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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
5.4.1 Prepulse Setup
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
Chapter 2 Theoretical Background 12
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
Chapter 2 Theoretical Background 24
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
Chapter 2 Theoretical Background 15
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
Chapter 2 Theoretical Background 16
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.
Chapter 2 Theoretical Background 17
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.
Chapter 2 Theoretical Background
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.
Chapter 2 Theoretical Background 19
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
Chapter 2 Theoretical Background 20
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.
Chapter 2 Theoretical Background
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
Chapter 2 Theoretical Background
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
Chapter 2 Theoretical Background 25
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.
Chapter 2 Theoretical Background 27
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.
Chapter 2 Theoretical Background 28
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].
Chapter 2 Theoretical Background 29
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 -
Chapter 2 Theoretical Background
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 - -
Chupter 2 Theoretical Background 33
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)).
Chapter 2 Theoretical Background 34
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.
Chapter 2 Theoretical Background 35
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
Chapter 2 Theoretical Background 36
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.
Chapter 2 Theoretical Background 38
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
Chupter 2 Theoretical Background 40
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?
Chapter 2 Theoretical Background 41
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-
Chapter 2 Theoretical Background 42
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
Chapter 2 Theoretical Background
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
Chapter 3 Development of the Toronto FCM-CPA Laser System
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
Chapter 3 Development of the Toronto FCM-CPA Laser System 49
- - -- -
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
Chapter 3 Development of the Toronto FCM-CPA Laser System 50
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.
Chapter 3 Development of the Toronto FCM-CPA Laser System
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.
Chapter 3 Development of the Toronto FCM-CPA Laser System 53
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
Chapter 3 Development of the Toronto FCM-CPA Laser System 57
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
Chapter 3 Development of the Toronto FCM-CPA Laser System
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.
3.4.2 Experimental Results
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.
Chapter 3 Development of the Toronto FCM-CPA Laser System 69
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.
4.4.1 Prepulse Setup
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).
4.4.2 Experimental Results
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.
5.4.1 Prepulse Setup
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.
5.4.2 Experimental Results
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
Chapter 6 Discussion and Conclusions
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)
Chapter 6 Discussion and Conclusions
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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