THz pulse generation and detection

Goals:

• Explain why THz pulses are “useful”• Explain conceptually some common

methods to generate THz pulses• Photoconductive switches• Rectification

• Explain some common methods for phase-sensitive THz detection

Ultrafast Laser Physics

More in-depth courses (in case you want more):

1) Modern Topics in THz Science (Fall semesters)

2) Ultrafast Methods in Solid State Physics (Spring semesters)

Y.-S. Lee, Principles of Terahertz Science and Technology

Decent general reference:

Chapter 1Terahertz Radiation

Introduction to THz Radiation

Various frequencies are spaced along the frequently used electromagnetic spectrum,including microwaves, infrared radiations, visible lights, and X-rays. Between themicrowave and infrared frequencies lies terahertz (THz) radiation (Fig1.1). In theelectromagnetic spectrum, radiation at 1 THz has a period of 1 ps, a wavelength of300 µm, a wave number of 33 cm–1, a photon energy of 4.1 meV, and an equivalenttemperature of 47.6 K. In the same way that visible light can create a photograph,radio waves can transmit sound, and X-rays can see shapes within the human body,terahertz waves (also called as T-rays) can create pictures and transmit information.

103 106 109 1012 1015 1018 1021 1024100

microwaves visible

kilo mega giga tera peta exa zetta yotta

x-ray g -ray

THz GapElectronics industry Photonics industry

Hz

Frequency (Hz)

dc

Waveguide Lens and mirror Classical transport Quantum transition

Fig. 1.1 The electromagnetic spectrum. The development of efficient emitters and detectors withineach of the spectral regimes has resulted in the birth of numerous industries. The search forpotential applications using THz radiation is steadily intensifying as materials research providesimproved sources and detectors

Plenty of THz radiation sources surround us, from cosmic background radia-tion to blackbody radiation from room temperature objects (Fig.1.2). Most of thoseTHz sources are incoherent and can hardly be utilized. Until recently, however, thevery large THz portion of the spectrum has not been particularly useful becausethere were neither suitable emitters to send out controlled THz signals nor efficientsensors to collect them and record information. As a result, the THz portion of

1X.-C. Zhang, J. Xu, Introduction to THz Wave Photonics,DOI 10.1007/978-1-4419-0978-7_1, C⃝ Springer Science+Business Media, LLC 2010

2 1 Introduction

will also be used when they are appropriate. Frequently used units and theirconversions at 1 THz are as follows:

• Frequency: ∫ = 1 THz = 1000 GHz• Angular frequency: ! = 2º∫ = 6.28 THz• Period: ø = 1/∫ = 1 ps• Wavelength: ∏ = c/∫ = 0.3 mm = 300 µm• Wavenumber: k = k/2º = 1/∏ = 33.3 cm°1

• Photon energy: h∫ = h! = 4.14 meV• Temperature: T = h∫/kB = 48 K

where c is the speed of light in vacuum, h is Plank’s constant, and kB isBoltzmann’s constant. Physicists tend to use µm and meV as units of photonwavelength and energy, respectively; chemists use cm°1 as a unit of wavenum-ber; engineers use mm and GHz as units of wavelength and frequency, respec-tively. In physics, angular wavenumber (k = 2º/∏) is usually abbreviated aswavenumber. In this book, we will use the abbreviated notation when it isclearly defined.

Fig. 1.1. Terahertz band in the electromagnetic spectrum

The THz band does not have a standard definition yet. Commonly useddefinitions are included in the spectral region between 0.1 and 30 THz. Therange of 10-30 THz, however, exceeds the far-IR band and intrudes on the mid-IR band, where well established optical technologies exist. Unless we deal with

2 1 Introduction

will also be used when they are appropriate. Frequently used units and theirconversions at 1 THz are as follows:

• Frequency: ∫ = 1 THz = 1000 GHz• Angular frequency: ! = 2º∫ = 6.28 THz• Period: ø = 1/∫ = 1 ps• Wavelength: ∏ = c/∫ = 0.3 mm = 300 µm• Wavenumber: k = k/2º = 1/∏ = 33.3 cm°1

• Photon energy: h∫ = h! = 4.14 meV• Temperature: T = h∫/kB = 48 K

where c is the speed of light in vacuum, h is Plank’s constant, and kB isBoltzmann’s constant. Physicists tend to use µm and meV as units of photonwavelength and energy, respectively; chemists use cm°1 as a unit of wavenum-ber; engineers use mm and GHz as units of wavelength and frequency, respec-tively. In physics, angular wavenumber (k = 2º/∏) is usually abbreviated aswavenumber. In this book, we will use the abbreviated notation when it isclearly defined.

Fig. 1.1. Terahertz band in the electromagnetic spectrum

The THz band does not have a standard definition yet. Commonly useddefinitions are included in the spectral region between 0.1 and 30 THz. Therange of 10-30 THz, however, exceeds the far-IR band and intrudes on the mid-IR band, where well established optical technologies exist. Unless we deal with

1.2 Terahertz Generation and Detection 3

ultrabroadband THz pulses, we will use 0.1-10 THz as a universal definitionof the THz band. Figure 1.1 illustrates the THz band in the electromagneticspectrum. The THz band merges into neighboring spectral bands such asthe millimeter-wave band, which is the highest radio frequency band knownas Extremely High Frequency (EHF), the submillimeter-wave band, and thefar-IR band. The definitions of these bands are as follows:

• Millimeter wave (MMW): 1-10 mm, 30-300 GHz, 0.03-0.3 THz• Submillimeter wave (SMMW): 0.1-1 mm, 0.3-0.3 THz• Far infrared radiation (Far-IR): (25-40) to (200-350) µm, (0.86-1.5) to (7.5

to 12) THz• Sub-THz radiation: 0.1-1 THz

These bands are also distinguished by their characteristic technologies. Mil-limeter wave emitters and sensors are solid-state devices based on microwavetechnologies. Traditionally, far-IR applications rely on optical and thermaldevices.

1.2 Terahertz Generation and Detection

Technological advances in optics and electronics have resulted in many dif-ferent types of THz sources and sensors. Chapters 3 and 4 are devoted tobroadband and continuous-wave (CW) THz technologies, which are classifiedby similarities in radiation characteristics. In this section, we make brief de-scriptions of the schemes used for THz generation and detection, grouped byoperational concepts.

1.2.1 Terahertz Sources

c(2)

c(2)

!"#$%&"'%() *+&",-./*&" (%(*0("+,-',1&$+*

)0%)"#0',%2+3"

%.$0'+*-4"+$

4,%+)4+()-567-,+)0$+0%(

89-567-,+)0+$0%(

89-567-,+)0+$0%(

(%(*0("+,-',1&$+*

:.$0'+*;"'$0!0'+$0%(

<0!!","('"=,">/"('1?"(",+$0%(

=,">/"('1@/*$0.*0'+$0%(-%!

=,">/"('1<%2(8%(3",&0%(

=,">/"('1A.

B/*&")

89

@/*$0.*0'+$0%(-%!@0',%2+3"&A.8%(3",&0%(

Fig. 1.2. Terahertz generation in nonlinear media

Other names….

THz interactions: atoms

Low values of n: transitions frozen out for low fields

n ~ 50: level spacing matches for 1 THzh⌫

Two main possibilities:1) Tunnel ionization (high field limit)

E ⇠ Ea ⇡ 5⇥ 109V/cm

THz interactions: atoms

Low values of n: transitions frozen out for low fields

n ~ 50: level spacing matches for 1 THzh⌫

Two main possibilities:2) Rydberg state transitions

big dipole moments

long lifetimes (microseconds)

Crystals: vibrational excitations

44 2 Basic Theories of Terahertz Interaction with Matter

ad

. . .. . .

nu ,-

naan )1( - an )1( +

1k2k

-m +m

nu ,+

Fig. 2.21. Harmonic model for a one-dimensional lattice with two ions in a unitcell. a: lattice constant, m±: masses of the ions, u±,n: displacements of the ions fromequilibrium positions at nth unit cell, ∑1,2: spring constants

We consider a one-dimensional lattice with two species of ions to describethe normal modes, and discuss how they interact with external electromag-netic waves. Figure 2.21 illustrates the harmonic model for a one-dimensionalionic crystal. It is convenient to assume that (i) the number of unit cells inthe system, N, is large, yet finite, and (ii) the displacements of the ions satisfythe periodic boundary condition, u

1

= uN . The equations of motion at thenth unit cell are written as

m+

u+,n = °∑

1

(u+,n ° u°,n)° ∑

2

(u+,n ° u°,n°1

),m°u°,n = °∑

1

(u°,n ° u+,n)° ∑

2

(u°,n ° u+,n+1

), (2.179)

where m± are the masses of the ions, and u±,n are the displacements of theions from equilibrium positions at nth unit cell. A normal mode solution withangular frequency ! and wavenumber k has the form

u+,n = u

+

ei(kna°!t),

u°,n = u°ei(kna°!t). (2.180)

Inserting Eq. 2.180 into Eq. 2.179 we obtain two coupled equations,£

m+

!2 ° (∑1

+ ∑2

)§

u+

+£

∑1

+ ∑2

e°ika§

u° = 0,£

∑1

+ ∑2

eika§

u+

+£

m°!2 ° (∑1

+ ∑2

)§

u° = 0. (2.181)

The solution of these equations requiresØ

Ø

Ø

Ø

m+

!2 ° (∑1

+ ∑2

) ∑1

+ ∑2

e°ika

∑1

+ ∑2

eika m°!2 ° (∑1

+ ∑2

)

Ø

Ø

Ø

Ø

= 0, (2.182)

which leads to the dispersion relation,

!2 =∑

1

+ ∑2

2µr

"

1±

s

1° 8µr∑1

∑2

µc(∑1

+ ∑2

)2(1° cos ka)

#

(2.183)

with the reduced mass, µr = m+

m°/(m+

+ m°), and the total mass, µc =m

+

+m°. The dispersion relation is defined in a reciprocal unit cell, °º/a <

2.2 Terahertz Radiation and Elementary Excitations 45

)(kw

optical branch

acoustic branch

ck=w

ap-

ap k

Fig. 2.22. Dispersion relation for a one-dimensional ionic crystal. The upper andlower curves are optical and acoustic branches, respectively.

k < º/a as shown in Fig. 2.22. The two curves are referred to as the optical

branch and the acoustic branch.Analyzing the dynamics of lattice vibrations in the long wavelength limit

helps us to understand how normal modes interact with external electromag-netic fields and where the branch names come from. In the limit of k ø º/a,the dispersion relation is approximated as

! ª=r

∑1

+ ∑2

µr: optical branch, (2.184)

! ª=r

∑1

∑2

µc(∑1

+ ∑2

)(ka) : acoustic branch. (2.185)

The frequency of an optical mode depends on the reduced mass, but not thetotal mass; the opposite is true for the acoustic mode. This is because opticalmodes are associated with relative motions between two ions, while acous-tic modes are associated with center-of-mass motions (Fig. 2.23). Acousticmodes of long wavelength are responsible for sound propagation in media.The linear dispersion relation is a characteristic of sound waves, of which thevelocity is constant. Now imagine that an electromagnetic wave with polariza-tion parallel to the lattice axis is applied to the ionic crystal. Because the ionshave opposite charges, the field exerts only relative motion. Therefore, theelectromagnetic wave can only interact with optical modes. The light-matter

Optical mode Acoustic mode

Fig. 2.23. Optical and acoustic modes are associated with relative and center-of-mass motions of the ions, respectively.

Light-Induced Superconductivity in aStripe-Ordered CuprateD. Fausti,1,2*†‡ R. I. Tobey,2†§ N. Dean,1,2 S. Kaiser,1 A. Dienst,2 M. C. Hoffmann,1 S. Pyon,3

T. Takayama,3 H. Takagi,3,4 A. Cavalleri1,2*

One of the most intriguing features of some high-temperature cuprate superconductors is theinterplay between one-dimensional “striped” spin order and charge order, and superconductivity.We used mid-infrared femtosecond pulses to transform one such stripe-ordered compound,nonsuperconducting La1.675Eu0.2Sr0.125CuO4, into a transient three-dimensional superconductor.The emergence of coherent interlayer transport was evidenced by the prompt appearance of aJosephson plasma resonance in the c-axis optical properties. An upper limit for the time scaleneeded to form the superconducting phase is estimated to be 1 to 2 picoseconds, which issignificantly faster than expected. This places stringent new constraints on our understanding ofstripe order and its relation to superconductivity.

High-temperature cuprate superconductorsare synthesized by chemically dopingthe parent compound, an antiferromag-

netic Mott insulator. An example of a parentcompound is La2CuO4, which turns into an un-conventional metal as holes are doped into itsCuO2 planes by substitution of La by Ba or Sr.La2-x(Ba/Sr)xCuO4 becomes superconductingfor x > 0.05, reaching the highest critical tem-peratures near x = 0.16. The x = 1/8 compounddeserves special attention, because it hosts one-dimensional (1D) modulations of charge andspin (1) and exhibits sharp reduction in criticaltemperature Tc (superconducting transition tem-perature). In the Ba-doped system, these “stripes”become static, enhanced by the buckled Cu-Oplanes in the so-called low-temperature tetrag-onal (LTT) phase (2, 3). Static stripes, LTTphases (4), and suppressed superconductivityare also detected in La1.48Nd0.4Sr0.12CuO4 (5, 6)and La1.675Eu0.2Sr0.125CuO4 (LESCO1/8) (7).Figure 1 shows a schematic phase diagram ofLa1.8-xEu0.2SrxCuO4, in which Tc is stronglyreduced in the stripe region, for all doping val-ues below x = 0.2 (8, 9).

The transition between a doped Mott insula-tor and a superconductor has long been at theheart of research into cuprate superconductivity.Virtually all studies have explored this transitionby changing static doping or by adiabaticallytuning an external parameter, such as pressure, to

demonstrate that superconductivity can be re-stored if the equilibrium crystallographic struc-ture is perturbed (10).

We dynamically perturbed the nonsuper-conducting LESCO1/8 with mid-infrared (mid-IR)radiation (11, 12), inducing superconductivity onthe ultrafast time scale. Optical excitation in thevisible or near-IR has been used in the past tostudy (13–18), and sometimes even enhance(19), superconductivity. However, in all thesecases, superconductivity could be achieved onlyafter the relaxation of hot incoherent carriers backto the ground state and was not triggered directlyby the light field.

Nonsuperconducting LESCO1/8, held at a basetemperature of 10 K, was excited with 15-mm–wavelength pulses (80 meV of photon energy),made resonant with an in-plane, near–600 cm−1,Cu-O stretch. The time-dependent intensity re-flectivity,R = Irefl/Iinc (refl, reflected; inc, incident),was measured in the near-IR (1.5 eV), a photonenergy at which the optical properties are indi-rectly related to the appearance of superconductivi-ty (20–22).Aprompt reflectivity change, remainingconstant up to the longest time delays probed(100 ps), was observed (Fig. 2). Photoexcitationwith the electric field polarized orthogonal to theplanes resulted in only a small reflectivity changeduring the pump pulse and no long-lived response.

The long-lived photoinduced state of LESCO1/8,can be shown to be superconducting by time-resolved terahertz spectroscopy. At equilibrium,superconductivity in cuprates is reflected in theappearance of a Josephson plasma resonance(JPR) in the c-axis terahertz optical properties.This is a general feature of cuprate supercon-ductors (23–25), well understood by noting that3D superconductivity in these compounds can beexplained by Josephson coupling between capac-itively coupled stacks of quasi-2D superconductinglayers (26). This effect is shown in Fig. 3A foroptimally doped La1.84Sr0.16CuO4. A plasma edgein the reflectance appears near 60 cm−1 when thetemperature is reduced below Tc = 38 K.

Figure 3C reports mid-IR pump, terahertzreflectance-probe measurements in nonsuper-conducting LESCO1/8. The equilibrium electricfield reflectance, as in other striped cuprates (27),

1Max Planck Research Department for Structural Dynamics,University of Hamburg–Centre for Free Electron Laser Science–Hamburg, Germany. 2Department of Physics, Clarendon Lab-oratory, University of Oxford, Oxford, UK. 3Department ofAdvanced Materials Science, University of Tokyo, Tokyo, Japan.4IKEN Advanced Science Institute, Hirosawa 2-1, Wako 351-0198, Japan.

*To whom correspondence should be addressed. E-mail:andrea.cavalleri@mpsd.cfel.de (A.C.); daniele.fausti@mpsd.cfel.de (D.F.)†These authors contributed equally to this work.‡Present address: University of Trieste, Trieste, Italy.§Present address: Physics Division, Brookhaven National Labo-ratory, Upton, NY, USA.

Fig. 1. Schematic phase diagram for La1.8-xEu0.2SrxCuO4. Superconductivity (yellow area) is quenched atall doping levels (gray area) below 0.2, emerging only at very low temperatures. At 0.125 doping, a static1Dmodulation of charges and spins, the stripe state, emerges in the planes. This stripe phase (left inset) isassociated with a LTT distortion, in which the oxygen octahedrals in the crystal are tilted (right inset). Thered dashed curve marks the boundary for superconductivity in compounds of the type La2-xSrxCuO4, inwhich the LTT structural modulation is less pronounced.

www.sciencemag.org SCIENCE VOL 331 14 JANUARY 2011 189

REPORTS

on

Febr

uary

16,

201

3w

ww

.sci

ence

mag

.org

Dow

nloa

ded

from

DOI: 10.1126/science.1197294, 189 (2011);331 Science

et al.D. FaustiLight-Induced Superconductivity in a Stripe-Ordered Cuprate

This copy is for your personal, non-commercial use only.

clicking here.colleagues, clients, or customers by , you can order high-quality copies for yourIf you wish to distribute this article to others

here.following the guidelines

can be obtained byPermission to republish or repurpose articles or portions of articles

): February 16, 2013 www.sciencemag.org (this information is current as of

The following resources related to this article are available online at

http://www.sciencemag.org/content/331/6014/189.full.htmlversion of this article at:

including high-resolution figures, can be found in the onlineUpdated information and services,

http://www.sciencemag.org/content/suppl/2011/01/12/331.6014.189.DC1.html can be found at: Supporting Online Material

http://www.sciencemag.org/content/331/6014/189.full.html#ref-list-1, 3 of which can be accessed free:cites 35 articlesThis article

http://www.sciencemag.org/cgi/collection/physicsPhysics

subject collections:This article appears in the following

registered trademark of AAAS. is aScience2011 by the American Association for the Advancement of Science; all rights reserved. The title

CopyrightAmerican Association for the Advancement of Science, 1200 New York Avenue NW, Washington, DC 20005. (print ISSN 0036-8075; online ISSN 1095-9203) is published weekly, except the last week in December, by theScience

on

Febr

uary

16,

201

3ww

w.sc

ienc

emag

.org

Down

load

ed fr

om

Collective Coherent Control: Synchronization of Polarization in Ferroelectric PbTiO3

by Shaped THz Fields

Tingting Qi,1 Young-Han Shin,1 Ka-Lo Yeh,2 Keith A. Nelson,2 and Andrew M. Rappe1

1The Makineni Theoretical Laboratories, Department of Chemistry, University of Pennsylvania,Philadelphia, Pennsylvania 19104–6323, USA

2Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA(Received 16 November 2008; published 19 June 2009)

We show that properly shaped terahertz (THz) fields can be used to move ions in ferroelectric crystals

from their positions in an initial domain orientation along well-defined collective microscopic paths into

the positions they occupy in a new domain orientation. Collective coherent control will enable direct

observation of fast highly nonlinear material responses and far-from-equilibrium structures that can be

harnessed in electro-optic devices and nonvolatile computer memory.

DOI: 10.1103/PhysRevLett.102.247603 PACS numbers: 77.80.Fm, 71.15.Pd, 77.84.Dy, 87.50.U!

Coherent optical control over ultrafast molecular behav-ior including chemical reactions has been explored inrecent years [1], spurred by the application of optimalcontrol theory and related methods [2,3] and by the devel-opment of femtosecond pulse shaping techniques [4–6]through which complex optical waveforms have beencrafted and optimized to induce specified molecular re-sponses. Here, we propose and model theoretically theextension of coherent control to collective structuralchange. We show through numerical simulations that tem-porally shaped THz fields can be used to induce ferroelec-tric domain switching with extensive control over thecollective microscopic pathway from initial to final struc-ture, in a coherent process that is very different from theconventional stepwise switching mechanism [7].

Perovskite ferroelectric crystals have simple collectivelattice vibrational modes that describe the microscopicpathways along which structural change occurs [seeFig. 1(a)]. For this reason, these crystals are prototypesfor the study of collective structural rearrangements, withmany modelling studies interrogating both static and dy-namic aspects of their phase transitions [8,9]. A particu-larly important aspect is domain switching, the process ofreorienting part or all of a domain so that its macroscopicpolarization points in a different direction. We and others[10–14] have sought to illuminate how microscopic inter-atomic interactions affect the rate and mechanism of fer-roelectric domain switching.

In the tetragonal phase of lead titanate (PbTiO3, PTO),the crystal has two domain orientations characterized byopposite polarization directions along the tetragonal axiswith symmetrically equivalent ground states separated byan energy barrier. The polarization direction can be re-versed under an electric field. This is exploited extensivelyin ferroelectric memory devices, so the dynamics of do-main switching have been of technological as well asfundamental interest. There is great experimental interestin rapid ferroelectric polarization switching under strong

electric fields, with most experimental approaches limitedto the thin film regime [7,15–17]. Most studies of polar-ization reversal focus on domain wall properties and dy-namics under the influence of an electric field that isapplied through electrodes at the sample surfaces[13,18,19]. Earlier attempts to control crystalline softmodes and phase transitions through impulsive stimulatedRaman scattering used nonresonant optical pulses withouttailored pulse profiles [20–22] and were based on simplemodels for the impulsively driven lattice vibrations and thecrystalline responses to them; so far, such attempts havefailed to find experimental validation because the highlight intensities needed to reach sufficient vibrational am-plitudes far exceed typical material damage thresholds.In contrast, here we explore the fundamental limit of the

polarization switching time of ferroelectric PTO under the

FIG. 1 (color online). (a) PTO unit cell in the tetragonalferroelectric phase, with a þz domain orientation. The softvibrational mode is indicated by the arrows on the ions.(b) Time-dependent lattice response to a single asymmetricTHz pulse (shown by a blue dashed line) with its large lobepolarized along the !z direction, i.e., ‘‘antiparallel’’ to the staticferroelectric polarization. The z-component Pz (shown by agreen solid line) oscillates about its static nonzero value as theTi and other ions oscillate about their lattice positions in the þzdomain. No significant responses of the other components Px

and Py (shown by a black dotted and a red dashed-dotted line,respectively) about their static values of zero are induced.

PRL 102, 247603 (2009) P HY S I CA L R EV I EW LE T T E R Sweek ending19 JUNE 2009

0031-9007=09=102(24)=247603(4) 247603-1 ! 2009 The American Physical Society

Collective Coherent Control: Synchronization of Polarization in Ferroelectric PbTiO3

by Shaped THz Fields

Tingting Qi,1 Young-Han Shin,1 Ka-Lo Yeh,2 Keith A. Nelson,2 and Andrew M. Rappe1

1The Makineni Theoretical Laboratories, Department of Chemistry, University of Pennsylvania,Philadelphia, Pennsylvania 19104–6323, USA

2Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA(Received 16 November 2008; published 19 June 2009)

We show that properly shaped terahertz (THz) fields can be used to move ions in ferroelectric crystals

from their positions in an initial domain orientation along well-defined collective microscopic paths into

the positions they occupy in a new domain orientation. Collective coherent control will enable direct

observation of fast highly nonlinear material responses and far-from-equilibrium structures that can be

harnessed in electro-optic devices and nonvolatile computer memory.

DOI: 10.1103/PhysRevLett.102.247603 PACS numbers: 77.80.Fm, 71.15.Pd, 77.84.Dy, 87.50.U!

Coherent optical control over ultrafast molecular behav-ior including chemical reactions has been explored inrecent years [1], spurred by the application of optimalcontrol theory and related methods [2,3] and by the devel-opment of femtosecond pulse shaping techniques [4–6]through which complex optical waveforms have beencrafted and optimized to induce specified molecular re-sponses. Here, we propose and model theoretically theextension of coherent control to collective structuralchange. We show through numerical simulations that tem-porally shaped THz fields can be used to induce ferroelec-tric domain switching with extensive control over thecollective microscopic pathway from initial to final struc-ture, in a coherent process that is very different from theconventional stepwise switching mechanism [7].

Perovskite ferroelectric crystals have simple collectivelattice vibrational modes that describe the microscopicpathways along which structural change occurs [seeFig. 1(a)]. For this reason, these crystals are prototypesfor the study of collective structural rearrangements, withmany modelling studies interrogating both static and dy-namic aspects of their phase transitions [8,9]. A particu-larly important aspect is domain switching, the process ofreorienting part or all of a domain so that its macroscopicpolarization points in a different direction. We and others[10–14] have sought to illuminate how microscopic inter-atomic interactions affect the rate and mechanism of fer-roelectric domain switching.

In the tetragonal phase of lead titanate (PbTiO3, PTO),the crystal has two domain orientations characterized byopposite polarization directions along the tetragonal axiswith symmetrically equivalent ground states separated byan energy barrier. The polarization direction can be re-versed under an electric field. This is exploited extensivelyin ferroelectric memory devices, so the dynamics of do-main switching have been of technological as well asfundamental interest. There is great experimental interestin rapid ferroelectric polarization switching under strong

electric fields, with most experimental approaches limitedto the thin film regime [7,15–17]. Most studies of polar-ization reversal focus on domain wall properties and dy-namics under the influence of an electric field that isapplied through electrodes at the sample surfaces[13,18,19]. Earlier attempts to control crystalline softmodes and phase transitions through impulsive stimulatedRaman scattering used nonresonant optical pulses withouttailored pulse profiles [20–22] and were based on simplemodels for the impulsively driven lattice vibrations and thecrystalline responses to them; so far, such attempts havefailed to find experimental validation because the highlight intensities needed to reach sufficient vibrational am-plitudes far exceed typical material damage thresholds.In contrast, here we explore the fundamental limit of the

polarization switching time of ferroelectric PTO under the

FIG. 1 (color online). (a) PTO unit cell in the tetragonalferroelectric phase, with a þz domain orientation. The softvibrational mode is indicated by the arrows on the ions.(b) Time-dependent lattice response to a single asymmetricTHz pulse (shown by a blue dashed line) with its large lobepolarized along the !z direction, i.e., ‘‘antiparallel’’ to the staticferroelectric polarization. The z-component Pz (shown by agreen solid line) oscillates about its static nonzero value as theTi and other ions oscillate about their lattice positions in the þzdomain. No significant responses of the other components Px

and Py (shown by a black dotted and a red dashed-dotted line,respectively) about their static values of zero are induced.

PRL 102, 247603 (2009) P HY S I CA L R EV I EW LE T T E R Sweek ending19 JUNE 2009

0031-9007=09=102(24)=247603(4) 247603-1 ! 2009 The American Physical Society

coherent control of a THz-frequency electromagnetic driv-ing field that permeates the sample and is resonant with itssoft mode frequency. Using a well validated atomic poten-tial model of PTO [13,23], we consider the coherent reor-ientation of a large region, without domain wall formationor movement, and we consider a THz-frequency drivingfield with tailored amplitude, phase, and polarizationprofiles, motivated by recent progress in the generationof large-amplitude shaped THz fields and in the observa-tion of anharmonic responses of ferroelectric soft modesto them [24]. We examine the possibility of coherentcontrol over domain reversal to ‘‘read’’ or ‘‘write’’ bulkferroelectric data storage media on picosecond time scales.

We carried out molecular dynamics (MD) simulations ofPTO with a 6! 6! 6 supercell using a classical potentialformulated and parameterized [23] to reproduce the ener-gies and all atomic forces encountered in Car-Parrinellosimulations for a large set of thermally accessed structures.The interatomic potential consists of four parts: a term withthe bond-valence [25] potential energy form (but modifiednumerical constants), a Coulomb potential energy termwith modified charges, a r"12 repulsion term, and a har-monic term to reduce the angle tilts of octahedral cages.This potential [23] reproduces the ferroelectric behavior ofPTO accurately without being fit to any experimental ob-servations [9,13,26].

To simulate THz experiments, we set the tetragonal

lattice constants to the experimental values (a ¼ 3:9 !A,c ¼ 4:15 !A) and one or more electric field pulses wereapplied to the system. All the pulses had an asymmetricelectric field profile with a large-amplitude lobe of about150 fs duration (to include frequency components up toabout 6.6 THz) and a lower-amplitude lobe of longerduration in the opposite polarity. The electric field integra-tes to zero as required for optical pulses [Fig. 1(b)]. Theasymmetric field profile is well suited for driving nonlinearresponses in the direction of the large-amplitude lobe.Even shorter pulses could also drive polarization oscilla-tions similar to the pulses we chose. However, to flippolarization with the same number of shorter pulses,much higher electric field amplitude is required, which isvery challenging to generate and could lead to materialdamage.

To switch the polarization from þz to "z, the mostdirect way is to apply electric field pulses along "z.Figure 1(b) shows that applying a "z-oriented electricfield pulse causes the z-component of the polarization(Pz) to oscillate in time about its nonzero static value.The other polarization components (Px and Py) remainessentially zero. The oscillation period of about 240 fs,which corresponds to 4.2 THz, is independent of pulsemagnitude, indicating an essentially harmonic mode (thePb-O or so-called Last mode) at these amplitudes. Thephonon frequency is in good agreement with density-functional theory (DFT) calculations and the experimentalvalue [27] of 4.5 THz.

In order to reorient the lattice polarization, the coherentvibrational amplitude must be made large enough to over-come the potential energy barrier between the two stablepolarization states. The Pz vibrational coherence could bereduced or enhanced by successive pulses depending ontheir timing. As shown in Fig. 2(a), polarization reversalcan be achieved within 15 ps with seven pulses of ampli-tude 3 MV=cm. In order to suppress coherent return of thepolarization to its original direction and multiple succes-sive domain flipping events, we applied one additional"z-oriented pulse out of phase with the Pz oscillations.This guaranteed that after the system acquires sufficientenergy to cross the barrier freely, we can then trap it in thedesired polarization state. It is important to note that theout-of-phase pulse cools down the system substantially(%95 K) since much of the energy is in the coherentmode after the first six pulses. In order to avoid excessiveheating of the system, such an out-of-phase pulse could beuseful not only at 0 K but also at finite temperature.It is well known from the quasi-dc limit that polarization

rotation offers lower-energy pathways to polarization flip-

FIG. 2 (color online). Collective coherent control over ferro-electric polarization with shaped THz waveforms. (a) Sequenceof seven asymmetric THz pulses (blue dashed line), allz-polarized with large lobes (3 MV=cm) along the "z direction.Each successive pulse increases the polarization (Pz is shown bya green solid line) oscillation amplitude by driving the soft modein phase with the oscillation already present. The time intervalbetween pulses is an integer number of soft mode periods whichgradually grow longer due to anharmonicity. (b) Lattice potentialenergy surface (PES) with respect to Px and Pz, calculated usingour MD model. A PES local maximum appears at the high-symmetry cubic structure with Px ¼ Pz ¼ 0. The z-polarizedTHz field in (a) drives the system over this potential energybarrier. Domain switching can occur with lower energies alongtrajectories that pass through or near the saddle points in thePES. (c) Sequence of four THz pulses with x-oriented fieldsfollowed by a final THz pulse with "z-oriented field. (d) Powerspectrum from Fourier transformation of Px and Pz in (c). Astrong peak stems from Px oscillations at the 1.6 THz phononfrequency. The smaller peak shows the second harmonic fre-quency of oscillations in Pz.

PRL 102, 247603 (2009) P HY S I CA L R EV I EW LE T T E R Sweek ending19 JUNE 2009

247603-2

Sn2P2S6: THz-induced switching

§ Simulated dynamics in simplified 2-well potential suggest nonlinearity, flip for multi-MV/cm, single cycle pulses

Int. J. Mol. Sci. 2012, 13 14358

Figure 1. The crystal structure of Sn2P2S6 ferroelectric phase [20]. The tin atoms positionsin the paraelectric phase [14] are shown in red. The shape of the Brillouin zone with denotedsymmetrical points illustrates the primitive monoclinic lattice.

Sn2P2S6 crystals are ferroelectric semiconductors with promising photorefractive [21],photovoltaic [22], electrooptic [23] and piezoelectric [24] characteristics. Their ferroelectric propertiesare effectively influenced by the state of the electronic subsystem [25]. The influence of the sulfur andtin vacancies on semiconductive and optic properties of Sn2P2S6 crystals has recently been studied [26].These data motivate the electronic structure investigation for Sn2P2S6 crystals in the paraelectric andthe ferroelectric phases.

The first-principles calculations in LDA approach of Density Functional Theory (DFT) for Sn2P2S6

ferroelectric phase were carried out by several groups [27–29]. Grigas et al. [19,30] calculated theelectronic structure of both paraelectric and ferroelectric phases of Sn2P2S6 using the cluster approach.For the Sn2P2Se6 selenide analog, the electronic structure have been investigated [31] by first-principlescalculations only for the paraelectric phase. The electronic structure and phonon spectra pressuredependence for the acentric layered rhombohedral crystal SnP2S6 were investigated theoretically bythe LDA approach [32]. For this compound, the tin cations are almost fully ionized (Sn4+ charge state),which excludes the possibility of stereochemical activity of their 5s2 electron lone pair. The electronicstructure of high-charged (P2S6)4− and (P2Se6)4− anion clusters was discussed in papers [29,31,32] atanalysis of Sn2P2S6, Sn2P2Se6 and SnP2S6 electron energy spectra. Analysis of P2S6 cluster chemicalbounding was also done using the Hartree–Fock approach [33]. The anion arrangements have been inves-tigated experimentally and theoretically in different approximation for the layered crystals like M2P2S6

(M = Fe, Ni, Mn, . . . ) [34–38]. For the CuInP2Se6 layered compound with two differently chargedcations, the SOJT effect was established as an origin of the ferroelectric ordering in Cu [39].

In this paper, the first-principles calculations in LDA approach of DFT for electronic structure ofSn2P2S6 crystal in the paraelectric and the ferroelectric phases were used for analysis of chemical bondtransformation at the spontaneous polarization appearance and for establishing the ferroelectric state

[ S. Grübel et al., submitted]

5

FIG. 4. One-dimensional FDTD simulation of a free spaceTHz pulse interacting with a bulk Sn2P2S6 crystal. The di-electric function of Sn2P2S6 is based on the anharmonic modelof the electric polarization described in the text. The figuresa-d) show the electric polarization and the THz electric fieldinside the material at the interface with air as a function oftime and for di↵erent amplitudes of the THz electric field.The inset of the top eft

:::left

:figure shows a zoom into the

dashed regions.

Grolimund and C. Borca for experimental help. We ac-knowledge financial support by the NCCR Molecular Ul-trafast Science and Technology (NCCR MUST), a re-search instrument of the Swiss National Science Founda-tion (SNSF).

⇤ sebastian.gruebel@psi.ch[1] T. Tybell, P. Paruch, T. Giamarchi, and J. M. Triscone,

Physical Review Letters 89, 097601 (2002).[2] A. Grigoriev, D.-H. Do, D. M. Kim, C.-B. Eom,

B. Adams, E. M. Dufresne, and P. G. Evans, PhysicalReview Letters 96, 187601 (2006).

[3] S. Fahy and R. Merlin, Physical Review Letters 73, 1122(1994).

[4] Y. Yan and K. A. Nelson, The Journal of ChemicalPhysics 87, 6240 (1987).

[5] H. J. Zeiger, Phys. Rev. B 45, 768 (1992).[6] T. Qi, Y.-H. Shin, K.-L. Yeh, K. A. Nelson, and A. M.

Rappe, Physical Review Letters 102, 247603 (2009).[7] H. Hirori, A. Doi, F. Blanchard, and K. Tanaka, Applied

Physics Letters 98, 091106 (2011).[8] C. Vicario, C. Ruchert, and C. P. Hauri, Journal of

Modern Optics , 1 (2013).[9] M. Shalaby and C. P. Hauri, Nature Communications 6

(2015).[10] I. Katayama, H. Aoki, J. Takeda, H. Shimosato,

M. Ashida, R. Kinjo, I. Kawayama, M. Tonouchi, M. Na-gai, and K. Tanaka, Physical Review Letters 108, 097401(2012).

[11] T. Elsasser and M. Worner, The Journal of ChemicalPhysics 140, 020901 (2014).

[12] M. Forst, R. Mankowsky, and A. Cavalleri, Accounts ofChemical Research 48, 380 (2015).

[13] A. Cavalleri, S. Wall, C. Simpson, E. Statz, D. W. Ward,K. A. Nelson, M. Rini, and R. W. Schonlein, Nature442, 664 (2006).

[14] G. Dittmar and H. Schafer, Z. Naturfosch 29b, 312(1974).

[15] B. Scott, M. Pressprich, R. D. Willet, and D. A. Cleary,Journal of Solid State Chemistry 96, 294 (1992).

[16] Y. M. Vysochanskii, V. Y. Slivka, A. P. Buturlakin, M. I.Gurzan, and D. V. Chepur, Fiz. Tv. Tela 20 (1978).

[17] A. A. Grabar, Y. M. Vysochanskii, and V. Y. Slivka,Fiz. Tv. Tela 26 (1984).

[18] S. W. Eijt, R. Currat, J. E. Lorenzo, P. Saint-Gregoire,B. Hennion, and Y. M. Vysochanskii, Eur. Phys. J. B 5,169 (1998).

[19] P. Beaud, S. L. Johnson, A. Streun, R. Abela, D. Abram-sohn, D. Grolimund, F. Krasniqi, T. Schmidt, V. Schlott,and G. Ingold, Physical Review Letters 99, 174801(2007).

[20] F. D. Brunner, O. P. Kwon, S.-J. Kwon, M. Jazbinsek,A. Schneider, and P. Gunter, Optics Express 16, 16496(2008).

[21] C. Hunziker, S.-J. Kwon, H. Figi, F. Juvalta, O. P. Kwon,M. Jazbinsek, and P. Gunter, Journal of the OpticalSociety of America B 25, 1678 (2008).

[22] O. P. Kwon, S.-J. Kwon, M. Jazbinsek, F. D. J. Brunner,J.-I. Seo, C. Hunziker, A. Schneider, H. Yun, Y.-S. Lee,and P. Gunter, Advanced Functional Materials 18, 3242(2008).

[23] C. Ruchert, C. Vicario, and C. P. Hauri, Optics Letters37, 899 (2012).

[24] S. L. Johnson, P. Beaud, C. J. Milne, F. S. Krasniqi,E. S. Zijlstra, M. E. Garcia, M. Kaiser, D. Grolimund,R. Abela, and G. Ingold, Physical Review Letters 100,155501 (2008).

[25] G. Gallot and D. Grischkowsky, Journal of the OpticalSociety of America B 16, 1204 (1999).

[26] A. Volkov, G. Kozlov, N. Afanaseva, M. Yu, Y. M.Vysochanskii, A. A. Grabar, and V. Y. Slivka, Sov. Phys.Solid State 25 (1983).

[27] See the supplemental information at [URL] for a descrip-tion of how the index of refraction is estimated self con-sistently within the framework of the fitting process.

[28]::See

::::the

:::::::::::::supplemental

::::::::::information

::::at

:[::::URL]

::for

::a

:::::::definition

::of::::the

::::x-ray

:::::::::scattering

::::::factor.

[29] Y. M. Vysochanskii, T. Janssen, R. Currat, R. Folk,J. Banys, J. Grigas, and V. Samulionis, Phase transitionsin ferroelectric phosphorus chalcogenide crystals, 2nd ed.(Vilnius University Publishing House, Lithuania, Vilnius,Lithuania, 2008) p. 455.

[30] See the supplemental information at [URL] for a descrip-tion of the proportionality factor.

[31] K. Z. Rushchanskii, Y. M. Vysochanskii, and D. Strauch,Physical Review Letters 99, 207601 (2007).

[32] V. Y. Slivka, Y. M. Vysochanskii, M. I. Gurzan, andD. V. Chepur, Fiz. Tv. Tela 21, 2396 (1979).

[33] A. V. Gomonnai, Y. M. Vysochanskii, and V. Y. Slivka,Sov. Phys. Solid State 4 (1982).

How to make THz?Photoconductive switches

Photoconductive switch

Chapter 2Generation and Detection of THz Waves

Before discussing the nature of THz waves and their applications, it is suitable tointroduce how THz waves are generated and detected. As mentioned in Chapter 1,this book will focus on pulsed THz technologies. A typical pulsed THz wave gener-ation and detection system is a pump and probe setup as presented in Fig. 2.1. Themost common way that pulsed systems work is by splitting a beam from a femtosec-ond (fs) laser into two beams: the probe and the pump beams. The pump beam isused to generate the THz pulse, while the probe beam is used to sample and obtainthe pulse profile. Detecting of THz field is performed by modulating the probe pulsewith the THz field or by accelerating free carriers induced by the probe pulse withthe THz field. A mechanical delay line is used to change the time delay betweenTHz pulse and the probe pulse. The THz waveform can be obtained by scanningthis time delay. To increase the sensitivity, the pump beam is modulated by an opti-cal chopper, and the THz-induced modulation on the probe beam is extracted by alock-in amplifier. This pulse information acquired in the time domain is transformedto the frequency domain with a Fourier transform from which spectral informationcan be obtained.

Fig. 2.1 Pulsed THz wavegeneration and detectionsetup

27X.-C. Zhang, J. Xu, Introduction to THz Wave Photonics,DOI 10.1007/978-1-4419-0978-7_2, C⃝ Springer Science+Business Media, LLC 2010

Photoconductive switch

28 2 Generation and Detection of THz Waves

Photoconductive Antenna

The photoconductive (PC) antenna is one of the most frequently used componentsfor THz generation as well as detection. It generates and detects THz pulses by tran-sient photocarriers induced with ultrafast laser pulses. Figure 2.2 gives a sketch ofa PC antenna and concept of how to use a PC antenna to generate THz pulses. APC antenna consists of two metal electrodes that are coated on a semi-insulationsemiconductor substrate with a gap between these two electrodes. To generateTHz pulses, voltage is applied across the electrodes. Since the substrate is semi-insulating, electric energy is stored in the gap area. Ultrafast laser pulses act liketransient switches to open this reservoir of electric energy and release it in the formof THz pulses. Polarization of the THz wave radiated is parallel to the biased field,which is perpendicular to the strip lines in Fig. 2.2. Polarization of THz wave canbe altered by switching polarization of bias. By doing so, the laser pulses must haveenough photon energy in order to generate photoinduced free carriers in the sub-strate. Generally, the photon energy of the excitation optical pulse should be higherthan band gap of the substrate. Sometimes, multiphoton absorption could be used,and an excitation laser with lower photon energy can also generate free carriers.Free carriers are driven by bias field across the gap and produce photocurrent. Sinceelectrons usually have much higher mobility than holes, the contribution of holescan be ignored in most cases. The current density is described as

J(t) = N(t)eµEb, (1)

where N is density of photocarriers, e denotes the elementary charge, µ is the mobil-ity of electron, and E b is the bias electric field. The photocarrier density N is afunction of time, whose format is determined by the laser pulse shape and the carrierlifetime. Since the photocurrent varies in time, it generates electromagnetic pulse,whose electric field is approximately

Fig. 2.2 PC antenna and THzemission from PC antenna (optional: silicon lens)

Semiconductor substrate, usually “low temperature grown (LT)” GaAs

Metal electrodes on surface

“simple dipolar antenna”

Photoconductive switch

28 2 Generation and Detection of THz Waves

Photoconductive Antenna

The photoconductive (PC) antenna is one of the most frequently used componentsfor THz generation as well as detection. It generates and detects THz pulses by tran-sient photocarriers induced with ultrafast laser pulses. Figure 2.2 gives a sketch ofa PC antenna and concept of how to use a PC antenna to generate THz pulses. APC antenna consists of two metal electrodes that are coated on a semi-insulationsemiconductor substrate with a gap between these two electrodes. To generateTHz pulses, voltage is applied across the electrodes. Since the substrate is semi-insulating, electric energy is stored in the gap area. Ultrafast laser pulses act liketransient switches to open this reservoir of electric energy and release it in the formof THz pulses. Polarization of the THz wave radiated is parallel to the biased field,which is perpendicular to the strip lines in Fig. 2.2. Polarization of THz wave canbe altered by switching polarization of bias. By doing so, the laser pulses must haveenough photon energy in order to generate photoinduced free carriers in the sub-strate. Generally, the photon energy of the excitation optical pulse should be higherthan band gap of the substrate. Sometimes, multiphoton absorption could be used,and an excitation laser with lower photon energy can also generate free carriers.Free carriers are driven by bias field across the gap and produce photocurrent. Sinceelectrons usually have much higher mobility than holes, the contribution of holescan be ignored in most cases. The current density is described as

J(t) = N(t)eµEb, (1)

where N is density of photocarriers, e denotes the elementary charge, µ is the mobil-ity of electron, and E b is the bias electric field. The photocarrier density N is afunction of time, whose format is determined by the laser pulse shape and the carrierlifetime. Since the photocurrent varies in time, it generates electromagnetic pulse,whose electric field is approximately

Fig. 2.2 PC antenna and THzemission from PC antenna

Microscopic mechanism

initially, (almost) no electron-hole pairs exist

+Vb/2-Vb/2

Bias field near surface

Eb

Microscopic mechanism

Laser pulse arrives, makes e-h pairs

+Vb/2-Vb/2

Microscopic mechanism

Laser pulse arrives, makes e-h pairs

+Vb/2-Vb/2

Microscopic mechanism

Electrons and holes see oppositely directed forces

from bias field

+Vb/2-Vb/2

Microscopic mechanism

Quickly brought to drift velocity,resulting in a current

+Vb/2-Vb/2

Microscopic mechanism

Assume acceleration to drift velocity is fast

Also assume hole mobility is much smaller thanelectron mobility (often true)

vd = µEb

“mobility” is proportionality constant between E-field and drift velocity

J(t) = N(t)evd = N(t)eµEb

density of electrons

Microscopic mechanism

J(t) = N(t)evd = N(t)eµEb

In the far field (i.e. several wavelengths away from antenna):

ETHz =1

4⇡✏0

A

c2z

@J(t)

@tsin ✓

✓z

ETHz =Ae

4⇡✏0c2z

@N(t)

@tµEb sin ✓

A ⌘ Illuminated gap area

PC switch performance

At low rep rates, can get ~ 1 microJ

Usually ~10 kV/cm peak field

Broadband, single cycle, ~ 1 THz center freq.Usually limited by phonons in substrate (8 THz

TO phonon in GaAs)

Introduction to Terahertz Pulses 23

Fig. 16. Schematic view of the PC dipole antenna (a), the PC stripline (b), andthe bow-tie PC antenna (c). Closed circles show illuminating laser spots

Fig. 17. (a) THz pulse emitted and detected with dipole antennas on LT-GaAs.The vertical axis indicates the DC signal current detected with the PC detector,(b) Fourier-transformed amplitude spectrum of (a) [23]

are shown in Fig. 16 and we made emission-detection experiments using theTHz-TDS system such as the one shown in Fig. 15a.

The setup is evacuated to avoid water-vapor absorption. The temporalbehavior of the emitted THz field looks like that predicted by the calculationbased on the classical Drude model and taking the optical pulse width intoaccount (Fig. 5). Figure 17 shows an experimental result with a 30 µm dipoleon LT-GaAs as the emitter and a 10 µm dipole on LT-GaAs as the detector.

Both the emitter and the detector were illuminated with the optical pulsehaving a pulse width of 80 fs at ≈ 780 nm and a repetition rate of 82 MHz.This pulse width and the antenna structure limit the Fourier-transformedamplitude to about 4 THz.

The output amplitude (or power) is influenced by the applied bias voltage,pump laser power, antenna pattern and mobility of the photoconductor.

Figure 18a shows the peak-amplitude dependence of THz radiation onthe applied bias voltage and Fig. 18b is the dependence on pump-laser powerfor a dipole antenna. The amplitude increases linearly with bias voltage but

Optical rectification

Optical rectification

Pi(t) =X

j

�(1)ij Ej(t) +

X

jk

�(2)ijkEj(t)Ek(t) + . . .

zero in inversion-symmetric materials

Zinc blende:non-inversion symmetric

GaAs, InSb, …

Diamond structure:inversion symmetricDiamond, Si, Ge,…

Optical rectification

Pi(t) =X

j

�(1)ij Ej(t) +

X

jk

�(2)ijkEj(t)Ek(t) + . . .

E(t) E2(t)

Optical rectification

Pi(t) =X

j

�(1)ij Ej(t) +

X

jk

�(2)ijkEj(t)Ek(t) + . . .

= +

THz

Second harmonic

Optical rectification

Pi(t) =X

j

�(1)ij Ej(t) +

X

jk

�(2)ijkEj(t)Ek(t) + . . .

ETHz ⇠ @2P (t)

@t2Far field:

Phase matching

!1 � !2 = ⌦THz

k1 � k2 = kTHz

For two frequencies, DFG phase matching conditions:

Process is equivalent to DFG mixing for wavelengths within wavepacket

!1 � !2

k1 � k2=

⌦THz

kTHz=) @!

@k=

⌦THz

kTHz

=) vg(pump) = vp(THz)

Phase matching

Question: what happens if phase matching conditions satisfied but

vg(pump) 6= vg(THz)

?

Optical Rectification: Phase matching

“Accidentally” true in some materials:

ZnTe and GaP at 800 nm pumpDAST, OH1, DSTMS at ~ 1.5 microns pump

=) vg(pump) = vp(THz)

Possible using birefringence in GaSe at 800 nm

(800 nm is convenient since this is where Ti: Sapphire femtosecond lasers like to lase)

Optical Rectification: General requirements

• Material must be transparent at both pump and THz wavelengths

• Material cannot possess a center of inversion symmetry

• Second-order susceptibility should be high• Phase matching over all THz frequencies in pulse

(need low dispersion of permittivity)

ZnTe: GaP:

!TO ⇡ 5 THz

!TO ⇡ 11 THz

How to “cheat” at phase matching

• Tilted pulse front

LiNbO3

Good: robust, transparent, reasonable nonlinear coefficient

Bad: vph(THz) ⌧ vg(800nm)

(mismatch by about a factor of 2)

How to “cheat” at phase matching

• Tilted pulse front

J. Phys. D: Appl. Phys. 44 (2011) 083001 Topical Review

Figure 6. Velocity matching using TPFP. The thick red/solid lineindicates the pump pulse front, the thick grey/dashed line indicatesthe THz phase front. The arrows indicate the propagations directionand velocities of these two surfaces.

the THz radiation generated by the tilted pulse front of thepump propagates perpendicularly to this front (figure 6) withthe THz phase velocity v(!), according to Huygens’ principle.This leads to a noncollinear propagation geometry, where theangle between the propagation directions of the THz radiationand the pump pulse is equal to the tilt angle γ of the pump pulsefront relative to the pump phase fronts (which is perpendicularto the pump propagation direction). The THz wave propagateswith a fixed phase relative to the pump pulse front if thefollowing velocity-matching condition is fulfilled:

vg(ω0) cos γ = v(!). (6)

In the case of LN where vg(ω0) ! v(!), or equivalentlyng(ω0) " n(!), equation (6) can be fulfilled by choosingan appropriate pulse-front-tilt angle γ . We note that thevelocity-matching condition given by equation (6) is equivalentto a noncollinear phase-matching condition according toequation (2) [71]. To show this one needs to take into accountthe relation [83–85]

tan γ = [n(ω0)/ng(ω0)]ω0 (dε/dω)|ω0, (7)

which links pulse-front tilt and angular dispersion (dε/dω)|ω0 .Here ε is the angle of deviation between an incoming andoutgoing ray introduced by a dispersive element such as a prismor a grating.

In the Cherenkov geometry (figure 7), which was firstused for THz generation by OR [19, 86, 87], THz radiationfrom bulk LN or LiTaO3 is generated by OR of a femtosecondlaser pulse with a tight point or line focus. Here, the samecondition is obtained for the angle θC as that given by equation(6) for the pulse-front-tilt angle γ , therefore the two anglesare equal. However, the conical THz emission geometryis disadvantageous for applications due to practical issueswith collimating and guiding the THz radiation. Further,the Cherenkov geometry does not allow the use of anextended pump spot [86]. In [88] a series of spatially andtemporally shifted focused pump pulse replicas were used forcoherent control of the generated THz-frequency lattice waves.However, because THz damping occurs between as well aswithin the irradiated regions, this approach yields considerablylower overall THz conversion efficiency than TPFP. In contrast,the TPFP technique allows using an extended pump spot,thereby enabling high-energy THz pulse generation.

Figure 7. Cherenkov-like cone of emitted radiation due to OR of asubpicosecond optical pulse moving at a velocity vg(ω0), which isgreater than the THz phase velocity v(!), of the emitted radiation.After [87].

Due to the large difference between n(!) and ng(ω0),TPFP in LN requires a pulse-front tilt as large as 63◦–65◦. Inorder to provide such large tilt angle (and the correspondinglarge angular dispersion, cf equation (7)) a pulse-front-tiltingsetup consisting of a grating and a lens is used in experiments(figure 8). The angular dispersion introduced by the grating isfurther enlarged by the lens, which also recreates the originalshort pulse duration inside the medium by imaging the gratingsurface into the crystal. Additionally, a half wave plate isused to match the polarization of the pulse to the z-axis of theLN crystal. The generated THz polariton wave is coupled outinto free space through the surface of the crystal cut at the tiltangle γ .

By changing the grating and imaging parameters, theexperimental setup can easily be adapted to different pumpwavelengths and repetition rates (table 2). For example,TPFP with sLN at 1033 nm wavelength was demonstratedin [89] using an Yb-doped amplified fibre laser system. Here,repetition rates up to 1 MHz and pump pulse energies in the10 µJ range were employed. A reliable source of broadbandTHz pulses with high average power at MHz repetition ratesis a prerequisite for applications in rapid THz spectroscopicimaging, high throughput screening and signal processing.The THz output frequency in TPFP can be tuned by changingthe pulse-front-tilt angle [67] in TPFP. Tuning the THzfrequency by varying the pump pulse-front-tilt has also beenrecently demonstrated in a thin planar LN waveguide [90],where also the waveguide dispersion has to be taken intoaccount.

Figure 9 summarizes the scaling behaviour of achievableTHz output with pump pulse energy. The figure shows resultsobtained with various sources based on LN (with TPFP), andZnTe. At low pulse energies, quadratic scaling is observedfor both materials, as expected for a second-order process. InZnTe saturation and linear scaling dominates in when pulseenergies of 50 µJ are exceeded. The scaling behaviour can bedescribed using a model from SHG theory where the efficiencyη is described as η ∝ tanh2(const×

!Iopt) [95]. In contrast, the

8

How to “cheat” at phase matching

• Tilted pulse front

J. Phys. D: Appl. Phys. 44 (2011) 083001 Topical Review

Figure 6. Velocity matching using TPFP. The thick red/solid lineindicates the pump pulse front, the thick grey/dashed line indicatesthe THz phase front. The arrows indicate the propagations directionand velocities of these two surfaces.

the THz radiation generated by the tilted pulse front of thepump propagates perpendicularly to this front (figure 6) withthe THz phase velocity v(!), according to Huygens’ principle.This leads to a noncollinear propagation geometry, where theangle between the propagation directions of the THz radiationand the pump pulse is equal to the tilt angle γ of the pump pulsefront relative to the pump phase fronts (which is perpendicularto the pump propagation direction). The THz wave propagateswith a fixed phase relative to the pump pulse front if thefollowing velocity-matching condition is fulfilled:

vg(ω0) cos γ = v(!). (6)

In the case of LN where vg(ω0) ! v(!), or equivalentlyng(ω0) " n(!), equation (6) can be fulfilled by choosingan appropriate pulse-front-tilt angle γ . We note that thevelocity-matching condition given by equation (6) is equivalentto a noncollinear phase-matching condition according toequation (2) [71]. To show this one needs to take into accountthe relation [83–85]

tan γ = [n(ω0)/ng(ω0)]ω0 (dε/dω)|ω0, (7)

which links pulse-front tilt and angular dispersion (dε/dω)|ω0 .Here ε is the angle of deviation between an incoming andoutgoing ray introduced by a dispersive element such as a prismor a grating.

In the Cherenkov geometry (figure 7), which was firstused for THz generation by OR [19, 86, 87], THz radiationfrom bulk LN or LiTaO3 is generated by OR of a femtosecondlaser pulse with a tight point or line focus. Here, the samecondition is obtained for the angle θC as that given by equation(6) for the pulse-front-tilt angle γ , therefore the two anglesare equal. However, the conical THz emission geometryis disadvantageous for applications due to practical issueswith collimating and guiding the THz radiation. Further,the Cherenkov geometry does not allow the use of anextended pump spot [86]. In [88] a series of spatially andtemporally shifted focused pump pulse replicas were used forcoherent control of the generated THz-frequency lattice waves.However, because THz damping occurs between as well aswithin the irradiated regions, this approach yields considerablylower overall THz conversion efficiency than TPFP. In contrast,the TPFP technique allows using an extended pump spot,thereby enabling high-energy THz pulse generation.

Figure 7. Cherenkov-like cone of emitted radiation due to OR of asubpicosecond optical pulse moving at a velocity vg(ω0), which isgreater than the THz phase velocity v(!), of the emitted radiation.After [87].

Due to the large difference between n(!) and ng(ω0),TPFP in LN requires a pulse-front tilt as large as 63◦–65◦. Inorder to provide such large tilt angle (and the correspondinglarge angular dispersion, cf equation (7)) a pulse-front-tiltingsetup consisting of a grating and a lens is used in experiments(figure 8). The angular dispersion introduced by the grating isfurther enlarged by the lens, which also recreates the originalshort pulse duration inside the medium by imaging the gratingsurface into the crystal. Additionally, a half wave plate isused to match the polarization of the pulse to the z-axis of theLN crystal. The generated THz polariton wave is coupled outinto free space through the surface of the crystal cut at the tiltangle γ .

By changing the grating and imaging parameters, theexperimental setup can easily be adapted to different pumpwavelengths and repetition rates (table 2). For example,TPFP with sLN at 1033 nm wavelength was demonstratedin [89] using an Yb-doped amplified fibre laser system. Here,repetition rates up to 1 MHz and pump pulse energies in the10 µJ range were employed. A reliable source of broadbandTHz pulses with high average power at MHz repetition ratesis a prerequisite for applications in rapid THz spectroscopicimaging, high throughput screening and signal processing.The THz output frequency in TPFP can be tuned by changingthe pulse-front-tilt angle [67] in TPFP. Tuning the THzfrequency by varying the pump pulse-front-tilt has also beenrecently demonstrated in a thin planar LN waveguide [90],where also the waveguide dispersion has to be taken intoaccount.

Figure 9 summarizes the scaling behaviour of achievableTHz output with pump pulse energy. The figure shows resultsobtained with various sources based on LN (with TPFP), andZnTe. At low pulse energies, quadratic scaling is observedfor both materials, as expected for a second-order process. InZnTe saturation and linear scaling dominates in when pulseenergies of 50 µJ are exceeded. The scaling behaviour can bedescribed using a model from SHG theory where the efficiencyη is described as η ∝ tanh2(const×

!Iopt) [95]. In contrast, the

8

Vg(800nm) cos ✓c = vph(THz)

How to “cheat” at phase matching

• Tilted pulse front

Grating

How to “cheat” at phase matching

• Tilted pulse front

How to “cheat” at phase matching

• Tilted pulse front

mum intensity around 1 THz and absorption lines caused bywater vapor because dry air purging was not performed.

Figures 4!c" and 4!d" show the THz image and intensityprofiles, respectively, at the focused point after the last off-axis parabolic mirror #PM3 in Fig. 1!b"$. The intensity pro-files in Fig. 4!d" show that the both THz spot diameters atFWHM in vertical and horizontal directions were around300 !m. The small spot size close to the diffraction limitimplies that our designed focusing optics shown in Fig. 1!b"directs a sufficiently tightly focused THz beam. The totalpulse energy was estimated to %2 !J by integrating the THzintensity both temporally and spatially,21 and the energy con-version efficiency was %1"10−3. THz pulse energy ob-tained by a pyroelectric detector !MicroTech Instruments"indicates a larger value of %3 !J.

In conclusion, we generated single-cycle THz pulses us-ing the tilted-pump-pulse-front scheme with LN crystals. Thecareful control of the pump-pulse front improved the beamcharacteristics of THz pulses with an optimal pump-to-THzconversion efficiency. The spatial shape and divergence ofthe THz beam leaving the output face of the LN crystal wascharacterized by the THz camera, and it is found that theTHz beam can be regarded as a collimated rather than pointsource. The designed focusing geometry, assuming genera-tion of the collimated THz beam source, enabled us to tightlyfocus the THz beam with a spot size of %300 !m for 1THz, and the peak THz electric field of 1.2 MV/cm with

energy conversion efficiency of %1"10−3 were obtained.

We are grateful to Mitsuru Namiki for valuable discus-sions and also to Iwao Hosako and Kazuhiko Oda for lettingus use the THz camera. This study was supported by a Grant-in-Aid for Scientific Research from JSPS !Grant No.21760038" and from MEXT of Japan !Grant Nos. 18GS0208and 20104007".

1M. Tonouchi, Nat. Photonics 1, 97 !2007".2A. Doi, F. Blanchard, H. Hirori, and K. Tanaka, Opt. Express 18, 18419!2010".

3B. E. Cole, J. B. Williams, B. T. King, M. S. Sherwin, and C. R. Stanley,Nature !London" 410, 60 !2001".

4S. Leinß, T. Kampfrath, K. v. Volkmann, M. Wolf, J. T. Steiner, M. Kira,S. W. Koch, A. Leitenstorfer, and R. Huber, Phys. Rev. Lett. 101, 246401!2008".

5K. Ishikawa, Phys. Rev. B 82, 201402!R" !2010".6L. Razzari, F. H. Su, G. Sharma, F. Blanchard, A. Ayesheshim, H.-C.Bandulet, R. Morandotti, J.-C. Kieffer, T. Ozaki, M. Reid, and F. A. Heg-mann, Phys. Rev. B 79, 193204 !2009".

7M. C. Hoffmann, J. Hebling, H. Y. Hwang, K.-L. Yeh, and K. A. Nelson,Phys. Rev. B 79, 161201!R" !2009".

8H. Hirori, M. Nagai and K. Tanaka, Phys. Rev. B 81, 081305!R" !2010".9K. Shinokita, H. Hirori, M. Nagai, N. Satoh, Y. Kadoya, and K. Tanaka,Appl. Phys. Lett. 97, 211902 !2010".

10M. Jewariya, M. Nagai, and K. Tanaka, Phys. Rev. Lett. 105, 203003!2010".

11S. Watanabe, N. Minami, and R. Shimano, Opt. Express 19, 1528 !2011".12W. Kuehn, P. Gaal, K. Reimann, M. Woerner, T. Elsaesser, and R. Hey,

Phys. Rev. Lett. 104, 146602 !2010".13J. Hebling, G. Almási, I. Z. Kozma, and J. Kuhl, Opt. Express 10, 1161

!2002".14K.-L. Yeh, M. C. Hoffmann, J. Hebling, and K. A. Nelson, Appl. Phys.

Lett. 90, 171121 !2007".15A. G. Stepanov, L. Bonacina, S. V. Chekalin, and J.-P. Wolf, Opt. Lett. 33,

2497 !2008".16J. A. Fülöp, L. Pálfalvi, G. Almási, and J. Hebling, Opt. Express 18,

12311 !2010".17Note that m of 1, #0 of 780 nm, np

gr of 2.23, and n of 5.16 are used for thecalculation in Fig. 2 !Ref. 18".

18J. Hebling, A. G. Stepanov, G. Almási, B. Bartal, and J. Kuhl, Appl. Phys.B: Lasers Opt. 78, 593 !2004".

19M. Jewariya, M. Nagai, and K. Tanaka, J. Opt. Soc. Am. B 26, A101!2009".

20An EO signal $I / I measured by balanced photodetectors was calibrated toelectric field amplitude ETHz with the formula sin−1!$I / I"=2%n0

3r41tGaPtSi6 ETHzL /#0 #see Q. Wu and X.-C. Zhang, Appl. Phys. Lett.

71, 1285 !1997"$; for the GaP detection crystal used here, the refractiveindex no=3.2 #see Handbook of Optical Constants of Solids, edited by E.D. Palik !Academic, London, 1985"$; the EO coefficient r41=0.88 pm /V #see Y. Berozashvili, S Machavariani, A Natsvlishvili, and AChirakadze, J. Phys. D: Appl. Phys. 22, 682 !1989"$; the thickness L=300 !m. Fresnel transimission coefficients tGaP=0.46 for the GaP crys-tal surface and tSi=0.7 for the Si wafer were used.

21M. Reid and R. Fedosejevs, Appl. Opt. 44, 149 !2005".

-1.0

0.0

1.0

Ver

tical

posi

tion

(mm

)

-1.0 0.0 1.0Horizontal position (mm)

(a) (c)

1

0

Inte

nsity

(arb

.uni

ts)

3210Frequency (THz)

(b) (d)1

0

Inte

nsity

(arb

.uni

ts)

-1.0 0.0 1.0Position (mm)

Vertical

Horizontal

1.5

1.0

0.5

0.0

-0.5

TH

zel

ectr

icfie

ld(M

V/c

m)

6420Delay time (ps)

FIG. 4. !Color online" !a" Measured THz temporal profile and !b" its Fouriercomponents. !c" The THz image measured at the focused point after the lastoff-axis parabolic mirror #PM3 in Fig. 1!b"$. !d" Cross-section intensityprofiles of the THz image in !c" with Gaussian fits.

091106-3 Hirori et al. Appl. Phys. Lett. 98, 091106 !2011"

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:192.33.100.85 On: Thu, 15 Oct 2015 14:18:48

Single-cycle terahertz pulses with amplitudes exceeding 1 MV/cm generated byoptical rectification in LiNbO 3H. Hirori, A. Doi, F. Blanchard, and K. Tanaka Citation: Applied Physics Letters 98, 091106 (2011); doi: 10.1063/1.3560062 View online: http://dx.doi.org/10.1063/1.3560062 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/98/9?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Erratum: “Single-cycle terahertz pulses with amplitudes exceeding 1 MV/cm generated by optical rectificationin LiNbO3” [Appl. Phys. Lett. 98, 091106 (2011)] Appl. Phys. Lett. 103, 259901 (2013); 10.1063/1.4854095 Fiber laser pumped high average power single-cycle terahertz pulse source Appl. Phys. Lett. 93, 141107 (2008); 10.1063/1.2998609 Novel setups for extremely high power single-cycle terahertz pulse generation by optical rectification Appl. Phys. Lett. 92, 171107 (2008); 10.1063/1.2907494 Generation of 10 μ J ultrashort terahertz pulses by optical rectification Appl. Phys. Lett. 90, 171121 (2007); 10.1063/1.2734374 Generation of narrow-band terahertz radiation via optical rectification of femtosecond pulses in periodicallypoled lithium niobate Appl. Phys. Lett. 76, 2505 (2000); 10.1063/1.126390

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:192.33.100.85 On: Thu, 15 Oct 2015 14:18:48

> 1 MV/cm using 10 Hz Ti:Sapphire drive laser

Can be improved by LN cooling

Phase sensitive detectors

• Measure electric field vs. time• As name suggests, gives phase information

that is lost in thermal detection• Most examples of phase sensitive detectors

look like pulse generators operated “in reverse”:• Photoswitches• EO sampling• ABCD detection

• All rely on some type of nonlinearity involving THz and optical/NIR light

Photoswitch

74 3 Generation and Detection of Broadband Terahertz Pulses

and the bias voltage of the PC switch. As we extract energy from the switchby optical excitation in the form of THz pulses, the THz pulse energy cannotexceed the amount stored in the closed gap of electrodes.

Some experimental measurements are shown in Fig. 3.23: the radiated fieldamplitude as a function of optical fluence from a 0.5-mm gap GaAs antenna atbias fields of 1.0 kV/cm, 2.0 kV/cm, and 4.0 kV/cm [26]. The maximum fieldamplitude is in the range of a few kV/cm. The curves show strong saturationat high optical excitation. In a separate study, the THz field amplitude reachedup to 150 kV/cm by using a pulsed bias of ª10 kV/cm, which increases theelectrical breakdown voltage [30].

3.2.5 Time-Resolved Terahertz Field Measurements withPhotoconductive Antennas

The underlying mechanism of THz field detection in a PC antenna is almostidentical with that of THz emission in a PC emitter. The carrier dynamicsdiscussed in the previous sections are applicable to THz field detection in aPC antenna. Figure 3.24 shows a schematic diagram of a time-resolved mea-surement of THz electric fields with a PC receiver. In the absence of a biasfield, the THz electric field induces a current in the photoconductive gap whenthe photocarriers are injected by the optical probe pulse. The photocurrentlasts for the carrier lifetime, which should be much shorter than the THz pulseduration for a time-resolved waveform measurement. The induced photocur-rent is proportional to the field amplitude of the THz radiation focused on thephotoconductive gap. The THz pulse shape is mapped out in the time domainby measuring the current while varying the time delay between the THz pulseand the optical probe. A typical photocurrent is in the sub-nanoamp range,thus a current amplifier is necessary to convert the weak current signals intomeasurable voltages. In order to enhance the signal-to-noise ratio, the sig-nal is processed by a lock-in amplifier synchronized with an optical intensitymodulator such as an optical chopper.

ammeter +

current amplifier

A

opticalprobe

THzpulse optical

probe THzpulse

Side view

Fig. 3.24. Schematic representation of THz pulse detection with a PC antenna

• Measure E-field via current across antenna• Similar bandwidth limitations as generator

(up to about 1.5 THz)

Photoswitch

• Measurement procedure: “pump-probe”• Vary relative delay between THz and NIR

pulses

A

EO Sampling

✏ij = �ij + �(2)ijkEkElectro-optic effect:

(in materials without inversion symmetry)

• Applied E-field changes dielectric tensor• New tensor may have different symmetry• Can measure changes to dielectric tensor

induced by THz field using higher frequency light

EO Sampling

3.4 Free-Space Electro-Optic Sampling 93

the applied field strength can be determined by measuring the field-inducedbirefringence.

l/4 plateEO

crystal Wollastonprism

Balancedphoto-detector

THz pulseOpticalpulse

021

II y =

Probe polarization

without THz field02

1II x =

)1(20 fD-= I

I x

without THz field

with THz field

)1(20 fD+= I

I y

Fig. 3.42. Schematic diagram of a typical setup for free-space EO sampling. Probepolarizations with and without a THz field are depicted before and after the polar-ization optics.

Figure 3.42 illustrates a typical setup of free-space EO sampling to measurefield-induced birefringence. Ideally, the optical group velocity matches wellwith the THz phase velocity in the EO crystal, then the optical pulse will feel aconstant electric field of the THz pulse while propagating. In the lower part ofFig. 3.42, evolution of the probe polarization is shown in series for the steps ofthe polarization manipulation with or without a THz field. While the linearlypolarized optical pulse and the THz pulse propagate through the EO crystal,the field-induced birefringence produces a slightly elliptical polarization ofthe probe pulse. The probe polarization evolves into an almost circular, butelliptical polarization after a ∏/4-plate. A Wollaston prism splits the probebeam into two orthogonal components, which are sent to a balanced photo-detector. The detector measures the intensity difference Is = Iy ° Ix betweenthe two orthogonal components of the probe pulse, which is proportional tothe applied THz field amplitude.

The useful characteristics of ZnTe for THz generation—velocity-matchingnear 800 nm, high transparency at optical and THz frequencies, and large EOcoefficient (r

41

= d14

= 4 pm/V)—are also desirable for efficient EO sampling.A typical arrangement of the optical and THz polarizations for EO samplingis shown in Fig. 3.43. The field induced birefringence is maximized when boththe THz electric field and the optical polarization are parallel to the [110]axis of an h110i oriented crystal. We can describe the nonlinear polarization

ABCD

(Air Break-down Coherent Detection)

• FWM-like effect where E-field bias on gas is used• Uses third order susceptibility to generate SHG• Very broad bandwidth

Detection of Broadband Terahertz Waves with a Laser-Induced Plasma in Gases

Jianming Dai, Xu Xie, and X.-C. Zhang*Center for Terahertz Research, Rensselaer Polytechnic Institute, Troy, New York 12180, USA

(Received 25 April 2006; published 8 September 2006)

We report the experimental results and theoretical analysis of broadband detection of terahertz (THz)waves via electric-field-induced second-harmonic generation in laser-induced air plasma with ultrashortlaser pulses. By introducing the second-harmonic component of the white light in the laser-inducedplasma as a local oscillator, coherent detection of broadband THz waves with ambient air is demonstratedfor the first time. Our results show that, depending on the probe intensity, detection of THz waves in aircan be categorized as incoherent, hybrid, and coherent detection. Coherent detection is achieved onlywhen the tunnel ionization process dominates in gases.

DOI: 10.1103/PhysRevLett.97.103903 PACS numbers: 42.65.!k, 52.38.!r

Coherent detection with a simultaneous measurement ofthe amplitude and phase of a pulsed terahertz (THz) waveis the basis of time-domain spectroscopy (TDS), which hasbecome one of the most active spectroscopic methods inthe physics and material science communities [1]. It pro-vides dynamic properties of various dielectric materialsover the frequency range from 0.1 to 10 THz, which waspreviously considered to be a difficult-to-access range. Forexample, the unique features of this coherent and time-resolved method provided direct measurement of dynamicformation of Drude model in photoexcited Coulombdressed free carriers [2]. Commonly used coherent detec-tors for detecting THz waves in the THz TDS are photo-conductive dipole antennas and electro-optic crystals [3,4].However, their bandwidth is limited by the carrier lifetimein semiconducting photoconductors and phonon absorp-tion in electro-optic crystals.

In this Letter, we present theoretical analysis and ex-perimental demonstration of both incoherent and coherentdetection of broadband THz waves using gases as thesensor medium through a third-order nonlinear opticalprocess with femtosecond (fs) laser pulses. We demon-strate that the field-induced second harmonic from thenonlinear optical interaction in the air offers time-resolvedmeasurement of pulsed THz waves. By using the whitelight from the laser-induced plasma as the local oscillator(LO), the detection could be coherent. Furthermore, byincreasing the probe beam intensity, the detection changesfrom incoherent detection at lower intensities to coherentdetection at higher intensities. Correspondingly, the laser-induced ionization of the gas changes from multiphotonionization (MI) to tunnel ionization (TI), which is indicatedby the Keldysh parameter ! [5,6].

Gases, especially ionized gases, have been demonstratedto generate intense THz waves through laser-induced pon-deromotive forces [7], Lorentz forces [8], and third-ordernonlinear optical processes [9–12]. Similar to the electro-optic detection of THz waves in nonlinear crystals bysecond-order optical nonlinearity, THz waves can be de-tected by third-order optical nonlinearity. Ambient air,

with a composition of about 78% nitrogen, exhibits re-markable performance for the generation and detection ofTHz waves with fs laser pulses.

Experimentally, a Ti:sapphire amplifier, generating800 nm, 120 fs, 800 "J pulses at a repetition rate of1 kHz, is used. The laser beam is split into two beams.One beam is used to generate THz waves, and the other isused to detect the THz waves. Figure 1 schematicallyillustrates this all-optical process for the generation anddetection of THz waves using air as the emitter and sensor.First, the fundamental (!) beam and its SH (2!), afterpassing through a 100 "m thick type-I beta barium borate(BBO) crystal, are focused in air to produce plasma [9]. An

Detector

BBO Lens

Plasma

Lens

Lens

Filter

Si filter

Parabolic mirror

/2 wave plate

Laser pulse 120 fs, 800 µJ

800 nm, 1 kHz

Beam splitter

Delay

THz pulses

Filter λ

FIG. 1. Schematic diagram of the experimental setup. TheTHz wave is generated by mixing the ! pump beam and itsSH (from a type-I BBO crystal) at the first air plasma point. Thefirst parabolic mirror collimates the THz beam. A high-resistivity silicon wafer blocks the residual 800 and 400 nmbeams. The second parabolic mirror focuses the collimated THzbeam. A #=2 wave plate controls the polarization of the probebeam. The THz wave is detected by measuring the time-resolvedSH signal produced by mixing the ! beam and the THz field atthe second plasma point.

PRL 97, 103903 (2006) P H Y S I C A L R E V I E W L E T T E R S week ending8 SEPTEMBER 2006

0031-9007=06=97(10)=103903(4) 103903-1 © 2006 The American Physical Society

intense, highly directional, broadband THz wave is gener-ated through four-wave mixing [11,12]. Detailed experi-mental results regarding the nonlinear process for the THzwave generation in air plasma are demonstrated in ourprevious publication [13], and references therein. To detectthe THz waves in air, the THz wave and the probe beam arefocused at the same point, with estimated focal spots ofabout 0.8 mm and 24 !m in diameter, respectively. TheTHz-field-induced second harmonic (TFISH) is detectedby a photomultiplier tube.

We measured time-resolved TFISH signals at differentprobe intensities. To eliminate the water vapor absorption,the entire THz system is purged with nitrogen gas. As theprobe intensity increases from 9:2! 1012 to 1:0!1015 W=cm2 while the THz field is kept the same, thedetected SH signal increases accordingly while the wave-form is kept the same with a unipolar feature until theprobe intensity reaches "1:8! 1014 W=cm2. Above thisintensity level, the waveform begins to change, and espe-cially above 3:3! 1014 W=cm2, the measured SH wave-form starts to change from the unipolar shape to bipolar.Figure 2 shows a typical unipolar waveform of incoherentmeasurement (upper), a bipolar waveform of coherentmeasurement (lower), and a waveform between them(middle), with their offsets shifted for clarity. When theprobe intensity is over"5:5! 1014 W=cm2, the SH wave-forms are nearly identical to those detected by the ZnTecrystal, indicating the coherent detection of the THzwaves.

In the reciprocal process of four-wave rectification, thegeneral physical concept of TFISH in third-order nonline-arity [14,15] can be understood as:

Esignal2! / "#3$E!E!ETHz; (1)

where "#3$ is the third-order susceptibility of air, and E is

the electric field component associated with the opticalfield or THz field. Since Esignal

2! / ETHz, the intensity ofthe measured SH is proportional to the intensity of the THzwave: I2! / ITHz. The phase information is lost; therefore,the measurement is incoherent.

When the SH LO contribution ELO2! is included into the

analysis, the total SH intensity in the time average valuesover one period of E-field oscillation has the form:

I2! / #E2!$2 % #Esignal2! & ELO

2!$2

% #Esignal2! $2 & #ELO

2!$2 & 2Esignal2! ELO

2! cos#’$; (2)

where ’ is the phase difference between the Esignal2! and

ELO2! . The LO ELO

2! is contributed from the white lightgenerated from the laser-induced air plasma through self-phase modulation and self-steepening, and it depends onplasma density, especially in the transition from ambientair to ionized air, and, accordingly, the LO should have awell-defined threshold. Equation (2) can be written as:

I2! / #"#3$I!$2ITHz & #ELO2!$2 & 2"#3$I!ELO

2!ETHz cos#’$:(3)

The first term is proportional to the intensity of the THzwave. With a zero or a weak LO (small ELO

2!), the first termis dominant, leading to I2! / ITHz. The second term is thedc contribution from the LO and can be filtered out throughthe use of a lock-in amplifier by modulating the THz beam.The third term is the interference term, which is propor-tional to ETHz. This term provides the basis of coherentdetection. With the above approximations, Eq. (3) can besimplified to the form:

I2! / #"#3$I!$2ITHz & 2"#3$I!ELO2!ETHz cos#’$: (4)

Equation (4) is obtained from the plane-wave approxima-tion. It should be pointed out that "#3$ could be probeintensity dependent, especially when the probe intensityapproaches the plasma threshold. A constant ’ is a goodapproximation because we experimentally proved that, inour setup, the only source for the SH LO is the 2!component of the white light, which has a fixed phaserelationship with the ! beam when the probe energy isfixed.

Equation (4) predicts that I2! / ITHz without a LO orI2! / ETHz with a strong LO. With probe intensity lessthan the air ionization threshold, the LO ELO

2! is negligible,and the total SH is dominated by the first term in Eq. (4);therefore, the measured I2! is unipolar, and the detection isincoherent. With the probe intensity much higher than theplasma threshold, the second term dominates. I2! is pro-portional to the THz electric field with a bipolar waveform,and the detection is coherent. The measured I2! wave-forms at three different probe intensities indicated inFig. 2 qualitatively agree well with the predication inEq. (4).

0 2 4 6 8 10 12 14

9.2 x 10 14 W/cm 2

4.6 x 10 14 W/cm 2

x 4.5

x 1.5

x 1

1.8 x 10 14 W/cm 2

Nor

mal

zed

i SH

Sig

nal

I 2ω (

a.u.

)

Delay (ps)

FIG. 2. Typical time-resolved SH waveforms (solid lines)measured with a gas sensor at three different estimated probeintensities: 1:8! 1014 W=cm2 (upper), 4:6! 1014 W=cm2

(middle), and 9:2! 1014 W=cm2 (lower), respectively. Thewaveform offsets are shifted for clarity.

PRL 97, 103903 (2006) P H Y S I C A L R E V I E W L E T T E R S week ending8 SEPTEMBER 2006

103903-2

ABCD

intense, highly directional, broadband THz wave is gener-ated through four-wave mixing [11,12]. Detailed experi-mental results regarding the nonlinear process for the THzwave generation in air plasma are demonstrated in ourprevious publication [13], and references therein. To detectthe THz waves in air, the THz wave and the probe beam arefocused at the same point, with estimated focal spots ofabout 0.8 mm and 24 !m in diameter, respectively. TheTHz-field-induced second harmonic (TFISH) is detectedby a photomultiplier tube.

We measured time-resolved TFISH signals at differentprobe intensities. To eliminate the water vapor absorption,the entire THz system is purged with nitrogen gas. As theprobe intensity increases from 9:2! 1012 to 1:0!1015 W=cm2 while the THz field is kept the same, thedetected SH signal increases accordingly while the wave-form is kept the same with a unipolar feature until theprobe intensity reaches "1:8! 1014 W=cm2. Above thisintensity level, the waveform begins to change, and espe-cially above 3:3! 1014 W=cm2, the measured SH wave-form starts to change from the unipolar shape to bipolar.Figure 2 shows a typical unipolar waveform of incoherentmeasurement (upper), a bipolar waveform of coherentmeasurement (lower), and a waveform between them(middle), with their offsets shifted for clarity. When theprobe intensity is over"5:5! 1014 W=cm2, the SH wave-forms are nearly identical to those detected by the ZnTecrystal, indicating the coherent detection of the THzwaves.

In the reciprocal process of four-wave rectification, thegeneral physical concept of TFISH in third-order nonline-arity [14,15] can be understood as:

Esignal2! / "#3$E!E!ETHz; (1)

where "#3$ is the third-order susceptibility of air, and E is

the electric field component associated with the opticalfield or THz field. Since Esignal

2! / ETHz, the intensity ofthe measured SH is proportional to the intensity of the THzwave: I2! / ITHz. The phase information is lost; therefore,the measurement is incoherent.

When the SH LO contribution ELO2! is included into the

analysis, the total SH intensity in the time average valuesover one period of E-field oscillation has the form:

I2! / #E2!$2 % #Esignal2! & ELO

2!$2

% #Esignal2! $2 & #ELO

2!$2 & 2Esignal2! ELO

2! cos#’$; (2)

where ’ is the phase difference between the Esignal2! and

ELO2! . The LO ELO

2! is contributed from the white lightgenerated from the laser-induced air plasma through self-phase modulation and self-steepening, and it depends onplasma density, especially in the transition from ambientair to ionized air, and, accordingly, the LO should have awell-defined threshold. Equation (2) can be written as:

I2! / #"#3$I!$2ITHz & #ELO2!$2 & 2"#3$I!ELO

2!ETHz cos#’$:(3)

The first term is proportional to the intensity of the THzwave. With a zero or a weak LO (small ELO

2!), the first termis dominant, leading to I2! / ITHz. The second term is thedc contribution from the LO and can be filtered out throughthe use of a lock-in amplifier by modulating the THz beam.The third term is the interference term, which is propor-tional to ETHz. This term provides the basis of coherentdetection. With the above approximations, Eq. (3) can besimplified to the form:

I2! / #"#3$I!$2ITHz & 2"#3$I!ELO2!ETHz cos#’$: (4)

Equation (4) is obtained from the plane-wave approxima-tion. It should be pointed out that "#3$ could be probeintensity dependent, especially when the probe intensityapproaches the plasma threshold. A constant ’ is a goodapproximation because we experimentally proved that, inour setup, the only source for the SH LO is the 2!component of the white light, which has a fixed phaserelationship with the ! beam when the probe energy isfixed.

Equation (4) predicts that I2! / ITHz without a LO orI2! / ETHz with a strong LO. With probe intensity lessthan the air ionization threshold, the LO ELO

2! is negligible,and the total SH is dominated by the first term in Eq. (4);therefore, the measured I2! is unipolar, and the detection isincoherent. With the probe intensity much higher than theplasma threshold, the second term dominates. I2! is pro-portional to the THz electric field with a bipolar waveform,and the detection is coherent. The measured I2! wave-forms at three different probe intensities indicated inFig. 2 qualitatively agree well with the predication inEq. (4).

0 2 4 6 8 10 12 14

9.2 x 10 14 W/cm 2

4.6 x 10 14 W/cm 2

x 4.5

x 1.5

x 1

1.8 x 10 14 W/cm 2

Nor

mal

zed

i SH

Sig

nal

I 2ω (

a.u.

)

Delay (ps)

FIG. 2. Typical time-resolved SH waveforms (solid lines)measured with a gas sensor at three different estimated probeintensities: 1:8! 1014 W=cm2 (upper), 4:6! 1014 W=cm2

(middle), and 9:2! 1014 W=cm2 (lower), respectively. Thewaveform offsets are shifted for clarity.

PRL 97, 103903 (2006) P H Y S I C A L R E V I E W L E T T E R S week ending8 SEPTEMBER 2006

103903-2

low probe intensity:

high probe intensity:

ISHG / (Esignal2! )22 / E2

THz

Simultaneous emission from plasma/self phase modulation

ISHG / (Esignal2! + ELO

2! )

2

/ (�(3)I2!)2ITHz + (ELO

2! )

2+ 2�(3)I!E

LO2! ETHz cos�

“heterodyne detection”

ABCD

(Air Break-down Coherent Detection, or Air-Biased Coherent Detection (if biased))

• Also variants where DC bias is explicitly applied, gives better sensitivity

• Advantage: huge bandwidth, overlaps with conventional FTIR

THz Radiation Enhanced-Emission-of-Fluorescence (THz-REEF) from Gas Plasma 119

Fig. 5.23 (a) Typical THz waveform with a 80 kV/cm THz field, using dry nitrogen as the THzwave emitter and sensor gas. As a comparison, the standard air dielectric breakdown field is about30 kV/cm. (b) The widest spectrum (linear plot 10% bandwidth: <0.1 to > 10 THz, tail reaches20 THz). Inset: Spectra of 2-2′ Biphenol taken using both the time-domain ABCD system and anFTIR spectrometer. The spectra are offset and baselines removed for clarity

carbon impurity absorption. Figure 5.23b shows that the measured 10% bandwidthspans from 0.3 to 10 THz. The broad spectral range and heterodyne detection capa-bility allow spectroscopic measurement across the full THz range. The inset plotin Fig. 5.23b compares the spectra of 2-2′ Biphenol taken by the THz time-domainABCD system and one measured by a traditional FTIR spectrometer (Bruker). Allthe major spectral features are reproduced within the overlapping spectral range ofthe two methods.

THz Radiation Enhanced-Emission-of-Fluorescence(THz-REEF) from Gas Plasma

The interaction between electromagnetic (EM) waves and laser-induced gas plasmahas been extensively studied in most of the spectral regions. Electric field mea-surements and plasma dynamics characterization in gas DC and RF discharge weredemonstrated by various schemes of laser-induced fluorescence spectroscopy (LIF).However, the study in the THz region (0.1–10 THz) has been a challenge in the pastdue to the lack of strong, tabletop THz sources. A short THz pulse is a promisingtool for a time-resolved investigation of plasma dynamics without the limitationof the detector response time. Low energy of the THz photon promises in-situ,non-invasive plasma characterization. For standard laboratory, laser-induced plasmawith electron densities of 1014–1019 cm–3, the plasma frequency lies in the range of90 GHz to 28 THz. The large frequency span of THz pulses developed recentlyencompasses a wide range of plasma densities and allows for the study of reso-nant interaction between THz wave and plasma. Recent major technical advances indeveloping intensive THz sources [8–10], have provided us with new opportunities