, lenses, f = IO cm; AOM, acousto-optic

modulator; SA, saturable absorber; LR, laser rod; TFP, thin-film polarizer; PC, Pockels cell; FC, electronic feedback controller. @) Oscilloscope trace of the

output pulse train. Label A identifes round-trip zero as used in Figure 3.3.

energy. The thin-film polarizer also functions as the output coupler. Figure 3.2@) shows

a typical feedback-controlled pulse train generated from the FCM oscillator, which

consists of 256550 pulses depending on the adjustment of the control level.

3.2.2 Pulse Development in the FCM Osciliator

Using a tunnel-diode discriminator and an external Pockels cell, we selected

single pulses at different positions in the FCM pulse train, and measured their temporal

width, spectral width and contrast ratio. The pulse duration and contrast measurements

were made with a conventional rnulti-shot autocorrelator (the same as that used in


Ref. [87]), using non-collinear second harmonic generation in a thin (1-mm) LiIO3

crystal. The spectmm was measured by a single-shot spectrograph (Amencan

Holographic). Figure 3.3 illustrates the results of these pulse-development

measurements. Due to instrumental intemal delays (-100 ns), we could not select the

very early pulses from the pulse train. The zero round-trip in Figure 3.3 corresponds to

the position marked by the arrow in Figure 3.2@).

In Figure 3.3(a), the measured pulse duration (filled circles) and spectral

bandwidth (open circles) are plotted against round-trip nuber . We can see that, starting

at about 8 ps early in the train, the pulse width continuously decreases and reaches a

minimum value of 1.5 ps at about 80 round-trips in this non-optimized operation. With

fresh dye, a shorter pulse width of 1.2 ps c m be routinely obtained in this FCM oscilIator.

Accompanying this pulse shortenhg process, the conjugate spectral width increased from

0.25 nm to a final bandwidth of 1.35 nm at about 150 round-trips. It is interesting to note

that at late times, after the pulse duration reaches its optimized value, its spectral width

continues to increase, presumably due to the effects of self-phase modulation inside the

laser cavity, accumulating more bandwidth than the Fourier-transform-limited situation.

The evolving tirne-bandwidth product of the pulse is shown in Figure 3.3(b)

(filled circles). M e r a quick decreasing from 0.6 to 0.44 (transform limit for Gaussian

pulse shape) in the early pulse train, it remains at this value for about 80 round-trips and

then increases again to about 0.7 late in the pulse train. By positioning the g las dye ce11

near the focus of the intracavity telescope or altering the peak circulating intensity, the

final bandwidth of pulse can be made as large as 6 nm, while leaving the pulse duration

development unchanged. An example of this extra-bandwidth case is included in

Figure 3.3(b) (open circles), where the pulse train has a f m d bandwidth of 3.6 m. If this

non-transform-limited pulse were recompressed, it is anticipated that the nonlinear partial

chirp of the puise would add to the pedestal of the recompressed pulse.


round-trip number

Figure 3.3. Pulse development inside the FCM oscillator. (a) Pulse width (fïiied circles) and spectral bandwidth (open circles). (b) Time-bandwidth product (filled circles) and extra-bandwidth case described in text (open circles). (c) Contrast ratio. In al1 these three plots, the lines are for visual guidance O*.

Chapter 3 Development of the Toronto FCM-CPA Laser Sysîem 52

Another aspect of the pulse development is the dramatic improvement of the pulse

contrast as the round-trip number increases. Figure 3.3(c) shows the developrnent of

nominal contrast as measured from the ratio of pulse intensity at the peak to that at the

pedestal (10 ps away fiom the peak). It increases exponentially from a value of 2 to

5 x 105 d e r about 100 round-trips. This contrast ratio improvement is mainly due to

reduction of the extended pulse background because of the saturable dye, which provides

different transmissions for the peak of the pulse and the for the background. Assuming

the dye ce11 has a round-trip transmission of T, for the peak of the pulse and T2 for the

pedestal, after n round-trips, the pulse contrast is expected to increase from an initial

contrast Co to a value given by

Cn = CO (T,IW (3.1)

Using Eq. 3.1 and the measured contrast, we obtain T~ /T* = ( 5 x 10'/2)'~'~~ = 1 . 9 13

which means the small signal transmission T2 was about 88% of the large signal

transmission Tl . It should be noticed that the pulse-width shortening ds:, reduces the

intensity of the pulse wing (see Figure 2.12), therefore improves the nominai contrast. It

can be shown, however, that this effect is negligibie comparing to above mechanism

(Eq. 3.1) at the selected pedestal position (+IO ps).

3.2.3 Aigh-Contrast Characterization of Pulses from the FCM Oscillator

The upper limit of the rneasurement shown in Figure 3.3(c) is about 5 x 105,

which is instrumental and results from residual scattering light inside the autocorrelator.

To produce a high-contrast autocorrelation, we searched the Li103 crystal for low-

scattering sites, and carefuIly constructed grouped apertures to minimize the scattered

single-beam harmonic Iight going to the detector-a high-sensitivity, low dark-current

photomultiplier (Hamamatsu R2 12UH). Caïibrated neutral density fdters were used to

attenuate the second harmonic signal to prevent saturation of the photomultiplier.


time delay (ps)

1 .O

Ah= 1.24 nrn 0.8 - (Gaussian fit) -

- -

0.6 - - - -

0.4 - -

-

0.2 - -

0.0 1050 1051 1052 1053 1054 1055 1 056

wavelength (nm)

Figure 3.4. Typical characterization of selected single pulse from the FCM oscillator. (a) Autocorrelation trace with Gaussian fit. Apparent satellites are actuaily trading pulses produced by residuai reflections in the wave plates. @) Spectrum wiîh Gaussian fit. The s m d npple indicates the existence of an etalon, with an optical thickness of about 0.66 mm, in the laser cavity.

Chapter 3 Development of the Toronto FCM-CPA Laser S y m 54

The improved autocorrelation measurement for a pulse selected after about 200

round-trips is shown in Figure 3.4(a). It can be seen that the 1.2-ps pulse is clean over

nearly 8 orders of magnitude and very well fits a Gaussian curve throughout this range;

its background is lower than Our detection limit. The apparent satellites proved to be

trading pulses produced by residual reflections in the wave plates dong the optical path,

since one could alter their ampl i~de and delay by substituting different wave plates.

Figure 3.4@) shows a typical pulse spectnim, which exhibits a Gaussian shape as well.

This FCM oscillator can also be configured to produce subpicosecond pulses;

pulse durations of 5 0 - 6 0 0 fs have been demonstrated in similar systems with different

saturabie dyes 1971. Dye 9860 is used routinely in our system because of its relatively

long Iifetime and because it produces stable operation of the oscillator, requiring only

minor attention between dye changes. Elsewhere, by integrating feedback-controlled and

additive-pulse mode-locking, pulse durations as short as 460 fs have been demonstrated

from a Nd:glsss osciLlator [98].

The single-pulse energy from the oscillator can be adjusted between 1-5 p l

Pulse-stability measurement shows a typical shot-to-shot amplitude fluctuation of

AEE - 5%, where E and AE are the average and the standard deviation of the output

energy per pulse. These high-contrast, high-energy and stable pulses from the FCM

osciliator serve as ideal seed pulses for our CPA laser system.

3.3 The FCM-CPA Laser System

3.3.1 The Laser Setup

The Toronto FCM-CPA laser system is shown schematically in Figure 3.5. Since

we start from high-contrast, transfom-limited 1-ps pulses, the traditional hybnd fiber-

grating expansion technique typically used with Nd:glass systems is no longer necessary,

and a gratings-only expansionlcompression scheme can be used. The pulse train from the

kinematic /

c, 2

FIG. 3.5. Schematic diagram of the FCMÇPA laser system. FR, Faraday rotator; PC, Pockels cell; SBE, spatial beamexpander; VSF's, vacuum spatial filters; PA'S, power amplifiers; CR, corner reflector.

Chpter 3 Development of the Toronto FCM-CPA Laer System 56

FCM osciliator is directed to a diffraction-grating expander [99], which consists of two

anti-parallel 1740-line/mm gold-coated holographie diffraction gratings (Jobin-Yvon)

separated by approximately 160 cm, and a pair of asphencal lenses with focal lengih

f = 60 cm separated by 2f (120 cm). The incident and diffracted angles for the f i s t

grating are 60.75' and 74-05' respectiveïy. This expander h a an effective length o f

82 cm and exhibits a positive group velocity dispersion. After double-passing the

expander, al1 pulses in the pulse train are stretched to about 410 ps as measured by a

cross-correlation method described later; a single puise is selected from the train by a

pulse selector on the r e m pass.

The selected stretched pulse (0.5 pJ, 1 Hz) is then coupled into a ring regenerative

amplifier [100] via mode-matching optics. The ring regenerative amplifier is a stable

TEMw cavity, which contains a 2-m focal length lem, a Nd:glass laser head (Kigre 498

athermal phosphate glass) and a double-crystd Pockels ce11 (Medox). The intracavity

Pockels ce11 is optically biased, yielding a stationary half-wave retardation. M e r the

injected pulse enters the cavity, a half-wave voltage (4 kV) is applied to the Pockels cel1,

trapping the pulse inside the cavity for amplification. The pulse is ejected from the cavity

after about 40-80 round-trips by switching the voltage applied on the Pockels ce11 to the

full-wave voltage (8 kV). Because of the microjoule injected pulse, a net gain of only

103-104 is required to bring the input pulse to millijoule level. Considering the cavity

losses, the whole gain is estimated to be about 105-106, which is relatively low compared

to other systems in which 100-pJ or 1-nJ seed pulses are injected. This results in

relatively little gain-bandwidth narrowing in the regenerative amplifier. Experimentally,

we found the input pulse bandwidth of 1.3 nm to be preserved in the amplified output

pulse. The relatively low amplification by the regenerative amplifier also means that

greater contrast between the amplified pulse and the amplified spontaneous ernission

(ASE) background is expected.

The regenerative amplifier output (2 mJ, 1 Hz) is beam-expanded by 3 x, then


injected into a coliinear four-pass amplifier PA1 (IO-mm x 165 mm, phosphate glass)

through a Pockels celI pulse selector (10-ns window) which provides additional contrast

against pulse leakage and ASE background from the regenerative ampiifîer. The 100-mJ

output pulse (at 4 pulses/min) fkom PA1 next passes a vacuum spatial filter VSFl (f/30,

M = 2.5), and then is amplified by a double-pass amplifier PA2 (20-mm@ x 200 mm,

phosphate glass), producing 1.5-J pulses at 1 pulse/min. An additional pulse selector

with a 30-1s temporal window is placed between PA1 and PA2, to prevent feedback

damage from pulses reflected back into the early amplification stages.

M e r PA2, the bearn is again spatialiy fdtered in a vacuum spatial filter VSF2 and

expanded to 50 mm in diameter before entering the grating pulse compressor. The

compressor gratings are identical to the expander gratings except for their sizes. The

larger one has a ruled area of 21.5 cm x 16 cm. The gratings are parailel to each other,

set with the same incident and diffracted angles as those in the expander. At a 74-cm

center-to-center grating spacing, the amplified pulse is recompressed back to 1.2 ps. The

compressor efficiency is rneasured to be 65%, corresponding to a single-pass diffraction

efficiency of 90%. The final recompressed energy is 1 J.

This 1-J. 1.2-ps TW laser has become a routine tool for the ongoing picosecond

laser-produced plasma studies in Our laboratory. Longer-pulse and higher-energy

experirnents (such as the XW laser experiment 1671) are accommodated by an additional

two-pass amplifier PA3 (Quantel 64-mm + x 100 mm, borosilicate glass), which can

deliver up to 5-J, 410-ps pulses.

3.3.2 Characterization of Beam Focus in the Target Chamber

The recompressed 1 4 pulse is directed to a U3.5 fmal focusing lens at the target

chamber for the picosecond-laser-produced plasma studies. In most of the experiments

the most important parameter is the laser intensity on target, which in tum depends to a

large degree on the focusabiiity of the beam. So it is crucial to characterize the spot size

Chupter 3 Development of the Toronto FCM-CPA Laser System 58

at the focus in order to determine the acnial intensity on target. The confocal parameter

of the focused beam also determines the accuracy required for the target positioning

system in order to keep the target at best-focus nom shot to shot.

To measure the laser intensity distribution near the focus, the focal spot was

imaged with 15-times magnification ont0 a CCD camera (Hitachi) using a 10 x

microscope objective. The measured results are shown in Figure 3.6. By translating the

objective lens along the optical axis (Az > O corresponded to moving the objective lens

away from the focusing lens), a series of beam images were obtained at different

positions around the focus (Figure 3.6(a)). This measurement was performed with the

properly attenuated regeneratively-amplified and recompressed pulses. In Figure 3.6@),

beam sizes W (w) dong horizontal (x) and vertical (y) axes are plotted, together with

the best fits to the Gaussian beam equation. It c m be seen that the beam is slightly

astigmatic, and the confocal parameter along the horizontal direction (20, = 1 13 pm) is

about 61% of that dong the vertical direction (Gy = 185 p). The beam profile at the

best focal position (z = O, where W, = Wy) is plotted in Figure 3.6(c), which shows a

smooth Gaussian distribution with a spot size of L 1.6 pm FWHM. This corresponds to 1.4

times the diffraction lirni t .

Thermal distortions introduced by the power amplifiers were dso studied, These

were done through M n g PA1 andor PA2 at full powers, while keeping the regen

amplification at low level. When PA1 was fired, no obvious effect on the final beam

focusability was observed. When the 20-mm diameter PA2 head was fired, however,

both thermal-birefringence and a negative thermal-lensing were produced, which peaked

at about one minute after the finng. The tirne-dependent thermal lens in PA2 effectively

causes a shift of the best focal position in the target chamber; the amount of shift depends

on the rate at which PA2 is fired. When PA2 was f ied at a rate of one shot per two

minutes, for example, we found the best focus shifted to z = 140 p, as compared with

z = 0 when PA2 was not fired. This focal shift becarne unnoticeable when PA2 was f d

Chapter 3 Developrnen? of the Toronto FCM-CPA Laser System

Chapter 3 Development of the Toronto FCM-CPA Laer System 60

at one shot per 3 minutes. Based on this measurement, the FCM-CPA laser is normalIy

operated at a rate not faster than one shot per 3 minutes whenever PA2 is needed.

3.3.3 Compressed Pulse Characterization Using High-Contrast Cross-correlation

As discussed in 5 2.3, for a TW-laser system, the pulse contrast is a very

important parameter. To characterize the contrast of the FCM-CPA laser, a cross-

correlation method was used. Since we have very high contrast 1.2-ps oscillator pulses

left over in the osciilator train, we can use them as 'probe' pulses to cross-correlate

against pulses farther down in the CPA chah and analyze their shape, contrast and

possible satellites. Because both probe pulse and unlmown pulse are initiated from the

same oscillator pulse train, thei. relative time jitters are negligible. This cross-correlation

technique has proved to be very useful in our laboratory. Using another Pockels ceIl (not

shown in Figure 3.9, a single unstretched pulse is selected from the same osciiIator pulse

train and sent to the cross-correlator together with the unknown pdse. The cross-

correlator is identical to the autocorrelator described in § 3.2.3, except one delay-arm of

the autocorrelator carries the probe pulse. With the help of a fast photodiode and

osciiloscope, the relative timing between the probe pulse and the unknown pulse can be

adjusted to within 200 ps. Then by translating one delay-arm of the correlator, a cross-

correlation signal between these two pulses cm be found.

Figure 3.7 shows the result of two typical cross-correlation measurements. In

Figure 3.7(a), we cross-co~elated the temporaily s tretched regenerative amplifier output

against the 1.2-ps probe pulse. A 410-ps Gaussian shaped pulse is detedned, which

well agrees with Our calculation based on the input pulse bandwidth and the expander

geometry. In Figure 3.7@), we cross-correlated the regeneratively amplified and

recompressed 1.2-ps pulse with the high-contrast probe pulse. It shows that the leading

edge of the recompressed pulse is clean to the 2 x level, which corresponds to a

contrast of 5 x 107. It also clearly identifies postpulses resulting from residual Fresnel


time delay (ps)

time delay (ps)

Figure 3.7. Cross-correlation of the clean oscillator pulse with (a) the temporally stretched pulse and @) the recompressed pulse. The negative time delay represent the front edge of the pulse being studied.

Chapter 3 Development of the Toronto FCM-CPA Luser System 62

reflections in the CPA system. Small pulses on the leading edge of the main pulse appear

to be intemal reflectims of the clean probe pulse within the cross-correlation crystal.

The above measurements demonstrate that the cross-correlation chamcterization is

a significant improvement over what we could have provided by conventional second-

order or third-order autocorrelation. The very high contrast and the relatively high encra of the oscillator pulse are important factors for the success of the high-dynamic-range

measurement described in this section.

3.3.4 Single-Shot Autocorrelation

The multi-shot correlation techniques described in the previous sections becorne

tedious and impractical when used to study the fully amplified pulses because of the

relatively low repetition rate of our laser system (one shot per 3 minutes). The multi-shot

measurernent may also average out possible laser pulse-width fluctuations during the

operation. In order to monitor the laser parameters for a given shot, it is necessary to

build an autocorrelator which can measure the pulse width on one-shot basis.

The single-shot autocorrelator built in our lab is similar to the multi-shot one

explained in 5 3.2.3, but two cylindrical lenses (instead of the two spherical lenses) are

used to produce horizontal line-focuses on the LiI03 crystal. The photomultiplier is

replaced here by a CCD linear array (Thompson). To minirnize the effect of pulse spatial

distribution on the temporal measurernent, expansion of the incident beam size is

sometimes necessary. Calibration of the autocomlator is done by translating one of its

arms by a known amount and recording the corresponding shift of the autocorrelation

peak on the detector. By lirniting the room light and by carefully subtracting the CCD

thermal background, rneasurernent with a dynamic range of 103 can be routinely achieved

with this single-shot autocorrelator.

Figure 3.8 shows the typicd sin@--shot autocorrelation traces of (a) a pulse from

the FCM oscillator, and (b) a regeneratively amplified and recornpressed pulse. Both

Chapter 3 Developmenf of the Toronto FCM-CPA Laser System

time delay (ps)

time delay (ps)

Figure 3.8. Single-shot autocorrelation of (a) an oscillator pulse (At = 1.03 ps) and (b) a recompressed regen pulse (At = 0.94 ps). The dashed-lines are the Gaussian fi&. The broad wings in both plots are believed to be an artifact from the autocorrelator.

Chapter 3 Development of the Toronto FCM-CPA Lacer System 64

plots show a broad wing at the 10" level. Since the oscillator pulse is known to be clean

down to the l e level (see Figure 3.4(a)), we believe this broad wing is an artifact of the

autocorrelator. The osciiIator pulse shows a perfect Gaussian pulse shape with a pulse

width of 1.03 ps. The recompressed regen pulse exhibits a slightly narrower width of

0.94 ps, and shows a clear shoulder at the 10-2 level. This shoulder is indeed associated

with the compressed pulse, as it also appears on the leading edge of the pulse in the cross-

correlation measurement (Figure 3.7(b)). One possible explanation for this shoulder is

the high-order phase errors in the CPA system. In practice, a perfectly rnatched

expander-compressor system, where the total phase shift introduced equals to zero to ail

orders, is very difficult to obtain [101]. Even if this is done, there are still phase shifts

produced by the optical materials in the rest of the CPA system. The latter cannot be

completely compensated by a simple change in the compressor length, because the phase

function of the material does not match that of the compressor. Consequentiy, some

high-order (cubic and/or quartic) phase errors c m be lefi over in the compressed pulse,

producing a weak shoulder [ 1021.

The single-shot autocorrelation of a fully amplified and recompressed pulse was

also measured with suitable attenuation of the pulse going into the autocorrelator. The

measurement gave a very similar result to that shown in Figure 3.8(b).

In some experiments, the duration of the compressed pulse must be continuously

adjustable. This cm be done by changing the length of the compressor by translating one

of its gratings. Using the single-shot autocorrelator, the duration of the compressed pulse

was measured at different grating positions (Figure 3.9). The linear part of this

measurement agrees very well with the pulse width obtained from Our ray-tracing

calculation for a spectral bandwidth of 1.2 nm. The departure from linear at - 5 ps shows

the upper lirnit of this measurement, above which the spatial inhomogeneity 02 the

incident pulse to the autocorrelator starts to affect the tempord measurement.

Chapter 3 Developrnent of the Toronto FCM-CPA Laser System 65

grating position x (inch)

Figure 3.9. Compressed pulse width (At) measured at different positions (x) of

the translatable grating in the cornpressor. The solid lines are linear fits to data

with At c 5 ps. The departure from linear dependence, indicated by the dashed

line, shows the upper limit of the measurement, above which the spatial

inhomogeneity of the incident pulse starts to affect the temporal measurement.

3.4 A Novel Cross-correlation Technique

In rnany applications of picosecond light pulses, knowledge of the pulse shape is

of great interest. The commonly used intensity autocorrelation techniques are effective in

measuring the temporal width of optical pulses of picosecond to subpicosecond duration.

However, the intensity autocorrelation function

d2) (7 ) = r -- I(t)Z(r - r)dt (3 -2)

carries ody partial information about the temporal profile of the pulse, and therefore

cannot be used to determine the acnial pulse shape I(t). Higher order correlation

Chapter 3 Developrnent of the Toronto FCM-CPA Luser System 66

methods have been developed, which can give more detailed information on the pulse

shape. An even better approach is the cross-correlation (or optical sampling) technique,

in which the intensity profie of the pulse to be studied is temporally mapped by a much

shorter sarnpling pulse. In 8 3.3.3, we have shown an example of this technique, where

the clean 1.2-ps oscillator puise was used to sample the chirped 400-ps pulse

(Figure 3.7(a)). Limited by the 1-ps temporal resolution, however, that method cannot be

used to anaiyze picosecond or subpicosecond pulse shape. In this section we wili

describe an improved crosstorrelation technique in which 100-fs temporal resolution has

been achieved.

3.4.1 Design of the Novel Cross-correlator

The experimental arrangement is iliustrated in Figure 3.10. The 1054-nm, 1.2-ps

pulse from the FCM oscillator fist passes through a frequency doubler (KD*P crystal,

type 1) where about 10% of its energy is converted into the second harmonic (527 nm).

The 1054-nm and 527-nm beams are then separated by a hannonic beamsplitter. The

527-nm pulse is first coupled into a 67-cm long, 1.5-pm core diameter single-mode

polarization-preserving optical fiber where it experiences self-phase modulation (SPM)

and group-velocity dispersion (GVD), augrnenting its bandwidth and stretching its pulse

width. The output pulse is then compressed by a double-pass grating compressor,

yielding a - 100-fs, 527-nm probe pulse for crosscorrelation in a tripler crystal.

The compressed 527-nm probe pulse and the orthogonally polarized 1054-nm

pulse are then recombined by another hamonic beawplitter, and sent to a frequency-

mixing non-linear crystal (KD*P, type II). The sum-frequency signal at 351 nm is

isolated from the fundamental and the second harmonic by a pair of UV bandpass fdters

(Schott UG1 and UG11) and detected by a photomultiplier. By varying the relative delay

between the two pulses, a background-free cross-correlation can be recorded with a

temporal resolution detemiined by the pulse width of the green probe pulse (- 100 fs).

Chapter 3 Development of the Toronto FCM-CPA Laser Syste?n 67

nu-r doubler

single mode fiber

Figure 3.10. Setup of the fiber-compressed subpicosecond cross-correlator. H B S , harmonic beamsplitter; G1, G2, diffraction gratings.

This experirnental configuration can also be seen as an improved version of the standard

third-order autocorrelation technique [103] in which the SHG signal is directly mixed

with the fundamental.


The spechum of the frequency-chirped green pulse at the output of the fiber was

measured, exhibiting the characteristic structure of SPM and a bandwidth of about 3.0 nm

( F m ) . High-dynarnic-range autocorrelation of the recompressed 527-nm pulse was

done by non-collinear frequency doubling in a KDP crystal and measuring the 264-nrn

SHG signal. By varying the grating separation in the cornpressor, an optimized

autocorrelation width of 168 fs (F"wKM) was obtained for the recompressed green pulse.

This corresponds to a pulse width of 84 fs if a Lorentzian pulse shape is assumed

(Figure 3.1 l(a)).

Chapter 3 Development of the Toronto FCM-CPA Laer System 68

time delay (ps)

-4 -2 O 2 4 6

time delay (ps)

Figure 3.11. (a) Autocorrelation of the fiber-sîretched and grating-compressed 527-nm probe pulse. Puise width At = Ar/2 = 84 fs, assuming a Lorentzian pulse shape. (b) Cross-correlation of the compressed 527-nm pulse with an IR pulse from the FCM oscillator. Negative time delay corresponds to the leading edge of the pulse.


Detailed pulse-shape analysis of Our FCM oscillator is one interest for this

scheme. The 84-fs probe pulse was sent collinearly with the 1-ps pulse from the FCM

oscillator to a KDP crystal where the cross-correlation was measured. Figure 3.1 1(b)

shows the measured actual pulse shape of the oscillator pulse together with a Gaussian fit.

The leading edge of the pulse, shown with negative time delays in the figure, appears to

be more steep than that of the falling edge. This weakly asyrnmetric pulse shape is. in

fact, expected as a consequence of the passive mode locking employed in the oscillator.

Since the recovery time of the saturable absorber (4.2 ps in this case) is shorter than the

round-trip time of the cavity but much longer than the pulse duration, for each round trip

the leading edge of the pulse interacts with a recovered dye, while the falling edge

interacts with a dye which is partidy bleached. As a result, more light is absorbed from

the front of the pulse, leading to a pulse shape with sharper front edge than the trailing

edge (1041.

3.5 Conclusions

In this chapter, an dl-Nd:glass CPA terawatt laser system built at the University

of Toronto has been described. Using very high-contrast, high-energy 1 -2-ps pulses from

the FCM oscillator as seed pulses, and employing a gratings-only temporal stretching and

cornpressing scheme, we have obtained an output pulse of 1 J, 1.2 ps with a prepulse

contrast greater than 5 x 107 without the help of additional pulse cleaning techniques.

Focusing this TW pulse in the vacuum chamber, an intensity greater than 1017 W/cm2 can

be achieved. Alternatively, the system can also be configused to generate 410-ps

uncompressed pulses of up to 5-J energy. Finally a novel cross-correlation technique is

descnbed, which can provide 100-fs resolution and map asymmetrical pulse shapes from

subpicosecond flashlarnp-pumped lasers.

Chapter 4 Experimental Results of Second Harmonic Generation

This chapter describes the experimental work of second harmonic generation from

laser-solid target interaction. This work was done at the University Toronto using the

FCM-CPA laser system. As pointed out in 5 2.3, laser pulse contrast is of crucial

importance in the interaction of intense ultrashort laser pulses with solid surfaces.

Preplasma produced by smail prepulses alters the interaction pichue and cm significantly

degrade the quality of harmonic emission. The focus of the work descnbed in this

chapter is to investigate this hypothesis systematically and to study the effect of

preplasma on harmonic conversion efficiency, angular distribution, as well as spatial and

spectral characteristics. At the end of the chapter, experimental attempts on observing

hannonic higher than the second order using the FCM-CPA laser are also discussed.

The experimental layout is shown schematically in Figure 4.1. The 1.2-ps, 1 . O S

nm laser pulses from the FCM-CPA system were delivered to the evacuated target

chamber, and were focused by a f73.5, 16-cm focal-length multi-element lem onto the

target at an incident angle of 35' to the target normal. This angle was chosen because it

allowed the spectrometer to be conveniently positioned at the specula. reflection angle of

the incident laser.

Chapter 4 Eiperimenral Resulrs of Second Hamonic Generation

vacuum chamber

incident laser beam A

7 filter set

spectrograph /spectrometer

Figure 4.1. Schematic diagram of experimental setup for the

harmonic measurement.

In the middle of the target charnber was the target positioning system built by

three Linear translation stages and one rotational stage, ail driven by Encoder Mike motors

(Oriel). It held up to seven Bat targets each tune, and aliowed each target to be moved in

the three orthogonal directions with a precision of 10 p. The positioning system was

remotely controlied by a cornputer, and a LabVIEW program was written to automate the

target positioning procedures. After each laser shot, the target was translated within its

plane by a certain amount so that a fresh surface would be available for the next shot.

Polished silicon wafers were used as the primary target for this study, because of their

high-quality surface f ~ s h . During the experirnent, the target chamber was pumped down

to a pressure of 2 x 10d Torr by an oil diffusion pump with liquid nitrogen cold trap.

The specularly reflected Iight from the target was collected by a lens and was sent

to the spectrometer (Jarrell-Ash) where the harmonic spectrum was analyzed. A group of

optical band-pass filters (Schott glass) were used to prevent the strong fundamental light

Chapter 4 Ehperimental Resu2t.s of Second Hannonic Generation 72

from entering the spectromeer and interferhg the measurement of the relatively weak 2 0

signal. At the output of the spectrometer, either a CCD camera (Hitachi) or a

photomultiplier (PMT) (Hamamatsu R212UH) could be attached as the detector. The

CCD camera was used for the second harmonic measurement; in this case, the

monochromating output slit was removed so that a one-shot spectrum could be recorded.

We also tried to measure the third or higher harmonies using the same experimental

setup. In these experiments, the PMT was used because of its much higher detection

efficiency and wider spectral response. The lack of spatial resolution for the PMT,

however, meant that these experiments had to be done on a multi-shot basis. The

wavelength readout of the spectrometer was calibrated to an accuracy of - 1 A using the

atomic lines fkom a Hg lamp.

To measure the laser energy on target, the light leakage through the fmt mirror of

the penscope (used to lift the laser beam to the height of the target charnber) was detected

with a large area photodiode (UDT), which had been calibrated using a pyroelectnc

energy meter (Molectron).

4.2 Laser Pulse Cleaning with Saturable Absorber

As discussed in Chapter 3, one of the important features of the Toronto FCM-

CPA laser system is the high pulse-contrast it produces: its intrinsic pulse-to-pedestal

contrast is better than 5 x 107, as shown by the high-dynamic range cross-correlation

measurernent. However, when using a fast oscilloscope to examine this intrinsic-

configuration pulse in a larger tirne range, we observed a prepulse at 1 W energy level

and 1.5-ns ahead of the main peak. The prepulse, which we believe resulted from

Pockels-cell leakage in the system, appeared to be as short as the main peak, although no

detailed measurement was made because of the limited temporal resolution of the

osciIloscope.

Chapter 4 Ejrperimental Results of Second Harrnonic Generation 73

In order to clean up the inainsic pulses, a saturable-absorber dye ce11 [87] was

used. The dye cell was 2-cm thick, and contained the same saturable absorber as that

used in the FCM oscillator (5 3.2.1), i-e., Kodak Q-switch II (dye 9860) with 1,2-

dichioroethane as the solvent. The relaxation tirne of this dye is 4.2 ps, which is much

shorter than the tirne delay between the prepulse and the main peak. Uniike in the

oscillator, where the dye ce11 has a single-pass small-signal-transmission of about 80%,

the dye concentration here is much higher. the low-intensity transmission is < 10-5.

The dye ce11 was placed directly in the fmal output line of the system, without

using any focusing lens in front of it. It provided an attenuation of about 10-5 for the

low-intensity pulses, while allowing a 30% transmission for the high-intensity main peak,

increasing the intrinsic pulse contrast by a factor of at least 104. M e r a certain number

of laser shots, the dye usually deteriorates and becomes more transparent for the Iow-

intensity Iight. So a routine check on the dye-ce11 transmission was performed before

each experiment, and new dye would be added if the transmission was too high.. To

extend the lifetime of the saturable absorber, the dye ce11 was normally kept in a dark

room and was used only when high-contrast pulse was required. With the dye cell in the

beam line, the final pulse contrast was estimated to be greater than 10lO.

4.3 Second Harmonic Generation (SHG) and the Effect of Prepulse

With the dye-cell in and out of the beam h e , two different laser conditions could

be created: the dye-cell-cleaned pulse with a contrast greater than 10Io and the intrinsic

configuration pulse which contains a fixed-fraction (104) prepulse at 1.5 ns ahead of the

main peak. By comparing the harmonies generated under these two laser conditions, we

did a series of experiments to study the effect of preplasma on harmonic generation. To

be bnef, these two laser conditions are referred in the following as the 'clean pulse' and

the 'intrinsic pulse', respectively.

Chupter 4 Experimental Results of Seconà Hannonic Generation

43.1 Power Scaling of SHG

We f i t measured the 2 0 yields generated with the clean pulse and the intrinsic

pulse at different laser intensities. Since the CCD-carnera had a dynamic range of - 102,

calibrated neutrai density fdten (Schott glas) were used in fiont of the spectrometer

when the signal was too strong. The laser intensity was controlled maidy by varying the

amplification of the regenerative amplifier. For the low-energy shots the PA2 amplifier

was turned off. Figure 4.2 shows the dependence of the spectraily integrated 2 0 energies

measured with the clean pulse (faed circle) and with the intrinsic pulse (open circle) on

laser intensity.

When the clean pulse was used, the 2 0 yield, which was collected dong the

specular direction, was found to increase with the fundamental laser intensity 1,

following a power dependence of b2e4. This observed power dependence is slightly

faster than the conventional square-law observed for SHG in other nonlinear media at

lower laser intensities. This, however, is not surprising if one considers that in this

experiment both the plasma and the SHG from the plasma were generated by the very

same Iaser pulse. This result is also consistent with the observation made in an earlier

expenment by von der Linde's group [los] in which a power of 2.6 was reported.

As the target was irradiated by the intrinsic pulse, we found that the harmonic

yield was identical to that generated by the clean pulse when the laser intensity was

below 1 x 1015 W/cmZ. As the laser intensity increased above 1 x 1015 Wfcm*, the

collected 2 0 energy with the intrinsic pulses fxst began to show a saturation and then

started to pick up the same power dependence (dashed line) as that of the clean-pulse

harmonic (soiid line) when the laser intensity was higher than 1 x 1016 W/cm2.

Chapter 4 Experimental Results of Second Harmonie Generation

fit: E = 1 2-4 20 O

laser intensity (w/cm2)

Figure 4.2. Measured SH yield per steradian with clean pulses (solid circles) and intrinsic pulses (open circles), scaled with laser intensity. The solid Iine is a power fit for the clean-pulse harmonic. The dashed line illustrates that, after a period of 'saturation', the intrïnsic-pulse harmonic eventually picks up the same power dependence as that of the dean-pulse harmonic.

Chapter 4 Ejcperirnental Results of Second Hannonic Generation 76

Since the intrinsic puise contained a fixed-fraction ( I V ) prepulse, as we

increased the laser intensity the intensity of the prepulse was also increased. So the result

shown in Figure 4.2 (open circle) can be also seen as the 2 0 yield measured with

increasing level of prepulse intensities. At the laser intensity of 1015 W/cm2, where SHG

started to saturate, the corresponding prepulse intensity was - 10" W/cm2, which was

about the intensity threshold for plasma production. Therefore we can conclude that the

observed initial saturation of SHG with intnnsic pulses was actually a result of beginning

to make preplasma by the smail prepulses.

It should be emphasized that the 2 0 energies plotted in Figure 4.2 are only those

energies collected by the spectrometer, which was positioned at the specular reflection

angle of the incident laser and intercepted a total solid angle of i& = 3.1 x 102 sr. If the

harmonics actually spread out in a solid angle greater than Ro, then the 2 0 yields we

measured above would represent only partial yields. The angular distribution of SH

emission has to be known in order for us to compare the total harmonic yields generated

by the clean pulse and by the intrinsic pulse.

4.3.2 Angular Distribution of SHG

When a laser pulse interacts with a flat cntical density surface of plasma, the

hannonics generated are expected to have a narrow angular distribution dong the

specular direction. If prepulses are present, however, the laser pulse will interact with a

observation

target

Figure 43. Schematic diagram of measuring the non-specular harmonics.

Chapter 4 Ejcperimental Results of Second Hannonic Generation 77

expanding non-fiat preplasma, and the consequently generated harmonics might emit in a

larger solid angle.

In measuring the harmonic angular distribution, we used the same experimental

arrangement described in 4.1 to observe hannonics in the non-specular direction (see

Figure 4.3). Ideally, this should be done by changing the observation angle eobs while

keeping the incident angle ei constant. But this was impracticable as the direction of the

incident laser beam and that of the observation were fxed in our target chamber. So

instead of rotating both the target and the incident Iaser direction (in order to keep Oi

constant), ody the target was rotated in this experiment. This simple method ailowed us

to measure the non-specular harmonics at different observation angles Bab, = 2(ei - 357,

without making major modifications in the experimental setup; it had a tradeoff, though,

in such that the effect of laser incident angle on harmonic generation was also integrated

in our measured results.

1 O-' : \

\ :

- \ - - - - - - 20 profile -

- - - - - IO"?

laser profile (1 O* FWHM) - - - - specular - -

8 (degrees) obs

Figure 4.4. Angu1a.r distribution of SH generated with clean pulses (solid-line).

The dashed-line represents a laser profile with an angular width of 10' ïWHbi.

Chapter 4 Experirnental Results of Second Hamonic Generation

8 (degrees) obs

8 (degrees) O bs

Figure 4.5. (a) Angular distribution of SH generated with intrinsic pulses at

various laser intensities. (b) Cornparison of SH angular distributions measured with clean pulses (solid-line) and with intrinsic pulses (dashed-line) at the same laser intensity .

Chapter 4 Fxperimental Results of Second Harmonic Generaîion 79

We fmt measured the angular distribution of SH produced by the clean pulses.

Using four targets mounted with different incident angles, Le., Oi = 33.4', 35.1 O , 36.7',

and 37.2', SH emission was measured at observation angles from -3.5' to 8' relative to

the center of the reflected laser beam (the specular direction). The result is shown in

Figure 4.4. For comparison, the profile of the reflected laser beam-a cone with a .

angular width of 10' I3vI-i~-is also plotted. We can see that, for a laser intensity of

1.8 x 1016 W/crn2, the SH emission was centered at the specular direction, with a cone

angle smaller than that of the incident laser. Considering that the change of the incident

angle was small, Le., a total of 3.8', we could assume that its effect on SHG efficiency

was negligible in this measurement. Therefore the result shown here represents the actual

angular distribÿtion of the SH generated with the clean pulses.

Using a similar method, the angular distribution of SH generated by the intrinsic

puises was also studied. Figure 4.5(a) shows the angular distributions of the intrinsic-

pulse-produced SH measured at various laser intensities. We found that as the laser

intensity (and concurrently the prepulse

intensity) increased, no ton ly did the inz::y;'y collected SH energy increase, but the 2w by

intrinsic harmonic emission also spread out into an pulse increasing solid angle.

A direct comparison of the angular

distributions of SH emission using clean and

intrinsic pulses is presented in Figure 4.5(b). 20 by

At a laser intensity of 1.5 x 10'6 W/cm2, a clean pulse

very sharp specular distribution was

observed for the clean-pulse harmonic Figure 4.6. Illustration of SH cone-

(solid-line) , while a muc h broader angular emissions generated by a clean pulse and

distribution was recorded for the htrinsic- by a intrinsic pulse.

Chapfer 4 EXperimental Results of Second Hannonic Generation 80

pulse harmonic (dashed-line). The corresponding SHG cone-angles (m) were found

to be al = 6' for the clean pulse and a2 = 60' for the intrinsic pulse, respectively (see

Figure 4.6). Assuming the two harmonic cone-emissions had cylindrical symmetry, the

ratio of their corresponding solid angles can be calculated as:

Integrating the harmonic energies within the respective cone envelopes of each, it is

significantly found that the overd total yields are almost identical. This indicates that

the apparent saturation of the collected harmonic yield using intrinsic pulse in Figure 4.2

is alrnost entirely due to the spread of harmonic production into larger solid angles, under

the effect of preplasma.

4.3.3 Imaging of the SHG Emission

The spatial and spectral structures of the harmonic source also provide useful

information for the h m o n i c generation process. In an ideal situation, one would expect

a hannonic to have a sirnilar intensity distribution to that of the fundamental, both in

space and in frequency. Any deviation from the ideal situation can be used as a

diagnostic for the conditions of the laser-plasma interaction. From the application point

of view, the intensity distributions of a hannonic in space and in frequency also

characterize the quality of the harmonic source-a small smooth source with narrow

spectral distribution means the radiation it generates will have good spatial and temporal

coherence and high spectral brightness.

A modified experimental setup, as shown in Figure 4.7, was used to image the

SHG source with both spatial and spectral resolution. A pair of achrornats (Meiles Griot,

f = 200 mm, 6 = 40 mm) used in an unitconjugate-ratio configuration [106] replaced the

Chapter 4 Experimental Results of Second Hamonic Generntion

vacuum chamber

incident / laser beam , target

filter set Q CCD camera 2 H

+I filter set

spectrog imaging rap h I Figure 4.7. Modified expeiimental setup with imaging system.

harmonic collecting lens in the previous setup (Figure 4 4 , and relayed a nearly

aberration-free real image of the harmonic source to a point outside the target chamber.

This image was subsequently re-imaged and magnified by 23 times through a 10 x

microscope objective, split, and recorded by two CCD cameras: Camera 2 was used to

measure the spatial distribution of the harmonic source, whereas Camera 1 recorded a

two-dimensional image of the SH source with both spatial and spectral resolution through

an imaging spectrograph.

Figure 4.8(a) shows a clean-pulse-generated 2 0 emission image superimposed on

image of a damage crater. Horizontal and vertical lineouts taken through the center of the

2w source are plotted in Figures 4.8(b) and 4.8(c), respectively. The results show that the

harmonic source has a smooth spatial distribution and is contained in an area of 7.4 p x

7.9 pm at FWHM.

Chapter 4 Evpeninental Results of Second Hannonic Generation 82

Figure4.8. (a) 20 emission image superimposed on image of darnage Crater.

(b) Horizontal and (c) vertical lineouts through the image of the 2w source.

Spatially-resolved SH spectra measured with clean and with intrinsic pulses are

shown in Figures 4.9(a) and 4.9(b), respectively. In each, the figure at left shows a

spectrum (resolved horizontally) for a vertical slit-image of the plasma, taken at the

center of the laser focus. The figure at right shows the lineout spectrum of SH generated

around the center of focus. The clean-pulse-generated SH spectrum shows an instrument-

ümited spectral iine that is red-shifted by about 10 A from k0/2 (5265A). This red-shift

of the 2 0 spectmm has k e n reported in a previous experùnent, and a detailed discussion

about its origin has been presented [107]. Here we will concentrate on the differences in

the 20 spectra generated by the clean pulse and by the intrinsic pulse.

Cornparhg Figures 4.9(a) and 4.9@), we can see that the presence of preplasrna

radically changes both the spatial and the spectral charactenstics of the harmonic

generated. The intrinsic-pulse-generated harmonic source showed a structure consisting

many 'hot spots' in both space and frequency dimensions.

Chapter 4 Experimental Results of Second Harmonic Generation

(a) clean pulse, I = 2.0~1016 W/cm2.

spectrum I 50 A

I

(b) intrinsic pulse, I = 4.5~1 O1

spectrum I I

Figure 4.9. Spatially resolved 2 0 spectmm measured with (a) clean pulse, (b) intrinsic pulse. The figure at Iefi is a spectrum (resolved horizontally) for a vertical slit-image of the plasma taken at the center of the laser focus, and the figure at right is a spectral iineout cut

across narrow spatial region. The spectra intensities were norrnalized for best cornparison.

Chapter 4 Expen'mental Results of Second Harmonie Generation 84

For the spectral broadening and breakup of the harmonic source, we believe they

are due to self-phase modulation experienced by the laser pulse when traveling through

the extended underdense part of the plasma [108]. As for the spatial hot spots, one

possible explanation is that they too are the result of beam breakup and filamentation as

the laser propagates through the underdense region before interacting with the critical

density surface of the plasma [log, 1101. This, though, is not necessarily the only

explanation. For example, they may also be caused by interference in light refiecting

from a non-homogeneous plasma formed by the prepulses, just as in the case of a mirage

or when light passes through a rippled glass. This interference interpretation, however,

may have the following limitation. If weU focused, the harmonic image we recorded is a

near-field image, which should exhibit less intensity modulation than from an equivaient

far-field image. This same issue is the reason why &am-relay optics are used to improve

spatial uniformity in intense laser amplification, since the beam has zero effective path-

length to diffkact. The argument is not definitive, but seems to favour filamentation in the

plasma preformed nanoseconds in advance as the cause of the distortions recorded.

Similar resdts on the spatial and the spectral breakup of the harmonies were also

reported in the VULCAN experiments 128, 291. Our experimental results clearly

demonstrated that this breakup was directly associated with the underdense plasma

created by the small prepulse, rather than caused during the generation of the hamionics

at the cntical density surface of the plasma.

4.4 SHG with Controlied Prepulses

To further study the effect of preplasma on SHG, we performed a pump/probe-

like experiment in which a weak prepulse was added deliberately at a controllable time

relative to the high-contrast main pulse. Since the preplasma will expand into the

vacuum once it is created, depending on the time-delay after the prepulse, the following

Chapter 4 Experimental Resulfs of Second Hannonic Generation 85

main pulse wiU interact with a plasma of varying scale-length. In this way, the relation

between SHG efficiency and the scale-length of the source plasma c m be studied.


The setup used to generate a controllable prepulse is shown in Figure 4.10. At the

output of the Toronto FCM-CPA system, the dye-cell-cleaned high-contrast I-ps pulse

was amplitude-split by an adjustable half-waveplate and a thin-film polarizer, then sent to

two delay annç where the am-length for the prepulse could be continuously adjusted.

The two beams, separated by 3.8 cm (center-to-center) sideways, were then made to

propagate in parallel to the target chamber. Before entering the target chamber, the

polarkation of the two pulses was rotated 90' by the periscope so that the main pulse and

the prepulse were p- and s-polarized, respectively, relative to the target. The energy ratio

of the two pulses was controiled by rotation of the half-piate.

I compressed 1-ps pulse

adjustable U2 plate

Figure 4-10. Expenmental setup for generating controllable prepulse. The SH detection scheme inside the target chamber is shown in the inset.

Chapter 4 Fxperïrnentul Results of Second Hannonic Generation 86

Inside the target chamber, a scheme like that in Ref. [IO71 was used. The two

p d e l beams were focused by the same focusing lens onto the same surface area of the

targets at different angles of incidence (see the inset in Figure 4.10). SH signal generated

by the main pulse was colIected d o n g its specular direction, while the refîected prepulse

beam was stopped by a beam-dump. The reiative timing between the two pulses was

measured to an accuracy of +3 ps using a x-ray streak camera mounted on the target

chamber. The spatial overlap of the two pulses at the focus was checked before each

experiment using the SH imaging system (Camera 2 in Figure 4.7).


In this experiment, the main pulse/prepulse energy ratio was set to 10: 1, and the

main pulse intensity was kept at 1.8 x 10'6 W/cm2. Control shots taken by blocking the

main pulse confirmed that no 2 0 signal generated by the prepulse was collected by our

detection scheme. This ensured that the measured harmonic yield was generated only by

the interaction between the main pulse and the plasma. The 2 0 yield was measured at

various prepuise delays. Because of the shot-to-shot fluctuation of the incident laser

energies, approximately five shots were made for each time delay. The averaged 2 0

yield as a fùnction of prepulse delay is plotted in Figure 4.11.

The overall features of the result can be described in the following: (1) When the

prepulse was behind the main pulse (t < O), the 2 0 yield was independent of the time-

delay between the two pulses, and stayed at the level as if no prepulse was present;

(2) When the two pulses were temporally overlapped ( t = O), a near three-fold

enhancernent of the 2 0 yield was observed; (3) When the prepulse came ahead of the

main pulse ( t > O), the 2 0 yield decreased monotonically as the tirne-delay between the

two pulses was increased.

Chapter 4 Erperirnental Results of Second Humonic Generation 87

time delay (ps)

Figure 4.11. Averaged 2 0 yield measured at different prepulse delays. Error bars represent the standard errors of the average. The soiid line is a guide for

view only.

The responses of SHG in regions (1) and (3) are easy to explain. Obviously, no

effect will be made by the prepulse when it lags the main pulse, as the main pulse will

interact directly with the solid surface. On the other hand, when the prepulse leads the

main pulse in tirne, preplasma will be made, and the main pulse will interact with an

expanding plasma whose scale-length increases with the delay of the main pulse. Since

longer scaie-length means less laser light will tunnel through the plasma and reaches the

critical surface, we expect to see a trend of a decreasing 2 0 yieid with the increasing of

plasma scale-length.

The observation of the 2w yield enhancement near t = O demonstrated that

hannonic generation could indeed be enhanced by a weak prepulse, presumabiy through

the resonant eKect discussed in 1 2.2.2. We noticed that the sarne phenomenon had also

been observed in an early experiment performed by von der Linde et al. [107], in which a

Chapter 4 Experimental Results of Second Harmonie Grneration 88

sharp peak of the 2 0 yield, comparable in duration with the laser puise width (65 fs), was

recorded at t,, = 170 fs after the prepulse. They atvibuted the observed 2 0 peak to the

expansion of the plasma to a state of maximum resonance enhancement of the

fundamental opticd fields, which, according to their numerical calculation, was expected

to occur for scale-lengths of 0.05Â < L < 0. la. Based on this interpretation, a plasma

expansion velocity of oq = L/t- = 2 x 107 cmls was suggested by the author.

On the other hand, if one knows the actual plasma expansion velocity, the

optimum plasma scde-length can be inferred from the time delay t,, of the observed

2 0 peak. Unfortunately, this cannot be done for our measured resdt because of the large

experimental error (B ps) in determinhg 'time zero' in Figure 4.1 1. Besides, considering

the laser intensity used in this experiment was 10-times higher than that in Ref. [107], the

ponderornotive modifications of the plasma profde [22, 11 11 might dso need to be taken

into account in order to interpret the observed 2 0 enhancement.

4.5 Experiments Beyond SHG

Experiments searching for harmonies above the second order were dso carried

out on the Toronto FCM-CPA laser system.

Third-harmonic generation fiom solid targets was studied using the experlmentd

setup shown in Figure 4.1. Since Our silicon CCD camera was not sensitive at the

wavelength of 3 0 (35 10 A), a photomuItipIier tube, together with a monochromating

output dit, was used as the detector. To reduce the signal background caused by

scattering of the relatively strong fundamental and second harmonic light, Schott g l a s

fdters (UG1, UG5 and KG3) were used at the entrance of the spectrometer-

A 3 0 spectrum measured with the dye-cell cteaned pulses at a laser intensity of

2.3 x 1016 Wkm2 is show in Figure 4.12, in which each data point represents an average

of four measurements. Despite the relatively Iow signal-to-noise ratio, a peak structure at

Chupter 4 Experimental Results of Second Hamonic Genemtioa

2.0, I 1 I t 1 I 1 I I I I I 1.

- piiii-1 30

J, I = 2.3 x 1 016 w/cm2

n u, 1.5 - C, 9-

I= 3 -

42 1.0- w

a ,- typical cn - c e rro r- bar a> c. r 0.5 - -

-

Wavelength (A)

Figure 4.12. Third harmonic from a silicon target measured with clean pulses.

Each data point represents an average of four measurements with the standard

error shown as the error-bar.

the wavelength of 3 0 can still be clearly identified in the spectrum. To compare the

relative intensities of the 3 0 and 2 0 signals, a spectrurn of 2w emission was also

measured using the same experimental scheme. After correcting for factors of filter

transmission and the spectral response of the PMT, a ratio of - l e was found between

the intensity of 3 c ~ and that of 2w at our experimental conditions.

In the experiments searching for higher ( n > 3) order harmonies, a 20-cm VUV-

spectrometer (Minuteman) equipped with a Micro-Channel-Plate (MCP) detector

(Galiieo) was used. The use of the MCP detector, which combined the advantages of the

high sensitivity of a PMT and the imaging capability of a CCD, enabled us to measure the

hannonic spectra in the VUV region with great sensitivity on a single laser shot. To

allow for detection of VUV light, the glass harmonie-coilecting lens and fdters shown in

Figure 4.1 were removed. This detection scherne was sensitive in the spectral region

Chapter 4 FJcpenhental Results of Second Hannonic Generation 90

from 600 A to 1800 A, which covered the 6th to 17th harmonies of the 1.053-nm

fundamental lighî.

Using the dye-ce11 cleaned pulses, experiments were done on several solid targets.

In addition to silicon and aluminum, solid plastic and carbon (graphite) targets were also

used because of their low recombination background and simple Iine structure. With

laser intensities as high as 5 x 1016 W/cm2, we observed strong plasma line-emissions

fiom a l l these targets. but could not identiQ any harmonic signal in the entire spectral

region fiom 600 A to 1800 A. Based on the results of these experiments, we concluded

that, under the experimental configuration we used and with laser intensities up to

5 x 1016 W / c d , the detection of the higher harmonic ( n > 3) emission was limited by the

plasma recombination background. There are two obvious solutions to this problem:

(1) further increasing the Iaser intensity, because it is believed that harmonic emissions

grow faster with laser intensity than the recombination background does; (2) using tirne-

resolved spectroscopy to distinguish the fast harmonic emission from the relatively slow

plasma recornbination background [23, 1 121. Following the f ~ s t solution, we performed

another series of experiments at laser intensities up to 1 x 1018 Wkm? Results of this

series of experiments are discussed in the next chapter.

4.6 Conclusions

Using the FCM-CPA laser system at the University of Toronto, second harmonic

generation from laser-plasma interaction was studied. Through experiments using very

high contrast pulses and pulses with fixed-fraction prepulses, we systematically

investigated the impact of preformed plasma on harmonic generation and characterized

its effect in the spatial and spectral breakup of the harrnonics and in spreading harmonic

emission into large soIid angles. By adding a deliberate and controlled prepulse, we also

measured the second harmonic yield in a pump/probe-like experiment in which the

Chaprer 4 Experimental Resulrs of Second Hamonic Generation 91

relation between the SHG efficiency and the scale-length of source plasma was studied.

Experiments to search for harmonics above the second order were also canied

out. At a laser intensity of 3 x 1016 W/cm2, third-hamionic signal fkom an silicon target

was recorded just above our detection b i t . Detection of higher order harmonic was

found to be limited by the plasma recombination background. which implied that even

higher laser intensities (> 5 x 10'6 W/cm2) were necessary for the observation of higher

(n > 3) harmonics.

Chapter 5 Experimental Results of Mid-Order Harmonic Generation

To extend our effort of searching for higher order (n > 3) harmonies from laser-

solid target interaction, a series of experiments were conducted on the T3 (Table-Top-

Terawatt) laser system at Center for Ultrafast Optical Science at the University of

Michigan. The experimental details and results are described in th is chapter.

5.1 The ï? Laser System

Unlike our Toronto dl-glas CPA system descnbed in Chapter 3, the T3 CPA

system is a hybnd one that inciudes a Ti:Sapphire osciliator (Coherent Mira-900) and

regenerative amplifier, followed by three single-pass Nd:glass power amplifiers. The

pulse expansion and compression scheme is similar to the Toronto system-no fiber is

needed because of the broad b d w i d t h of TkSapphire. The laser system operates at a

center wavelength of 1.053 p, and, for these experiments, produces 400-fs pulses with

an energy of up to 3 Joules, yielding a maximum power of 7.5 W.

The intrinsic contrast of the IR pulse from the T3 system is around 5 x 105. In

order to achieve higher contrast to avoid the production of preplasrna, the IR pulse was

converted to its second harmonic (h = 526 nm) using a 4-mm thick type4 potassium

dihydrogen phosphate (KD'P) crystal [113]. The nonlinear frequency-doubiing process,

with its yield being proportional to intensity squared at low laser intensities, significantly

Chapter 5 Experhental Results of Mid-Order Hamonic Genemtion 93

eliminated the wings and pedestals in the converted green pulses, leading to much higher

pulse contrast.

Figure 5.1 shows the optics setup used for the harmonic experiment. The 1053-

nm pulses from the T3 laser were &st frequency doubled by passing through the KD'P

crystal. In order to filter out the IR component in the 526-nm laser beam, four dielectric-

coated green &ors (Ml to M4) were used in series after the doubling crystal. Each of

these m o r s had a reflectivity of > 95% for the 526-nm pulse and about 3% for the IR

fundamentai. This provided an attenuation of about (0.03)4 = 8 x l e 7 for the relatively

low contrast IR light. A 2-mm thick green band-pass filter (Schott g l a s BG39) was used

before the parabolic &or to provide m e r discrimination against the IFt residual in the

green laser beam. With these mesures, the contrast for the green pulse was estimated to

be better than 1011, which was large enough to avoid the production of preformed

plasmas for al1 intensities up to 1019 Wfcm? Confirmation that the T3 system produces

negligible prepulses was provided by a previous study of solid-density laser-produced

plasmas using x-ray spectroscopy [114]. The frequency-doubling of the 400-fs

fundamental pulse should yield a Gaussian-shaped green pulse with a FWHM of

400/& = 280 fs. Because the frequency conversion was saturated, however, the actual

w of the green pulse was around 350 fs.

To monitor the energy of the 526-nm pulse on target, the 3% transmission of the

green pulse through mirror M l was picked up, fitered by other two green mirrors (M5

and M6) and a BG39 filter, and rneasured by a photodiode. To calibrate the photodiode,

a green mirror was temporally installed iaside the vacuum chamber (between the BG39

filter and the parabolic rnirror), which redirected the green pulse onto a calorimeter

located outside the vacuum chamber. The reading of the photodiode was then calibrated

against the calorirneter which measured the actual laser energy on target. The conversion

efficiency into a green pulse was found to be around 50% at moderate laser energies

(- 800 mJ of IR) and could reach as high as 70% at higher laser power (2 Joule of IR).

Chapter 5 Eipeninental Results of Mid-Order Hannonic Generation 94

beam di for IR pi

CCD A

Rowland Circle

\ l 1

1

IR pulse from the T3 laser

parabola zooming axis for focal scan

Figure 5.1. Experimental setup for mid-order harmonic generation from solid targets using the T3 laser system. PM is the parabolic mirmr; Ml to M6 are the green mirrors discussed in the text.

Chapter 5 Expehental Results of Mid-Order Hamonic Generation 95

The frequency-doubled green pulse was originally s-polax-ized relative to Our

target setup. However, for most parts of the harmonic experiment, a p-polarized Laser

pulse was required. To rotate the laser polarization, a quartz half-wave plate was

introduced after Ml. In the case when s-polarization was required, the wave-plate was

taken out the beam,

For laser pulses of terawatt ievel, the nonlinear ef5ects (Le., self-focusing and self-

phase-modulation) in air and in optical elements in the beam path become non-negligible.

These eflects would not ody broaden the laser pulse width, but also cause severe beam

distortion and breakup, producing hot spots within the laser beam which can seriously

damage the optical components in the laser system [Ils]. A conventionally used

critenon for these nonlinear effects is the B integral, which is defmed as

where 31 is the optical Kerr coefficient, and I is the iaser intensity in the media.

Generally speaking, a value of B S 3 - 5 is required to avoid serious nonlinear damage

and distortion effects in a conventional high-power system; in a CPA system the

condition is more stringent-B S 1 - 2. In order to reduce the B integral in the T3

system, the cornpressor and the following optical path are ai i operated under vacuum. In

addition, we found in our expenment that the transmissive media, such as the doubling

crystal, quartz wave-plate, and the BG39 glass filter, produced large enough B integrai

that significant beam breakup was observed at full laser power. For this reason, the laser

energy was limited to below 500 mJ for the green pulse (or 1 J for the IR pulse) in most

parts of the experiment.

5.2 Experimental Setup for the Harmonic Measmement

Figure 5.1 also shows a schematic diagram of the expenmental setup for

Chapter 5 &verintenta2 Results of Mid-Order Hannonic Generation 96

measuring the harmonic spectra. The apparatus consists of a 75-cm diameter cylindrical

target chamber and a 1-m focal length VUV spectrometer.

5.2.1 The Target Chamber

Inside the target chamber, a f73.0 off-axis (15') parabolic rnirror of 23-cm focal

length was used to focus the 43-mm diameter laser beam ont0 the solid target at an

incident angle of 60" to the target normal. Ray-tracing simulation Cl161 showed that the

size of the focal spot produced by a parabola was very sensitive to misalignment of the

incident bearn. Before the target was moved into place, the focusing properties of the off-

axis parabola were investigated using the IO-Hz repn-ampmed and frequency-doubled

green beam. The spatial intensity distribution in the focal plane was measured by a 10x

microscope objective and a CCD camera. By carefully adjusting the direction of the

incident beam into the parabola, a Gaussian-shaped focal spot of @ = 9 pm (FWHM) was

obtained. Taking into account the effect of incident angle Bi (60'). the actual area of the

spot on target c m be caiculated as A = 1r@~/(4cos ei) = 127 @ at m.

The laser beam was tightly focused and the confocal parameter was estimated to

be around 200 p at the focus. When the power amplifiers were fired, it was found that

the best focal position determined using the regen beam would shift, presumably due to

thermal lensing effect in the power amplifier chah. In order to compensate this focus

shift and to optimize the laser intensity at the interaction region, a focal scan was needed

before each series of hmon ic experiment For this purpose, a x-ray PIN-diode was

installed inside the target chamber to monitor the x-ray radiation from the laser-produced

plasma. To prevent hot electrons generated in the plasma source from reaching and

thereby saturating the diode, a pair of magnets were used in the path between the

radiation source and the PIN-diode. By shooting the target, and at the same time

scanning the parabolic rnirror dong the focal axis (see Figure 5.1). a focal position

correspondhg to maximum x-ray generation could be conveniently located. This method

Chapter 5 Experimental Resulfs of Mid-Order Hamonic Generution 97

proved to be very effective in b ~ g i n g the target to a position close to the best focus;

harmonic generation could then be easily optimized by scanning the target near this

position. The typical focal range in which hannonic could be observed was - 1 mm,

which was about 5 times of the confocal parameter of the laser focus.

As in the SHG experiment described in Chapter 4, the fiat solid targets were

mounted on a remotely controlled 3-axis transIation stage. After each laser shot, the

target was translated by a certain amount dong the target plane so that a fresh surface

would be avaiIabIe for the next shot. A telescope and a TV camera located outside the

vacuum chamber (not shown in Figure 5.1) were employed to monitor the target

condition and to guide the motion of the target positioner.

5.2.2 The VUV Spectrometer

The radiation from the plasma source was collected dong the specuiar direction of

the incident laser light by a V W spectrometer in which the harmonic spectra were

analyzed. The spectrometer used in this experiment was a l -m Seya-Namioka type VUV

spectrometer [117] (McPherson, Mode1 23 1), which was connected directly to the target

chamber. The spectrometer was slit-less-its entrance slit was served by the laser focal

spot on target (see Figure 5.1). Owing to the Iack of an entrance slit, this spectrometer

could collect light from a large solid angle and therefore had good detection efficiency.

To obtain the best spectral resolution, the laser focal spot was carefuliy positioned on the

Rowland circle of the spectrometer. At the exit image plane of the spectrometer, a

microchamel-plate (MCP) intensifier (Galileo) was used to ampli@ and convert the VUV

radiation into a visible signal. Outside the vacuum chamber, the visible output of the

MCP intensifier was coupled by a commercial SLR-camera lens to a 12-bits CCD camera

(Photometncs), and the spectral images were coiiected and analyzed by a personal

computer.

The V W spectrometer was equipped with a curved ( R = 1 m) 1200-lines/rnm

Chapter 5 Experimental Results of Mid-Order Hannonic Generation 98

gold-coated grating, which was blazed at 800 A. The first-order spectnim was used for

this experiment. In the spectral region of interest (300 A - 2000 A), this grating yields a

plate factor, defmed as the reciprocal of the linear dispersion, of F = 7.2 A/mm at the

exit image plane of the spectrometer. This results in an effective spectral window of

D x F = 300 A for each single-shot measurement, where D = 40 mm is the diameter of

the MCP detector. To cover different parts of the harmonic spectmm, this spectral

window c m be centered at different wavelengths, A,, by rotating the grating. It should

be noted that the plate factor is not a constant, but varies as a slow function of A, [117]:

This rneans that the linear dispersion will change slightly when the grating is rotated to

cover a different spectral region. So, in the final data analysis, when to convert the

spectral scale from pixels to A, different conversion factors (calculated using Eq. 5.1)

were used for the spectra rneasured at different center wavelengths Ac. The overall

spectral response of the system (the spectrometer grating and the MCP detector) is

sensitive in the spectral region of 300 A to 2000 A, which covers the 3rd to 17th

harmonic of the 526-nm input laser.

The VUV spectrometer and the target chamber were pumped independently by

two turbo-molecular pumps. A horizontally positioned differential-pumping slit (- 1-cm

wide and 1-mm high) was used to isolate the spectrometer vacuum from the target

chamber vacuum. The target chamber, which was ais0 connected directly to the

evacuated beam iine, had a base pressure of about 1 x 10-5 Torr, whiie the pressure inside

the spectrometer was maintained below 2 x l w Torr-safe for the operation of the MCP

intensifier.

Chnpter 5 Ekperimental Results of Mid-Order Harmonic Generation

53 R d t s of Mid-Order Harmonic Generation

5.3.1 Observation of the Third to Seventh Harmonies

When we irradiated flat solid targets with p-polarized high-contrast green laser

pulses and increased the laser intensity to above 5 x 1016 W/cm*, we started to observe

third and higher order hannonics. The recorded spectra were the-integrated, which

plasma background

\ i detector background ,

pixel number

Figure 5.2. (a) An example of raw data recorded by the CCD-

camera showing the third harmonic generated when solid Ni target

was irradiated with the 526-nm laser light. (b) Lineout of the

spectnim by averaging over box L indicated in (a).

Chapter 5 Qen'mental Results of Mid-Order Hannonie Generution 100

meant we could not distinguish the picosecond harrnonic emission from the nanosecond

plasma line emission. As a result, the harmonic spectra were accompanied by a broad

plasma background, presurnably due to recombination. Figure 5.2(a) illustrates an

example of raw data recorded by the CCD camera, showing the third harmonic spectnim

from a nickel target. The narrow 3 0 feature can be observed sining on top of the broad

plasma background (Figure 5.2(b)). The off-spectnim detector-background was due to

the thermal noise in the CCD camera, and was removed in the post-experirnent data

analysis.

Due to the limited spectrai range of the spectrometer, severai shots viewing

different parts of the spectnim were needed in order to cover the spectral range between

600 A and 2000 A, and compose a complete harmonic spectra in this range. Figure 5.3

shows a typicai time-integrated harmonic composite-spectrum recorded from a silicon

target (polished silicon wafer) irradiated in p-polarization at a laser intensity of 3.2 x 1 OI7

W/cm2. Hannonics from 3rd to 7th, of both odd and even orden, can be easily identified

sitting on top of the broad plasma recombination background.

Besides the silicon target, several other solid targets of various atomic-numbers

were also snidied in this experiment. The targets included beryilium, nickel, CH plastic

(Parylene-N) coating on glass substrates, and silicon wafers covered with vacuum-

evaporated duminum and gold coatings. Spectra measured from al1 these targets

exhibited similar features to spectra from the siiicon target, and harmonies from 3 0 to 6 0

were observed in each case except for the gold target, fiom which the highest harmonic

recorded was 5 0 (Figure 5.4). In addition, the broad plasma recombination background

was found to be more pronounced with high-Z targets, which was expected.

Chapter 5 Ekperimental Results of Mid-Order Hannonic Generation

wavelength (A)

Figure 5.3. Typical harmonic spectrum from a Si target at a laser intensity of 3.2 x 1017 W/cm2. The spectrum is composed of four separate laser shots with spectrometer set at different central wavelengths. The spectral lines at 8 13 A and 980 A are from plasma line emissions.

Chapter 5 Experimental Results of Mid-Order Hamonic Generation

(b) berylIium, 1 = 1.3 x 10" w/cm2 7 0 0 , I ~ l I , I , I

30

400

300

200-

(c) nickel, 1 = 3.4 x 1017 w/cmZ 5 0 0 - 1 1 1 1 1 1 1 1 1 t ,

- 6 0 50 4 0 30 -

(d) gold, I = 3.3 x 10" w/cm2 I

Figure 5.4. Harmonic spectra produced from materials of different atomic-

numbers (Z). The broad background underneath the harmonic lines is due to fluorescence

foliowing plasma recornbination. Note that the laser intensity in (b) is three-times higher

than that in other plots.

Chupter 5 Experimental Results of Mid-Order Hamonic Generation

5-32 Dependence on Laser Polarization

Using s- and p-polarized laser bearns, experiments were also carrïed out to study

the laser-polarization dependence of the harmonic generation process. The polarization

of the laser beam was changed by rotating the half-wave plate located after the doubling

crystal. A solid 100-p thick berylliurn target was used for this experiment. At a laser

intensity of 1 x 10'8 W/cd, we measured the third-harmonic generation with s- and p-

polarized incident laser pulses. The result, as shown in Figure 5.5, exhibits clear

differences for these two cases: for p-polarized irradiation, strong 3 0 signal was observed

with S N (signal-to-noise ratio) near 30; for s-polarized irradiation, no 3 0 signal was

observed at di.

It should be noted that in our current experimental setup, the harmonic output was

not polarization-analyzed, except by the intrinsic difference in reflectivity of the

" 1650 1700 1750 1800 1850 1900

wavelength (A)

Figure 55 . 3 0 spectra from beryllium target produced by p-polarized (solid

iine) and s-polarized (dashed line) incident laser pulses at an intensity of 1 x 1018 W/cm2. No 3 0 signal was observed when the incident laser was s-polarized.

Chapter 5 Experintental Results of Mid-Order Hannonic Grnerurion 104

spectrometer grating for s- and p-polarized light (the grating efficiency q is normally

lower for s-polarization than for p-polarization). Therefore we cannot draw defmitive

conclusions about the polarization of the hannonics generated and make a complete

cornparison between our experimental results and the theoretical polarization selection

d e discussed in 5 2.2-6.

However, we can constmct a qualitative analysis of the data based on some

reasonable assumptions. By assurning that a p-polaïzed pump laser aiways produces p-

polarized harmonies (8 2.2.6), and that the grating effkiency of the spectrometer is 3-

times greater for p-polarization than for s-polarization, the following c m be concluded

fiom our measured result: the p-polarized 3 0 yield due to s-polarized pump ( s + p) is

no more than 3% (1/30) of that produced with p-polarized pump (p + p); the s-

polarized 3 0 yield with s-polarized pump (s + s ) is less than 10% (3/30) of p-polarized

harmonic from p-polarized irradiation ( p + p). This experimentally observed

polarization selection rule for the third harmonic is summarized in Table 5.1.

Table 5.1. Measured polarization selection rule for the

third-harmonic generation in plasma.

3w polarization

* Assurning grating efficiency qp > 3r7, .

Chapter 5 Experimental Results of Mid-Order Hamonic Genernrion

53.3 Anguiar Distribution of the Harmonies

The same method described in 5 4.3.2 was used here to measure the angular

distribution of the mid-order harmonic emission (see Figure 4.3). By changing the

incident angle from 60' to 63', the angular distributions of the third and fourth hannonics

from the aluminum target were inferred, at an intensity of 1 x 10" W/cmZ. Again, we

assumed the effect of incident angle on harmonic generation was negligible because of

the smail angle change (maximum 3' in this measurement). Figure 5.6 shows the relative

intensities of 3 0 and 4 0 as a hinction of the observation angle. For comparîson, the laser

profile (assumed a Gaussian far-field shape with 10' FWHM) is also plotted. It shows that

the harmonies are distributed well within the laser cone-angle, in the specular direction,

with the 4 0 distribution slightly narrower than that of the 30, Le., es, = 5.3' f O S " , and

04" = 3.8' f 0.5".

8 (degree) obs

Figure 5.6. Angular distribution of the third (solid line) and fourth (dashed

line) harmonic signals measured from an Al target under laser irradiame of 1 x 1017 W/cm2. The laser profde is also plotted (dot-dash line).

Chapter 5 Experiimental Results of Mid-Order Harmonic Generarion 106

According to the perturbation theory of harmonic generation, one expects the

angular width of the n th harmonic to decrease as l/&, which means that the ratio of the

4 0 angular width to that of 3 0 should be J3/4 = 0.87. Comparing to this, Our

measurement resuits yield a ratio of 04m/03a> = 0.7 f 0.1, which is slightly lower than

the perturbation mediction. We also noticed that the experimentd error in this

measurement was too large that a refined experiment would be necessary to allow a

quantitative cornparison with the theoretical models.

5.4 Harmonic Generation with Controlled Prepulses

In 5 2.3.3, we discussed the possibility of using a deliberate prepulse to study

harmonic generation from plasmas of varying density scale-lengths. It is generally

believed that the effïciency of harmonic generation depends strongly on the gradient of

the plasma density profüe. Qualitative analysis, as well as recent PIC simulations, show

that there should be a optimum plasma scale-length around A (laser wavelength) where

harmonic generation is most efficient. Keeping this in mind, we performed an

expenment on third hamionic generation by adding a smaU prepulse at a controllable

time. This experiment is similar to the one performed on SHG (5 4.4), except with

improved control of the prepulse.


After the cornpressor, a smali portion (20%) of the infrared laser pulse was split

off, frequency-doubled in a siniilar KD*P crystal to the one descnbed in Q 5.1, and then

made to CO-propagate with the infrared pulse. The relative timing between the IR pulse

and the orthogondly polarized green pulse could be continuously adjusted with an

accuracy of il00 fs. as detemiined in another pump-probe experiment Cl181 in which

frequency-domain interferometry was used. The dual pulses then propagated dong the

Chupter 5 Eiperimentnl Results of Mid-Order Humonic Generatiun 107

beam-line into the harrnonic setup. Passing through the KD*P crystal shown in

Figure 5.1, the resulting two green pulses (the main pulse and the weak prepulse) were

sent to the target charnber and focused ont0 the target.

The intensity of the prepulse was controiied by an adjustable iris which, by

limiting the beam diameter, not only cut d o m the prepulse energy but also produced a

larger focal spot in the far-field distribution on target. The latter ensured that the

expanding preplasma would have a large aspect ratio and so would stay in one-

dimensional; it also made the spatial overlapping of the two pulses at focus easier. In

this experiment, the main pulse intensity was 5 x 1017 W/cm2, and the prepulse intensity

was set to be around 2.5 x 1016 W/cm2, which is about 5% of that of the main pulse.


Figure 5.7 shows 3w yield collected in the specular direction from a silicon target,

as the delay between the main pulse and the smali prepulse was increased. It can be seen

that the harrnonic efficiency starts to decrease once the prepulse moves ahead of the main

pulse, and it drops quickly by two orders of magnitude as the prepulse arrives 3 ps ahead

of the main pulse. There is an apparent 1.5-ps difference between time zero and the time

when the 3 0 yield starts to decrease-the prepulse seerns to arrive 1.5 ps earlier. One

possible explanation for this is that the leaûing edge of the 350-fs main pulse srarts to

produce pre-plasma before t = O. This, however, is not enough to explain the observed

1.5-ps time difference, given the fact that 1.5 ps before its peak the Gaussian-shaped main

pulse intensity is merely at 1û-22 of the peak level. The dispersion of the green and IR

puises in the KD*P crystal cannot explain this apparent time difference either.

The 'zero time' in Figure 5.7 represents the nominal position where the two

pulses coincide. It was adopted from the measurement done in Ref. 11 181, on the

assumption that the timing between the two green pulses used in Our experiment

remained the same. We notice that the 1.5-ps time different corresponds to a spatial

Chapter 5 Experimental Results of Mid-Order Harmonic Grneration

- --

silicon, 30

z =35Ofs laser

Figure 5.7. 3 0 yield from silicon target as a function of prepulse timing. The harmonic conversion efficiency drops dramatically when the weak prepulse anives ahead of the main pulse ( t > O). The solid line is drawn for visual guidance. The dashed line at

t = O represents the 'nominal position' where the two pulses are temporally coincident (see discussion in the text).

Chupter 5 Experimental Results of Mid-Order Harmonic Generation 109

difference of ody 0.45 mm. Considering the long optical path lengths (over - 10 m) of

which the two green pulses had to travel before meeting on the target, it is conceivable

that a 0.45-mm error could be introduced by non-collinearity in the actual beam-path.

Based on this discussion, we speculate that the observed time mismatch was due to

experimental error, and a 1.5-ps correction is added to the nominal t h e delay in our later

data anaiysis.

Combining this experimental result with the hydrodynamic rnodeling of plasma

expansion discussed in $2.3.3, a sense of the dependence of third-harmonic efficiency on

the scale-length initially seen by a generating pulse can be inferred. For each delay-time

in Figure 5.7 (adjusted based on the new zero-tirne), the scale-length of the evolving

plasma was calculated based on the result of MEDUSA calculations (Figure 2.1 1). The

new correspondence is plotted in Figure 5.8, which shows that the harmonic eEciency

Figure 5.8. Efficiency of third-harmonic generation vs. normalized plasma

scale-length, f = LIA, which is calculated by MEDUSA-modeling. The solid Iuie

represents an exponential fit, which gives fo = 0.14.

Chapter 5 Experimental Results of Mid-Order Hannonic Generatiun 110

decreases exponentially with the plasma scaie-length. As the scale-length changes from

about 0.1 A to about 0.6 Â , the third-hannonic efficiency drops by almost two orders of

magnitude. Surprisingly, no harmonic enhancement by the prepulse was observed in this

experiment. Possible expianations for this wiil be discussed in $ 6.1.2.

5.5 Observation of Satellite Stwcture in the Mid-Harmonies

In resoiving the structure of h m o n i c lines at higher irradiances, we observed the

appearance of satellite Lines, both red- and blue-shifted, which appea. to have a regular

Stokes- and anti-Stokes-like structure. These lines appeared around each of the 3rd - 6th

hannonics, apparently simultaneously across harmonic orders, but appreciably after the

appearance of the hamonics themseIves. The threshold intensity of these satellites was

around mid-10'7 Wkm? The satellites were repeatable and spectraliy narrow; in a few

cases, the red-shifted satellite line was as intense as the harmonic h e itself (Figure 5.9).

Figure 5.9. Detailed spectrum of 3 0 fiom CH target. A red-shifted satellite

appears beside the hannonic line. I = 3 x 1017 W/cm2, Aa = 7.6 x 1013 rads.

Chapfer 5 Experimental Results of M W r d e r Hannonic Generation 11 1

As the irradiance was increased to 7 x IOi7 W/cm2, we observed the sequential

appearance of three such peaks: fmt a red-shifted peak, then a blue-shifted peak, then an

additional red-shifted peak, each stepped in frequency by the same increment Aw.

Figure 5.10 shows this evolution of satellite structure from a CH target as the laser

intensity was varied from 4.5 x 1016 to 6.8 x 1017 Wkm? The spectrum of forward-

scattered fundamental light was also measured, which showed sudden line-center

depletion and large broadening exactly upon the appearance of the satellite features in the

harmonies (Figure 5.1 1). We further tried to measured the backscattered fundamental

spectrum. However, to a sensitivity of 10-4 of incident intensity, no backscattered light

was detected in our experimental geometry.

We also observed that the satellite structure depended on the target position,

relative to the position for maximum harmonic yield. Figure 5.12 shows a typical focal

scan for 3 0 generation from a CH target irradiated at a laser intensity - 5 x 1017 W/cm2.

We cm see that the satellite structure was most apparent not at the best focus (x = O), but

instead at a position where the laser focus was 300 pm behind the target surface.

These satellite structures were observed for all the lower-Z materials that we

used-Be, CH, and Si-but were not seen, under any of our conditions, for the higher-Z

elements, Ni and Au. Initial analysis suggests that the frequency step Am between the

satellite lines may be weakly Z-dependent, with a possible 10% difference between Be

and Si. For CH targets (Z = 3 S), this shift was found to be Am = 7.6 x 1013 rads, which

is much lower comparing to the electron plasma frequency ope at critical density, i.e.,

op = 2 m / A = 3.6 x 1015 rad/s, where A = 526 nm is the incident laser wavelength. On

the other hand, Am is very close to the ion plasma frequency mpi for a M y ionized CH

plasma at critical density. Using Eq. 2.7 and the CH-plasma parameters Z = Z = 3.5 and

A = 6.5, we fmd 61, = 6.1 x 1013 rads. This shows that the observed frequency shift for

the satellite iine is about 1.2 times of the ion plasma frequency, Le., Aw = L 2mPi.

Chapter 5 Eiperimental Results of Mid-Order Hamonic Generation

Figure 5.10. Satellite structures Erom CH target recorded at different laser intensities.

Chapter 5 Experimentul Results of Mid-Order Harmonie Generation

wavelength (A)

5175 5200 5225 5250 5275 5300 5325 5350

Wavelength (A)

Figure 5.11. Comparison of spectral changes for forward-scattered fundamental spectra from a CH target recorded at different laser intensities. (a) Spectra in actual intensity scaie; (b) Spectra plotted at the same peak intensity (normalized) to emphasize spectral features.

Eqethental Results of Mid-Order Hamonic Generation 114

1650 1700 1750 1800 1850 1900

wavelength (A) Figure 5.12. 3 0 spectra from a CH target measured at different focal positions.

x = O represents the best focus. x i O corresponds to the case where laser-focus

is beyond the target surface. Same intensity scale is used for each speccnim.

To Our knowledge, these satellite features have not been observed in previous

harmonies experiments. Their exact physical ongin is still not clear for us. We notice,

however, that the frequency shifts for the satellites are very close to the ion plasma

frequency, which rnight suggest that the satellites are resulted from the participation of

the ion plasma wave, a non-quasineutrd mode of ion oscillation, excited near the critical

surface. In pursuing this interpretation, we will discuss several mechanisms in the

following chapter ($6.1.6). which. under our experimental conditions of ultraintense

laser interacting with a steep-gradient plasma, might result in non-quasineutrd plasmas in

the interaction region.

Chapter 5 Experhental Results of Mid-Order Hannonic Generation

5.6 Conclusions

In this chapter, an experimental snidy of mid-order harmonic generation from

laser and solid target interaction is described. Tirne-integrated forward spectra were

measured from various solid targets of different atomic numbers. Harmonies of both odd

and even order, and up to 7th were found. The harmonics featured strong laser-

polarization dependence, and narrow angular distribution around specuiar. Experiments

using controllable prepulses demonstrated a strong dependence of harmonic yield on the

scale-length of the preformed plasma, through the expected resonant enhancement of

harmonic generation by the prepulse was not observed. FinaUy, we observed, apparently

for the first time, a reguIar Stokes-like and anti-Stokes-Iike satellite features

accompan y ing the mid- harmonics . and measured their dependence on target materials as

welI as on laser intensity.

Chapter 6 Discussion and Conclusions

6.1 Sumrnary of the Experimental Results

We have presented an experimental study of harmonic generation from solid

targets illuminated by picosecond ultra-intense laser pulses. The experiments were

performed on two laser systems: the 1-TW FCM-CPA laser at the University of Toronto

and the 10-TW T3 laser at the University of Michigan, where high contrast (> 1010) 1-ps,

1.053-pm. and 0.35-ps, 0.526-pm laser pulses were used. Important features of harmonic

generation, Le., the anguiar distribution of hamionic ernission, dependences on Laser

polarization and on plasma scale-length, and the effects of preformed plasmas were

characterized [119, 1201. The main experirnental observations are summarized in the

following sections.

6.1.1 Effects of Preplasrna on Harmonic Generation

By comparing the second harmonic generated by a high contrast pulse and by a

pulse containing a fixed-fraction (IO4) prepulse, the effects of preformed plasma on

harmonic generation were inves tigated sys tematicdy . One of the preplasma effects we observed was the spreading of harmonic

emission over increasing soLid angles as the prepulse intensity was increased. When the

prepulse intensity reached 3 x 1012 WIcm2, we observed a nearly unifom angular

Chapter 6 Discussion and Conclusions 117

distribution of harmonic emission, in contrast to a sharp distribution dong the specular

direction when the prepulse was not present. We attnbute this effect to a non-fiat critical

surface induced by the pre-formed plasma. We also found the observed temporary

saturation of the hannonic yield coiiected in the specular direction could be explained

almost entirely by this effect of increasing harmonic emission angle.

Spatidly resolved spectra of the second harrnonic emission were measured with

clean pulses and with pulses containhg prepulses. In the clean-pulse case, second

harmonic was emitted from a source with small and smooth spatial and spectral

distributions; in the prepulse case, however, severe breakup of the fiarmonic source, both

spectraliy and spatidy, was observed. This breakup of the harmonic source was possibly

due to modifications to the incident laser pulse via self-phase modulation (frequency

modification) and filamentation (spatial modification) in the underdense part of the pre-

fonned plasmas.

Both of the wide (near 27c) harmonic emission angle and the breakup of h m o n i c

spectra have been noted previously in numbers of experiments [26,28]. The significance

of our experimental results is that it clearly demonstrated, for the f i s t tirne in a systematic

manner, that these effects were directly associated with the underdense preplasma rather

than caused during the generation of the hamonics at the critical surface.

6.1.2 Plasma Scale-length Dependence

In using very high contrast pulses to which we have added controlled prepulses,

we largely separated the contributions of nonlinear hydrodynamics and nonlinear optics

in the generation of laser-plasma harmonies, and systematicdy quantified the sensitivity

of harmonic generation efficiency to the gradient of preformed plasma. Two separate

experiments were camied out: the 2 0 experiment on the FCM-CPA laser, and the 3 0

experiment on the T3 laser, both using identical silicon targets. Although both

experiments demonstrated a strong dependence of harmonic conversion efficiency on the


scde-length of the plasma, different dependences were observed.

In the 2 0 experiment, a near 3-fold enhancement of harmonic conversion

efficiency was recorded around t = O, where the main pulse and the prepulse were

temporally overlapped. This observation agreed with one mode1 prediction that there

exists an optimum scale-length for maximum harmonic generation [37]. Since the

position of the resonant peak could not be determined precisely, due to a relatively large

experimental error in the temporal measurement (f3 ps), only a rough estimation could be

made- By assuming that the prepulse-created plasma expands at the typical ion-sound

speed of 0.1 p d p s , the optimum plasma scale-length for harmonic generation was

estimated as LIA 5 1.

In the 3 0 experiment, the harmonie-generation efficiency was found simply to

decrease exponentially with the plasma scale-length-no resonant enhancement was

observed.

There are several differences between these two experiments, including: the

prepulse intensity and focal-spot size, wavelength and duration of the high-intensity

pulse, and differences in collinearity of the two pulses (the 2w experiment used two

different pulse-lines). Each might have an effect on the relation of prepulse and main

pulse, and affect the enhancement feature.

An obvious distinction between the two cases is that the prepulse intensity used in

the 3 0 experiment was 2.5 x 1016 W/cm2, which was more than one order of magnitude

higher then that used in the 2 0 experiment (1.8 x 1015 Wkm*). A faster expansion speed

as the result of greater plasma temperature, may make it more difficult to resolve the

enhancement if, Say, it results from the production of a special scale-length.

An interesting prospect, too, is that in the 2 0 case, where enhancement was seen,

the prepulse was delivered with the polarization onhogonul to the main pulse. In this

case, the prepulse does not simply add its intensity to the pulse, but produces some

elliptically polarized pulse during the time the two overlap; this polarization distinction

Chupter 6 Discussion and Conclusions 119

was also present in a similar experiment performed by von der Linde et al. [107]. At

times far from overlap, the prepulse might simply deposit energy into the plasma, without

a significant coherent relationship to the main pulse. In the 3 0 case, for which harmonic

enhancement was not observed, the prepulse was deiivered with vimially identical

polarization as the main pulse. For gas-interaction harmonics, eilipticaliy polarized light

leads to great reduction in harmonic efficiency, but the reasons there do not apply in our

case.

The most clear-cut distinction is that there are well-recognized qualitative

differences in 2 0 and 3 0 production. More than one process, from both underdense and

critical regions, can lead to 2 0 harmonic generation, whereas 3w production more clearly

belongs in the same camp as mid- and high-order harmonics (for this reason, harmonic

experiments examining 3 0 are more significant in the study of the production of rnid- and

high-harmonies in laser-plasmas). Thus, it may be that the enhancement results fiom the

production of 2 0 from a distinct mechanism driven only as the two pulses ovedap in time

and space. This may, in fact, tie together with the different polarizations of prepulse and

fundamental, if it should happen that elliptically polarized light preferentially drives a

different second-harmonic generation mechanism.

6.1.3 Mid-Order Harmonic Generation on DEerent Solid Targets

Mid-order harmonic generation was studied using high-contrast pulses from the

T3 laser at intensities between 1017 and 1018 Wcm2. We observed up to the 7th

harmonic, both odd and even orders, in the time-integrated forward spectra for various

solid rnaterials, from beryllium to gold. Similar harmonic spectra were obtained from

these targets, showing harmonic line emission sitting on a broad plasma recombination

background. For targets of increasing atomic number 2, the h m o n i c yield appeared to

decrease slowly with 2, while the plasma recombination background increased with Z as

expected. Among the six target materials used in our experiment, the CH target (2 = 3.5)


produced the cleanest harmonic spectnim with best signal-to-background ratio.

6.1.4 Angular Distribution of Harmonic Emission

The angular distributions of the second and mid-order harmonics were measured.

At laser intensities up to 1 x 1017 W/cm2, we found the harmonics were distributed well

within the laser cone-angle, dong the direction of specular reflection. These results

agreed with the theoretical predictions of a harmonic generated from a flat critical

surface, indicating that neither 2-D effects associated with preformed plasmas nor nppled

critical surfaces due to Rayleigh-Taylor instability [56]-both assumed in the analysis of

a previous Iaser-solid harmonic experiment [26]-occurred under our experimental

conditions.

6.1.5 Laser Polarization Dependence

The laser-polarkation dependence in the 3 0 generation was studied at an oblique

incidence (0 = 60') and a laser intensity of 1 x 1018 W/cm2. We observed strong 3 0

signal (SIN = 30) with p-polarized laser, but no indication of 3 0 at all with s-polarized

laser. The interpretation of this result became compiicated because of the absence of a

polarization analyzer in our expenmental setup and the uncertain polarization response of

the spectrometer we used.

However, a partial conclusion c m still be made based on some reasonable

assumptions. By assuming that the grating efficiency for p-polarkation in our setup was

3-times that of s-polarization, we could conclude that the 3 0 yield generated by s-

polarized irradiation was no more than 10% of that produced by p-polarized pump, if it

were s-polarized, and would be even weaker (< 3%) if it was p-polarized.

Chapter 6 Discrcssion and Conclusions

6.1.6 First Observations of Harmonic Satellite Structures

Finaily, we reported what we befieved the first observations of regular Stokes-like

and anti-Stokes-like satellite features accompanying the mid-order hamonics. These

satellites were seen ody in low-Z materials (Be, CH, Si), and their frequency shifts were

found to be weakly 2-dependent. The measured laser-intensity dependence of the

structure showed a threshold intensity of - 3 x 1017 Wfcrn2 for the appearance of the

satellites.

The physical explanation for the satellites is still not quite clear for us, but several

useful observations c m be offered:

The frequency shift d o of the satellite was noted to be approximately the ion

plasma frequency oPi, which begins to suggest a Langmuir wave of ions, Le., an ion

electrostatic plasma wave ( 5 2.1.2). This raises the prospect that the satellites are due to

scattenng from ion plasma waves, which are excited near the critical surface in the

density gradient and oscillate at frequency opi .

An obvious difficulty with this notion is that typicdy one assumes the Debye

shielding of ion density fluctuations, at this density and temperature, will result only in

ion-acoustic oscillations, and not 'naked' ion electrostatic waves for which UDe >> 1

(see 5 2.1.2). Assuming the harmonic conversion and satellite generation processes take

place together around the cntical surface, we can estimate the value of kADe for a

homogeneous plasma of cntical density. Since ilDe = uDlhe/mpe and at critical density

o, = o = c k , we have kaD, = ut&, the ratio of the electron thermal speed to the

speed of light. For a typical laser-plasma of Te= 300 eV, we have v,h= 7x 108 cm/s,

and so kaDe= 0.02 cc 1, which is in the ion-acoustic regime, rather than the ion plasma

regime (see Figure 2.2).

Two considerations might account for this difierence.

First, within steep gradients, under intense irradiation, the plasma may not be

quasi-neutral, as the electrons may possibly be 'pushed off their ion background due to

Chaprer 6 Discussion and Conclusiom 122

the relativistic ponderomotive force, which becomes significant at laser intensities > mid

1017 Wlcmz. This displacernent c m effectively reduce the local electron density,

increasing the Debye length and therefore reducing the shielding of the ions by the

electrons. If the electrons are pushed into the gradient, then the ion plasma wave excited

near the new critical surface would be at somewhat larger density than in a quasi-neutral

plasma. and so mpi would be increased by the square root of the density increase factor.

This picture would represent the non-steady equivalent of hydrodynarnic steepening of

the cntical density surface by the ponderomotive force, fust quantified in CO2 laser-

plasma interaction [Il 11.

In this case, the density change might be grossly estimated from the scaie-length

of the density profile together with the distance 6x by which the electrons might be

pushed off the ions, roughly as:

The distance 6x might be found by equating the restoring force in a capacitor mode1 of

plasma charge-separation and the ponderomotive force from the incident light. From the

whole light-pressure at 1018 Wfcm2, a rough calculation suggests that a displacement 6'

on the order of 0.1 pm is possible-a value which is appreciable in cornparison with o u

anticipated scale-lengths (0.01 - 0.1 p). A displacement of a distance comparable to

the scale-length or greater cm produce very substantial modification of the local electron

density . Secondly, the Debye length AD, found above is calcdated for a homogeneous

plasma, which may not be an appropriate mode1 in a steep gradient and with Te z> Ti.

For that matter, if the excursion distance of the oscillating electrons is suffkiently

far, longer than a Debye length and an ion-plasma wavelength, it may be that the

shielding effect of the electrons is reduced by averaging quickly over the ion density

fluctuations. The electron plasma frequency is characteristic of the electron-density

Chapter 6 Discussion and Conctusions 223

response time following charge redistribution, and Debye shielding cornes from the

electron response to imposed electric fields (e.g., test charge). But in Our case a new

electric field (laser) is competing with this and should be able to make the electrons see

only the ion density averaged over an electron cycle, which could reduce the shielding of

ion oscillations if the electron oscillation amplitude is Iarge enough. In this case again, it

may arise that kAD, >> 1.

6.1.7 High-Contrast CPA Laser

Prior to these laser-plasma studies, a Iarge amount of the experimentai effort in

this research was spent on building and developing of the FCM-CPA laser system at the

University of Toronto [91,92], which was a significant technical challenge at the time of

its construction. This work, particularly the high-dynamic range characterization of CPA

laser pulses using the cross-correlation technique, was an important contribution in

highlighting the issue of laser contrast, which was not widely emphasized among groups

working on high-intensity laser-solid experiments in the early 1990's. Many people had

thought the ponderomotive force would 'repair' the plasma density gradient in the

interaction with solid, so contrast would not much matter. Between that laser-contrast

work and these prepulse harrnonic experiments, we have shown that this assertion was

not true-sontrast is an essential issue in laser-solid interactions.

6.2 Suggestions for Future Experiments

The experiments presented in this thesis cover many aspects of harmonic

generation in laser-plasma interaction. It will be seen that they represent the fmt step in a

new trend to quanw the interaction, to dissect it into parts, and to separately identiQ the

nonlinear optics of harmonic conversion as distinct from nonlinear hydrodynamics.

They are, however, far from complete, and some results were quite preliminary.

Chupter 6 Discwsion and Conclusions 124

There is still much to be explored in this new field, and certain steps in these directions

will help:

Harmonic ernissions are usually accompanied by a strong plasma

recombination background. This is especially the case when a high-Z target is used. In

order to increase the sensitivity for harmonir- detection, this background has to be

removed. The-resolved measurements (using a streak camera, for example) [23, 1121

should be used, to yield cleaner hannonic specua and therefore lower hannonic detection

thresholds.

The pump-probe experiment c m be improved in the following aspects. To

completely isolate the nonlinear hydrodynamics from the noniinear optics in the overall

production of harmonies, a different color probe pulse could be used. In addition, rather

than relying on hydrocode simulations, direct measurement of the plasma density profile

is feasible using methods such as frequency-domain interferometry [12 11. This method

has been demonstrated in a recent experiment where laser light absorption was measured

in plasmas of varying scale-lengths [122]. - In analyzing the pump-probe results, we have assumed that the harmonic

angular distribution rernains unchanged. It is, however, possible that the spreading of the

harmonic emission gets steadily worse with increasing prepulse delay. If this were bue,

the harmonic yield we measured was not the total yield, just as in the case of SHG by

uncontrotled prepulses. This open question could be answered by an experiment

measuring the angular spread of the hamonics for different prepulse delays.

We have observed different scale-length dependences for the generation of 2 0

and 30; the biggest difference is that no resonance enhancement was observed for 3 0 .

We have discussed in the last section that this might be for several different reasons.

Experimentaily, this could be clarified by repeating these measurements under identical

experimental conditions, Le., prepulse intensity and polarkation, fundamental laser

wavelength, etc. Along the same line, enhancement of 2 0 could be compared using two

Chapter 6 Discussion and Conclusions 125

different prepulse polarizations. This would determine whether the relative prepulse

polarization is physically signifkant.

Harmonic generation in plasma is seen to exhibit strong dependence on laser

polarization. A polarization selection d e has been suggested, based on theoretical

models ( 5 2.2.6), which is ready to be verifed through experiment. By studying this

selection d e , one may obtain valuable information about the rnechanism by which the

harmonics are produced. The laser-polarization dependence of an odd-order hannonic

(3w) has been partially tested in this work. The same experiment could be extended to

study even harmonics, which, according to theoretical models, have a different

dependence on laser-polarization than odd harmonics. To have an unarnbiguous test, a

polarization analyzer should be added at the entrance of the spectrometer, and the

polarization response of the spectrometer should be weU characterized.

The effect cf incident angle on harmonic generation (also discussed in 1 2.2.6)

is another issue not examined by the work presented here, but it wouid be interesting to

study. Since, for a specular harmonie emission, the reflection direction changes with the

incident angle, a different harmonic-collecting scheme would have to be used, in which

the direction of at Ieast one of the incident or reflected beams could be freely rotated

about the laser focus. In our current setup, both of these directions are fixed.

Finally, the physical origins of the first observed harmonic satellites are still

not clear. Obviously this is a very interesting subject deserving further studies.

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