nonlinear optical techniques for thz pulse generation and...

41

2 Nonlinear Optical Techniques for Terahertz Pulse Generation and Detection—Optical Rectification and Electrooptic Sampling

Ingrid Wilke and Suranjana SenguptaRensselaer Polytechnic Institute

Contents

2.1 Introduction................................................................................................... 422.1.1 TerahertzTime-DomainSpectroscopy:AnOverview...................... 42

2.2 OpticalRectificationandLinearElectroopticEffect...................................442.3 ExperimentalResultsofTerahertz-FrequencyRadiationGeneration

byOpticalRectificationofFemtosecondLaserPulses................................ 492.3.1 Materials............................................................................................50

2.3.1.1 Semiconductors....................................................................502.3.1.2 InorganicElectroopticCrystals............................................ 522.3.1.3 OrganicElectroopticCrystals.............................................. 52

2.3.2 RecentDevelopments.........................................................................562.4 ExperimentalResultsofTerahertzElectroopticDetection.......................... 57

2.4.1 Materials............................................................................................ 572.4.1.1 SemiconductorsandInorganicCrystals............................... 572.4.1.2 OrganicCrystals...................................................................64

2.5 ApplicationofElectroopticSamplingofTerahertzElectricFieldTransients......................................................................................................65

References................................................................................................................69

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42 Terahertz Spectroscopy: Principles and Applications

2.1 IntroduCtIon

Thegenerationanddetectionofshortpulsesofterahertz(THz)frequencyelectromag-neticradiationareattractinggreatinterest.ResearchactivitiesinthisareaaredrivenbyapplicationsofTHz-frequencyradiationpulsesintime-domainTHzspectroscopyandtime-domainTHzimaging.1,2RecentexamplesofmajorscientificadvancementsinTHzwaveresearchincludethedetectionofsingle-basepairdifferencesinfemtomolarconcentrationsofDNA,3 theobservationof the temporalevolutionofexciton forma-tion in semiconductors4 and understanding of carrier dynamics in high-temperaturesuperconductors.5 Real-world applications of time-domain THz spectroscopy andimagingaddressimportantproblemssuchasnondestructivetesting,6aswellasnewapproachestomedicaldiagnosticsandrapidscreeningindrugdevelopment.7

OneoftheresearchdirectionsinTHzscienceandtechnologyistoincreasethebandwidthofshortTHz-frequencyradiationpulses.Nonlinearopticalphenomenasuchasoptical rectificationandthe linearelectroopticeffect (Pockels’effect)areattractiveoptionsforbroadbandgenerationanddetectionofTHzradiation.

This chapter provides an overview of the generation and detection of freelypropagatingTHzpulsesbasedonnonlinearopticaltechniques.InSection2.1.1ofthischapter,theprinciplesoftime-domainTHzspectroscopyandtime-domainTHzimagingusingnonlinearopticaltechniquesforTHzpulsegenerationanddetectionarebrieflydiscussed.Section2.2describestheprinciplesofgenerationanddetec-tionofTHz-frequencyradiationbyopticalrectificationoffemtosecondlaserpulsesandfemtosecondelectroopticsampling.THzradiationemissionhasbeenreportedfromavarietyofnonlinearmaterialssuchaslithiumniobate(LiNbO3),8,9lithiumtantalate (LiTaO3),9,10 zinc telluride (ZnTe),11,12 indium phosphide (InP),13 galliumarsenide (GaAs),14 gallium selenide (GaSe),15,16 cadmium telluride (CdTe),17 cad-miumzinctelluride(CdZnTe),18DAST,10,19andmetals.20,21Section2.3summarizestheperformanceofTHzemittersbasedonthesematerials in termsofbandwidthandsignalstrengthoftheemittedTHzradiation.MaterialsforthedetectionofTHzradiationbyfemtosecondelectroopticsamplingarethesubjectsofSection2.4.InSection2.5,anapplicationofelectroopticdetectionofTHz-frequencyelectromag-netictransientsisdiscussed.

2.1.1 TeraherTzTime-DomainSpecTroScopy:anoverview

Thebasicideasoftime-domainTHzspectroscopyandatime-domainTHzimagingsystemis illustratedinFigure2.1.AsubpicosecondpulseofTHz-frequencyelec-tromagneticradiationpassesthroughasampleplacedintheTHzbeamanditstimeprofileiscomparedtoareferencepulse.Thelattercanbeafreelypropagatingpulseor a pulsepropagating through amediumwithknownproperties.The frequencyspectraofthetransmittedandreferenceTHzradiationpulsesareobtainedbyFou-riertransformation.Analysisofthefrequencyspectrayieldsspectroscopicinforma-tiononthematerialunderinvestigation.Inthecaseoftime-domainTHzimagingtheTHzradiationfocalspotisscannedacrossthesampleandaTHzimageoftheobjectunderinvestigationisobtained.

Thetime-domainTHzspectroscopysystemshowninFigure2.1ispoweredbyalaser,whichemitsatrainoffemtoseconddurationpulsesatnear-infraredfrequencies.

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Nonlinear Optical Techniques for Terahertz Pulse Generation and Detection 43

Theinitiallaserbeamafterpassingthroughabeamsplitterissplitintotwoparts:thepumpandtheprobebeam.ThepumpbeamafterbeingmodulatedbyanopticalchopperisfocusedontheTHzemitter(asecond-ordernonlinearopticalmedium),whichreleasesasubpicosecondpulseofTHzradiationinresponsetotheincidentfemtosecondnearinfraredlaserpulse.ThegeneratedTHzradiationisfocusedontoadetectorusingtwooff-axisparabolicmirrors.Thedetectorisanelectroopticcrystal.Theprobebeamgatesthedetector,whoseresponseisproportionaltotheamplitudeandsignoftheelectricfieldoftheTHzpulse.Bychangingthetimedelaybetweenthepumpandtheprobebeamsbymeansofanopticaldelaystage,theentiretimeprofileoftheTHztransientcanbetraced.

Electrooptic detection of THz transients is possible when the THz radiationpulseandtheprobebeamscoincideinacopropagatinggeometryinsidetheelectro-opticcrystal.ApelliclebeamsplitterisputintheTHzbeamlineforthispurpose.As the THz pulse and probe beam copropagate through the electrooptic crystal,aphasemodulation is inducedon theprobebeamwhichdependson the electricfieldoftheTHzradiation.Thephasemodulationoftheprobebeamisanalyzedbyaquarterwave(l/4)plateandthebeamisthensplitintotwobeamsoforthogonal

Delay Stage

Probe Beam

PM I PM II

M3 M4

M5

M6

M7

QuarterWave Plate

L1

L2

THz Beam

Lock-inAmplifier

Data AcquisitionSoftware

Chopper

WollastonPrism

Diodes

Emitter Detector

BeamSplitter

PumpBeam

Laser

M1 M2

PBS

FIgure2.1 Experimentalarrangementsfortime-domainTHzspectroscopymeasurementsusing nonlinear optical techniques for the generation and detection of freely propagatingTHz-radiationpulses.(M1–M7opticalbeamsteeringmirrors,PMI,PMIIparabolicalTHz-beamsteeringmirrors,L1,L2lenses).

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polarizationsbyaWollastonprism.Atthispoint,thephasemodulationoftheprobebeamisconvertedtoanintensitymodulationofthetwoorthogonalpolarizationsoftheprobebeam,whicharethensteeredintoapairofphotodiodes.Alock-inampli-fiersubsequentlydetectsthedifferenceinprobelaserlightintensitiesmeasuredbythephotodiodes.

Next,thekeyaspectsofthenonlinearopticalprocessesinvolvedinthegenerationanddetectionofshortpulsesofTHz-frequencyradiationarediscussedindepth.

2.2 optICalreCtIFICatIonandlIneareleCtrooptICeFFeCt

Opticalrectificationandthelinearelectroopticeffect(Pockels’effect)arenonlinearopticaltechniquesforthegenerationanddetectionoffreelypropagatingsubpicosec-ondTHz-frequencyradiationpulses.

Generally, optical rectification refers to the development of a DC or low-frequencypolarizationwhenintenselaserbeamspropagatethroughacrystal.Thelinear electrooptic effect describes a change of polarization of a crystal from anappliedelectricfield.Optical rectificationand the linearelectroopticeffectoccuronlyincrystalsthatarenotcentrosymmetric.However,opticalrectificationoflaserlightbycentrosymmetriccrystalsispossibleifthesymmetryisbrokenbyastrongelectricfield.Furthermore,generationanddetectionofTHz-radiationpulsesbyopti-calrectificationandthePockels’effectrequirethatthecrystalsaresufficientlytrans-parentatTHzandopticalfrequencies.

FreelypropagatingsubpicosecondTHz-radiationpulsesaregeneratedbyopticalrectificationoffemtosecond(fs)nearinfraredlaserpulsesincrystalswithappropri-atenonlinearopticalpropertiesforthisprocess.ThedetectionoffreelypropagatingTHz-radiationpulsesisperformedbymeasuringthephasemodulationofanfsnearinfraredlaserpulsepropagatingthroughanelectroopticcrystalsimultaneouslywithaTHz-radiationpulse.TheelectricfieldoftheTHzradiationinducesaphasemodu-lationofthefslaserpulsethroughthelinearelectroopticeffect.

Inthefollowingsection,thetheoryofopticalrectificationandthelinearelectro-opticeffectisdiscussed.Thediscussionoftheoryislimitedtomaterialweconsiderusefulfor thereader togetageneral ideaof theunderlyingphysicsofTHzpulsegenerationanddetectionbynonlinearopticaltechniquesandtoequationsthatarerelevanttotheimplementationofthetechniquesinthelaboratory.Ourdiscussionmainlyfollowstheoriginalworkbypioneersinthefield.

First, DC optical rectification of 694 nm continuous-wave laser radiationin potassium dihydrogen phosphate and potassium dideuterium phosphate wasdemonstratedexperimentallybyBassetal.in1962.22Afterthat,monochromaticTHz-radiationgenerationat3THzbylow-differencefrequencymixingofnear-infrared(nir)laserradiation(lnir=1.059–1.073Nm)inquartzwasachievedin1965byZernikeandBerman.23Yangetal.demonstratedgenerationofbroadband(0.06–0.36THz)freelypropagatingTHz-radiationpulsesbyopticalrectificationofpicosecondNd:glass laser pulses in LiNbO3 in 1971.8 Eventually, Hu et al. produced free-spaceTHz-frequencyradiationwithabandwidthof1THzbyopticalrectificationoffem-tosecondCPMdyelaserpulsesinLiNbO3in1990.10

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In 1893, Friedrich Pockels discovered the linear electrooptic effect.24 Subse-quently,thephasemodulationofopticallaserlightatmicrowavefrequenciesusingthelinearelectroopticeffectwasdemonstratedin1962byHarrisetal.25Then,Vald-manisandcoworkersbuilt thefirstelectroopticsamplingsystemwithpicosecondresolutionforthemeasurementsofultrafastelectricaltransientsin1982.26Finally,electroopticsamplingoffreelypropagatingTHz-radiationpulseswasdemonstratedin1995byWuandZhang27andin1996byJepsenetal.28andNahataetal.29

Anexcellentdescriptionoflaserlightmodulationbasedonthelinearelectroop-ticeffectisgivenbyYariv.30RigorousquantummechanicalcalculationsofopticalrectificationwerecarriedoutbyArmstrongetal.31Previousreviewsofnonlineargenerationanddetectionofsub-picosecondTHz-radiationpulseswerepublishedbyBonvalentandJoffre,32Shenetal.,33andJiangandZhang.34

ThediscussionsofopticalrectificationandthePockels’effectbeginbyconsid-eringscalarrelationshipsofpolarizationP,electricsusceptibility,andelectricfieldE.35

P E E= c( ) (2.1)

TheelectricpolarizationPofamaterialisproportionaltotheappliedelectricfieldE.Here,c(E)istheelectricsusceptibility.Thenonlinearopticalpropertiesofthematerialaredescribedbyexpandingc(E)inpowersofthefieldE.

P E E E E= + + + +( )c c c c1 2 3

24

3 K (2.2)

Optical rectification and the linear electrooptic effect are secondorder nonlinearopticaleffectsP2

nl anddescribedbytheP2nl = c2E2termintheexpansion.

Forexample,consideranopticalelectricfieldEdescribedbyE = E0 coswt.Inthiscase,thesecond-ordernonlinearpolarization P2

nlconsistsofadcpolarizationc

2E02/2andapolarizationwithacos 2wtdependence.

P E

Etnl

2 22

20

2

21 2= = +c c w( cos ) (2.3)

TheDCpolarizationresultsfromtherectificationoftheincidentopticalelec-tricfieldbythesecond-ordernonlinearelectricsusceptibilityofthematerial.Thepolarization with the cos2wt dependence describes second harmonic generation.ThisnonlinearopticalprocessisnotrelevanttothegenerationanddetectionofTHzradiationbynonlinearopticaltechniquesandthereforenotdiscussedfurther.

Similarly,consider twoopticalfieldsoscillatingat frequenciesE1 = E0cosw1tandE2 = E0cosw2t.

P E EE

t tnl2 2 1 2 2

02

1 2 1 22= = - + +c c w w w w[cos( ) cos( ) ]

(2.4)

In this case, the DC second-order nonlinear polarization P2nl consists of a term

P2w1-w2proportionaltothedifferencefrequencyw1 + w2andatermP2

w1+w2propor-tional to thesumfrequencyw1 + w2.TheproductionofTHzradiationbyopticalrectificationreliesonlowdifferencefrequencygenerationandisdescribedbythe

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termP2w1 - w2.Again,sumfrequencygenerationP2

w1 + w2isnotrelevanttogenerationofTHzradiationbynonlinearopticaltechniques.

Inthesameway,generationofTHz-radiationpulsesfromopticalrectificationoffslaserpulsesisbasedondifferencefrequencymixingofallfrequencieswithinthebandwidthDwofanfsnearinfraredlaserpulse.

Specifically,anfspulse∆tischaracterizedbyalargefrequencybandwidthDw.ThebandwidthofthelaserpulseisdescribedbyaGaussfunctionofwidth1/4G.36

E ww w( ) ∝ --( )

exp 0

2

4G

(2.5)

Inthetimedomain,thefslaserpulseisdescribedbyanopticalfieldoscillatingatfrequencyw0withatimedependencedescribedbyaGaussfunction.

E t E i t t( ) exp ( )exp( )= -0 0

2w G (2.6)

Thebandwidthof theTHz-radiationpulse isdeterminedbydifference frequencygenerationbyallfrequencieswithinthebandwidthofthefslaserpulse.Thetimeprofile of the radiated THz pulse from optical rectification of the fs laser pulseis proportional to the second time derivative of the difference frequency termP2w1 - w2.ThetimedependenceofP2

w1 - w2isdeterminedbytheGaussiantimeprofileoftheopticallaserpulse.

ThephysicsofthelinearelectroopticeffectisdescribedbythesametermP2n1 =

c2E2intheexpansionofc(E)asopticalrectification.TounderstandtherelationshipbetweenopticalrectificationandthePockels’effect,itisnownecessarytodescribepolarizationPandelectricfieldEbyvectorsandthesusceptibilitycbyathirdranktensor.

Quantum mechanical calculations of the polarization for the case of two laserbeamswithfrequencies w2, w1presentinacrystaldemonstratethattheithcomponentofthesecond-ordernonlinearpolarizationpi

w1-w2 isrelatedtothecomponentsjandkoftheelectricalfieldsEj

w1andEkw2viathesusceptibilitytensorcomponentcijk

w1 - w235

p E Ei j kijk

w w w wcw w1 2 1 2 1 2- = - (2.7)

DCopticalrectificationandthelinearelectroopticeffectresultfromEquation2.7consideringthelimitsofw2 - > w1andw2 - > 0,respectively.

w w c w w

2 10 0 1 1→ =p E Ei j kijk (2.8)

w cw w w

200 1 1 1→ =p E Ei j kijk (2.9)

Equations2.8and2.9demonstratethatastrongelectricfieldatfrequencyw1givesrisetoadcpolarizationpi

0andaDCelectricfieldEk0changesthepolarizationpi

w1atfrequencyw1.

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Furthercalculationsdemonstratethatc 0ijkisequaltoc w1jik.Therefore,thethird

ranktensorsare identicalundersimple interchangeof indicesaswellasfrequen-cies.Thisdemonstratestheidentityofopticalrectificationandthelinearelectroopticeffect.Asaresultofthisidentity,itispossibletoestimatethemagnitudeofopticalrectificationfromthelinearelectroopticcoefficientsofamaterial.

The most widely employed crystals for nonlinear optical generation anddetectionofTHzradiationareZnTe,galliumphosphide(GaP),andGaSe.ZnTeand GaP exhibit zincblende structure and 43m point group symmetry. GaSeisahexagonalcrystalwith 62m pointgroupsymmetry.All threecrystalsareuniaxial.Uniaxialcrystalshaveonlyoneaxisofrotationalsymmetryreferredtoasthec-axisoropticalaxisofthecrystal.TheefficacyofZnTe,GaP,andGaSefornonlinearopticalTHzgenerationanddetection is ratedby the linearelec-troopticcoefficientofthematerials.ThelinearelectropticcoefficientsforZnTe,GaP,andGaSeare listed inTable2.1.The relationshipbetweensusceptibilitytensorelementsdescribingopticalrectificationcijk

0 andlinearelectroopticeffectc w

jik is:

c c c w

ijk ikj jik0 0 1

2+ = (2.10)

and the relationship between the linear electrooptic coefficient rjki and the linearelectroopticeffecttensorelement c w

jik is:

rn njki

ejik= -

4

02 2

p c w

(2.11)

Efficient generation and detection of THz radiation by optical rectification andthe Pockels’ effect require single crystals with high second-order nonlinearity orlargeelectroopticcoefficients,propercrystalthicknessandpropercrystalorienta-tionwith respect to the linearpolarizationof theTHz radiation.The surfacesofthecrystalsshouldbeopticallyflatatthelaserexcitationwavelengthsandofhighcrystalline quality (e.g., low levels of impurities, structural defects, and intrinsicstress).

Thebandwidthofanelectroopticcrystal forTHzgenerationanddetection isdeterminedbythecoherencelengthsandopticalphononresonancesinthematerial.

table2.1electroopticCoefficientsofsomeCommonlyusedterahertzemittersanddetectors

Material structure pointgroupsymmetry electroopticCoefficient(pm/V)

ZnTe Zincblende(30)43 30m( ) r41=3.9(30)

GaP Zincblende(30)43 30m( ) r41=0.97(30)

GaSe Hexagonal(53)62 30m( ) r41=14.4(76)

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Infraredactiveopticalphononresonancesresultinstrongabsorptionofelectromag-netic radiationat the absorption frequencies.Thephononabsorptionbands (opti-calphonons)ofamaterial in theTHz frequency rangearenotavailable forTHzgenerationanddetection.

IftherefractiveindicesofthenearinfraredlaserexcitationfrequencyandtheTHzradiationareidentical,thenthebandwidthsoftheTHzradiationdependonlyonthepulsewidthoftheincidentfemtosecondnearinfraredlaserbeam.Further-more,thestrengthofemissionandsensitivityofTHzdetectionwouldincreasesimi-larlyforallfrequencieswithinthebandwidthwithincreasingcrystalthickness.

However, therefractiveindicesforthenearinfraredlaserfrequencyandTHzfrequencyaregenerallynotidentical.Consequently,electromagneticwavesatTHzandnearinfraredfrequenciestravelatslightlydifferentspeedsthroughthecrystal.TheefficacyofnonlinearopticalTHzgenerationanddetectiondecreasesifthemis-matchbetweenthevelocitiesbecomestoolarge.Thedistanceoverwhichtheslightvelocitymismatchcanbetoleratediscalledthecoherencelength.Asaresult,effi-cientTHzgenerationanddetectionatagivenfrequencyonlyoccurforcrystalsthatareequalinthicknessorthinnerthanthecoherencelengthforthisfrequency.

Thecoherencelengthincaseofpulsednear-infraredlaserradiationisdefinedas:11

lc

n nc THzTHz opt eff THz THz

w pw w w

( ) =-| ( ) ( ) |0

(2.12)

with

n nn

opt eff opt optopt

opt

= -∂∂

( )w ll

l

(2.13)

InEquations2.12and2.13,c is thevelocityoflight,wTHz = 2p/uTHz theTHzfre-quency,w0isthenearinfraredexcitationfrequencynTHztherefractiveindexatTHzfrequencies,nopttheindexofrefractionatnearinfraredwavelengthlopt,andnopt effthegroupvelocityrefractiveindicesofthefemtosecondnearinfraredlaserpulse.

THzemissionstrengthofacrystalandsensitivityofanelectroopticTHzdetec-torareproportionaltothethicknessofthecrystal.However,thebandwidthoftheTHzemittercrystalandbandwidthoftheTHzdetectorcrystalalsodependonthecrystal thickness.GenerallyTHzemissionstrengthandTHzemissionbandwidthforacrystalhaveareciprocalrelationship.TheTHzemissionbandwidthincreaseswhenthecrystalbecomesthinner.TheTHzemissionstrengthdecreaseswhenthecrystalbecomesthinner.ThesameruleappliestothesensitivityofanelectroopticTHzdetectorandthedetectorbandwidth.Thinnercrystalshaveahigherbandwidthbutlowersensitivitythanthickercrystalsandviceversa.

ForefficientgenerationofTHzradiationbyopticalrectificationoffemtosecondlaserpulsesfromzincblendestructurecrystals,itisimportanttoselecttheproperorientationofthecrystalwithrespecttothelinearpolarizationofthelaserbeam.ThepreferredcrystalorientationsofselectedmaterialsarediscussedinSections2.3and2.4.

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Incaseofthelongitudinallinearelectroopticeffect,theelectricfieldisappliedparalleltothedirectionofpropagationoftheopticalprobelaserbeam.Incaseofthe transverse linearelectroopticeffect, theelectricfield isappliedperpendiculartothedirectionofpropagationoftheopticalprobebeam.DetectionofTHzradia-tionpulsesisgenerallyperformedusingthegeometryofthetransverseelectroopticeffect.

TheamplitudeandphaseofthesubpicosecondTHz-radiationpulsearemeasuredbyrecordingthephasechangeoffemtosecondnearinfraredlaserpulsestravelingcollinearlyandsimultaneouslywiththeTHzradiationpulsesthroughtheelectro-opticcrystal.TheelectricfieldoftheTHzradiationinducesachangeoftheindexofrefractionofthecrystalviathelinearelectroopticeffectsuchthatthematerialbecomesbirefringent.Thephase retardationGbetween theordinaryandextraor-dinaryrayafterpropagatingthroughthebirefringentcrystalisproportionaltotheamplitudeandphaseoftheTHzelectricfieldE,thecrystalthicknessl,thelinearelectroopticcoefficientr14,theindexofrefractionofthecrystalatthenearinfraredlaserfrequencyno,andthenear-infraredwavelengthl.30

G ∝ 10

341l

ln r ETHz

(2.14)

Furthermore, the phase retardation also depends on the orientation of the crys-tal and directions of polarization of the THz radiation pulse and the near infra-redlaserpulse.37For 43mzincblendestructurecrystals,preferreddirectionsoftheTHzelectricfieldETHz, opticalfieldEopt, andcrystalorientationarediscussed inSections2.3and2.4.

The temporalprofileof theTHzradiation ismappedout in timebydelayingthe much shorter femtosecond near infrared laser pulse with respect to the THzradiation pulse and measuring the phase retardation as a function of the delaybetweenTHzradiationpulseandopticalprobepulse.

2.3 experIMentalresultsoFterahertz-FrequenCyradIatIongeneratIonbyoptICalreCtIFICatIonoFFeMtoseCondlaserpulses

Inthischapter,wereviewtheexperimentalresultsforgenerationofTHzradiationpulsesbasedonopticalrectification.Severalnonlinearopticalmaterialshavebeenreported togenerateTHz radiationbyoptical rectificationofa femtosecondnearinfraredlaserpulse.Table2.2liststhevariouscrystalsinvestigatedforgenerationofTHzradiationbyopticalrectification.Forthesakeoforganization,theexperimentalresultswillbedividedinto threebroadmaterialcategories:semiconductors, inor-ganicelectroopticcrystalsandorganicelectroopticcrystals,andthecharacteristicsoftheemittedTHzradiationwillbediscussedinbriefundereachmaterialcategory.TheperformanceofvariousemitterswillbediscussedonthebasisofbandwidthandamplitudeoftheemittedTHzradiation.WeconcludeourdiscussionbypresentingrecentexperimentaldevelopmentsinTHzemitterresearch.

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2.3.1 maTerialS

2.3.1.1 semiconductors

Asignificantamountofresearchdatingbackasearlyasthe1970shasexploredthegenerationofTHzradiationbyopticalrectificationofpico-andfemtosecondopticalpulsesinnonlinearopticalcrystals.Experimentalworkintheearly1990sreportedthatTHz-frequencyradiationcouldalsobegeneratedbyfemtosecondopticalpulsesincidentonasemiconductorsurface.38,39Thisobservationwasinitiallyexplainedasthedipoleradiationofatime-varyingcurrentresultingfromphoto-excitedchargecarriers in the depletion field near the semiconductor surface.39–41 Although theultrafast photocarrier transport model successfully explained the transverse mag-neticpolarizationoftheemittedTHzradiationandtheobservedemissionmaximaforBrewsterangleincidence,theintensitymodulationoftheemittedTHzradiationobservedwhenthecrystalwasrotatedaboutitssurfacenormalindicatedthattherewasmorethanonemechanismresponsibleforthegenerationofTHzradiation.In1992,Chuangetal.42,43proposedatheoreticalmodelbasedonopticalrectificationoffemtosecondlaserpulsesatsemiconductorsurfaces,whichsuccessfullyexplainedalloftheearlierexperimentalobservations.Theinvestigationofthephysicsofopti-calrectificationindicatesthatdependingontheopticalfluence,theTHzradiationgenerationbyopticalrectificationiseitherasecond-ordernonlinearopticalprocessgovernedbythebulksecond-ordersusceptibilitytensorc2,orathird-ordernonlin-earopticalprocesswherebyasecond-ordernonlinearsusceptibilityresultsfromthemixingofastaticsurfacedepletionfieldandthethird-ordernonlinearsusceptibilitytensorc3.41,44

THzradiationgenerationfromopticalrectificationoffemtosecondlaserpulseshasbeenreportedfrom<100>,<110>,and<111>-orientedcrystalswithzincblendestructure commonly displayed by most III–V (and some II–VI) semiconductors.Thesecrystalshaveacubicstructurewith43mpointgroupsymmetryandonlyoneindependentnonlinearopticalcoefficient,namelyr41 = r52 = r63.30Theorypredictsthatfor<100>-orientedzincblendecrystals,thereisnoopticalrectificationfieldatnormalincidence(asthenonvanishingsecond-orderopticalcoefficientsr41,r52,and

table2.2Materialsusedforgenerationofterahertzopticalrectification

semiconductors InorganicelectroopticCrystals organicelectroopticCrystals

GaAs LiNbO3 4-N-methylstilbazoliumtosylate(DAST)InP LiTaO3 N-benzyl-2-methyl-4-nitroaniline(BNA)CdTeInAsInSbGaPZnTe

(-)2-(a-methylbenzyl-amino)-5-nitropyridine(MBANP)electroopticpolymers

ZnCdTeGaSe

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r63arenotinvolved),whereasathree-foldrotationsymmetryaboutthesurfacenor-malmaybeobservedfor<110>and<111>orientations.Experimentalstudiescon-ductedon<100>,<110>, and<111>orientedGaAs,CdTe,and indiumphosphide(InP)crystals13,17,41and<110>GaPcrystal45areinexcellentagreementwiththetheo-reticalresultsprovidingevidencethatsecond-orderbulkopticalrectificationisthemajornonlinearprocessundertheconditionofmoderateopticalfluence(~nJ/cm2)andnormalincidenceonunbiasedsemiconductors.Adramaticvariationintheradi-atedTHzsignalalongwithpolarityreversalisobservedin<110>and<111>CdTeandGaAscrystals,as theincidentphotonenergyis tunednear thebandgap.13,17,41Thisphenomenoncanbeexplainedasthedispersionofthenonlinearsusceptibilitytensorneartheelectronresonancestate.13,41

THzgenerationbyopticalrectificationhasrecentlyalsobeenreportedfromnar-rowbandgapsemiconductorssuchasindiumarsenide(InAs)andindiumantimonide(InSb)athighopticalfluence(1–2mJ/cm2)andoff-normalincidence.44,46–50Experi-mentalresultsofTHzemissionfrom<100>InSbcrystaland<100>,<110>,and<111>InAscrystalforbothn-andp-typedopingwereexamined.44,49ApronouncedangulardependenceoftheemittedTHzradiationonthecrystallographicorientationofthesamplesaswellasontheopticalpumpbeampolarizationwasobserved.Theexperi-mentalresultsareingoodagreementwiththetheory,whichpredictsthatforhighexci-tationfluence,THzemissionfromnarrowbandgapsemiconductorsresultsprimarilyfromsurfaceelectricfield-inducedopticalrectificationwithsmallbulkcontribution.50This observation is in contrast with the earlier results obtained for wide bandgapsemiconductorssuchasGaAs,inwhichtheTHzemissionisprimarilydominatedbystrongbulkcontribution.TheanomalycanbeexplainedinthelightofthetheoreticalcalculationsbyChingandHuang51wherebynarrowbandgapIII–Vsemiconductors(InAsandInSb)arepredictedtohavethird-ordernonlinearsusceptibilities(c3)sev-eralordersofmagnitudehigherthanthoseoflargerbandgapsemiconductors.

Amongthezincblendecrystals,perhapsthemostpopularcandidateforgenera-tionofTHzradiationbyopticalrectificationisZnTe.Nahataetal.11firstreportedTHzgenerationinZnTeinanexperimentthatusedapairofZnTecrystalsforbothgenerationanddetectionofTHzradiation.Intheirwork,a<110>ZnTecrystalwaspumpedby130femtosecondpulsesat800nmfromamode-lockedTi:sapphirelaser.TheFourierspectrumofthetemporalwaveformdemonstratedabroadbandwidthwithusefulspectralinformationbeyond3THz.Subsequently,Hanetal.12reportedahigherfrequencyresponseof17THzlimitedonlybyastrongphononabsorptionat5.3THz.SystematicstudieshavealsobeenconductedonTHzemitterapplicationofcadmiumzinctellurideternarycrystalswithvaryingCdcomposition.Ithasbeenreported18,52thattheoptimumCdcompositionx=0.05enhancesTHzradiationaswellascrystalqualityofZnTe.

Apart from the zincblende crystals described earlier, GaSe is a promisingsemiconductorcrystalthathasbeenexploitedrecentlyforTHzgenerationwithanextremely large bandwidth of up to 41 THz.15,53 GaSe is a negative uniaxial lay-eredsemiconductorwithahexagonal structurecharacteristicof 62mpointgroupandadirectbandgapof2.2eVat300K.Thecrystalhasa largenonlinearopti-calcoefficient(54pm/V),53highdamagethreshold,suitabletransparentrange,andlow absorption coefficient, which make it an attractive option for generation of

7525_C002.indd 51 11/15/07 10:47:07 AM


broadbandmidinfraredelectromagneticwaves.ForbroadbandTHzgenerationanddetectionusingasub-20fslasersource,GaSeemitter-detectorsystemperformanceiscomparabletoorbetterthantheuseofthinZnTecrystals.UsingGaSecrystalsofappropriatethicknessasemitteranddetectoritisalsopossibletoobtainafrequency-selectiveTHzwavegenerationanddetectionsystem.ThedisadvantageofGaSeliesinthesoftnessofthematerialthatmakesitfragileduringoperation.

2.3.1.2 InorganicelectroopticCrystals

In1971Yangetal.firstdemonstrated thegenerationofTHzradiationbyopticalrectificationofpicosecondopticalpulsesininorganicelectroopticmaterials.IntheirexperimenttheyobservedTHzradiationfromaLiNbO3crystalilluminatedbypico-secondopticalpulsesfromamode-lockedNd:glasslaser.8Inthelate1980s,AustonandcoworkersreportedTHzradiationgenerationbyopticalrectificationinLiTaO3withspectralbandwidthashighas5THz.54AmajordrawbackinthisexperimentwasthedifficultyinextractingtheTHzpulsesfromthegeneratingcrystalbecauseof total internal reflectionowing tosmallcriticalangle(andhighstaticdielectricconstant) inLiTaO3. In their laterpublicationsAustonetal. reportedanapproachthatminimizedthereflectionlossandpermittedtheextractionoftheTHzradiationinto free space.10Zhanget al.9 latermeasured and calculatedoptical rectificationfromLiNbO3andy-cutLiTaO3undernormalincidentopticalexcitation.Thespatio-temporalshapeoftheradiatedTHzpulsewasfoundtobesimilarforbothmateri-alswithLiNbO3emittingastrongersignalbecauseofasmallerdielectricconstantandhencesmaller reflection lossesat thecrystalboundary.ThemaximumsignalobtainedfromLiTaO3wasfoundtobe185timessmallerthanthatemittedbya4-N-methylstilbazoliumtosylate(DAST)organiccrystal.19

2.3.1.3 organicelectroopticCrystals

OrganiccrystalshavebeenarecentsourceofinterestasTHzemittersastheyhavebeenreportedtogeneratestrongerTHzsignalsthancommonlyusedsemiconduc-torsorinorganicelectroopticemittersowingtotheirlargesecond-ordernonlinearelectricsusceptibility.Zhangetal.19firstreportedTHzopticalrectificationfromanorganiccrystal,dimethylaminoDAST,whichisamemberofthestilbazoliumsaltfamily.Electroopticmeasurementsat820nmhavereportedahighelectroopticcoef-ficient(>400pm/V).19

In their work on THz emission by optical rectification of femtosecond laserpulsesinDAST,Zhangetal.observedastrongdependenceoftheradiatedTHzfieldamplitudeonsamplerotationaboutthesurfacenormal,forbothparallelandperpen-dicularorientationsoftheincidentopticalpumpbeam.Theangulardependencewasinexcellentagreementwiththepredictedtheory,withthemaximumsignaloccur-ringfortheangleatwhichtheopticalpolarization,thecrystalpolar“a”axisandthedetectordipoleaxis,werealigned in thesamedirection.19Zhangandcoworkers19alsoreportedthatwitha180-mWopticalpumpbeamfocusedtoa200-µmdiameterspot,thebestDASTsampleprovidedadetectedTHzelectricfieldthatwas185timeslargerthanthatobtainedfromanLiTaO3crystaland42timeslargerthanGaAsandInPcrystalsunderthesameexperimentalconditions.DASThasalsobeenshownto

7525_C002.indd 52 11/15/07 10:47:09 AM


performwellathigherfrequencieswithanobservablebandwidthupto20THzfroma100-µmDASTcrystalshowingasix-foldincreaseoverthatreportedfroma30-µmZnTecrystalunder similarexperimentalconditions.55The frequencyspectrumofDASTshowsacharacteristicstrongabsorption lineat1.1THz(fromTOphononresonance)alongwithsomeadditionalabsorptionlinesbetween3and5THz.Thelatter (with the exception of the line at 5 THz) are significantly weaker than theabsorptionlineat1.1THz,suchthattheTHzamplitudeatthesefrequenciesisstillwellabovethenoiselevel.56

Nahataetal.57advocatedtheuseoforganiccompoundsinpolymericformsforTHz-frequencyradiationgenerationinsteadofsinglecrystalsasthesecompoundsoffersignificantadvantagesoversinglecrystals. Inparticular theyareeasilypro-cessable, can be poled to introduce noncentrosymmetry and have higher nonlin-earcoefficientsthaninorganicmaterials.IntheirexperimentNahataandcoworkersusedacopolymerof4-N-ethyl-N-(2-methacryloxyethyl)amine-4′-nitro-azobenzene(MA1)andmethylmethacrylate(MMA)(commonlyknownasMA1:MMA)forgen-erationofTHzradiationviaopticalrectification.Theradiatedfieldamplitudefroma16-mmthicksample(electroopticcoefficient~11pm/V)wasfoundtobefourtimessmallerthanthatobservedfroma1-mmthicky-cutLiNbO3crystal.However,thecoherence length of the polymer was reported to be 20 times larger. Nahata andcoworkerssuggestedthattheconversionefficacyrelativetoLiNbO3couldbesub-stantiallyimprovedusingavailablepolymerswithsixtimesthenonlinearcoefficientandmillimeter-thickfilmspoledathighfields.Thiscouldbeeasilycreatedbyadielectricstackofthin-poledfilms.58

After the success of DAST and MA1:MMA as THz emitters, Hashimotoetal. reportedTHzemissionviaoptical rectification fromorganicsinglecrystalsof N-substituted (N-benzyl, N-diphenylmethyl, and N-2 naphthylmethyl) deriva-tivesof2-methyl-4-nitroaniline.59WhilenosubstantialemissionwasobservedfromN-diphenylmethylandN-2naphthylmethylderivatives(owingtothestrongphononmodesexistingintherange0to2.5THz),theintegratedintensityoftheTHzradia-tionemittedbyN-benzyl-2-methyl-4-nitroaniline(BNA)wasasintenseasthatbythe DAST crystal under similar experimental conditions. The dynamic range forBNA is limited to 2.1 THz because of a strong phonon mode that exists around2.3THz.Kuroyanagiandcoworkers60laterreportedimprovedsignalintensity(aboutthree timesgreater than thatgeneratedbyZnTe) and increasedbandwidth (up to4THz)fromhighlypurifiedBNAcrystals.

AlthoughDASTandBNAhavebeenreportedtoperformbetterthanZnTewhenusedforTHzgenerationbyopticalrectification, theTHzelectricfieldsgeneratedbythesecrystalsaremorecomplicatedinbothtimeandfrequencydomains.Pho-non bands in these crystals also result in theproduction of smaller rangeof fre-quenciesthanZnTe.Recentinvestigationsofarangeoforganicmolecularcrystalsrevealedthatthecrystal(–)2-(a-methylbenzyl-amino)-5-nitropyridine(MBANP)issuperiortoZnTewhenusedforopticalrectificationat800nm.61MBANPcrystal-lizesinP21monoclinic62andhastheadvantageofbeingrelativelyeasytogrowinsinglecrystals,probablybecauseofitsL-shapedstructureandstrongHbondingincertaindirectionsaswellasasuitablehabit.61Opticalrectificationof800-nmpulsesin<001>-orientedMBANPresulted inTHzpulses that arevery similar to those

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producedbyZnTebothinfrequencyandtimedomain.However,MBANPproducesasignalthatisanorderofmagnitudehigherbecauseofitslargerelectroopticcoef-ficient(18.2pm/Vat632.8nm).63SeveralothercrystalssimilartoMBANPhavealsobeenstudied.61Itwasfoundthat4-(N,N-dimethylamino)-3-acetamidonitrobenzeneand 4-nitro-4′-methylbenzylidene aniline (NMBA) produced THz pulses throughoptical rectificationof 800-nm pulses of comparable strength to MBANP. WhileNMBAiseasytogrow,4-(N,N-dimethylamino)-3-acetamidonitrobenzeneismuchmoredifficultowingtoitsneedle-likehabit,andobtainablecrystalsizeislimited.Strong phonon band absorption also limits the power in the range 1.6 to 3 THz,whichmakesthesecrystalsunsuitableforhigh-frequencyapplications.

We have thus reviewed THz optical rectification from a variety of materialsincludingsemiconductorsandinorganicandorganicelectroopticcrystals.Theper-formanceoftheseemittersintermsofbandwidthhasbeensummarizedinTable2.3.ZnTeisthemostpopularchoiceforTHzgenerationbyopticalrectificationbecauseitcangenerateextremelyshortandhigh-qualityTHzpulses.OrganiccrystalshavebeenofrecentinterestowingtotheirhigherelectroopticcoefficientandenhancedcapacitytogeneratestrongersignalsthanthecommonlyusedZnTe.However,theTHz fields generated by organic crystals such as DAST and more recently BNAaremorecomplicatedinbothtimeandfrequencydomain.Low-frequencyphononbandsalsolimitthebandwidthinthesecrystalsthancomparedwithZnTe.Organiccrystalsalsohavealargenaturallyoccurringbirefringence,whichcomplicatestheirapplication.55ThishasresultedinZnTeremainingtheTHzgeneratorofchoice.ThecomparativeperformanceofaZnTeTHzemitterpumpedbyanamplifiedtitaniumsapphirelasersystemisshowninFigure2.2.64

ThechoiceofasuitableTHzemitteralsolargelydependsontheoperatingcon-ditions.Asmentionedpreviously,toachievereasonableefficacyfornonlinearopti-cal processes, long interaction length and appropriate phase matching conditionsmustbemet.ThephasematchingconditionissatisfiedwhenthephaseoftheTHzwavetravelsatthegroupvelocityoftheopticalpulse.InthecaseofZnTe,thephasematchingconditionandthesubsequentenhancementofcoherencelengthareachievedat800nm,makingitthemostsuitableelectroopticcrystalforTHzwaveemissionanddetectionusingaTi:sapphirelasersystemwithacenterwavelengthof800nm.

table2.3bandwidthperformancesofsomeCommonterahertzemitters

Material

experimentalbandwidth

(thz)

lowestopticalphononresonance

(thz)at300K

Incidentpulse

Wavelength(nm)

IncidentpulseWidth(fs)

detectionscheme

GaAs 40(12) 8.02(71) 800(12) 12(12) ElectroopticGaSe 41(15) 7.1(15) 780(15) 10(15) ElectroopticZnTe 17(12) 5.4(12) 800(12) 12(12) ElectroopticGaP 3.5(45) 10.96(71) 1055(45) 300(45) PCantennaDAST 20(55) 1.1(56) 800(55) 15(55) ElectroopticBNA 2.1(59) 2.3(59) 800(59) 100(59) Electrooptic

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0.1

1

10

100

1000

Fit based on(Darrow et al.)

Estimated based on measuredsaturation properties of ZnTe

(a)

ETHz ∝ JoptPlas

ma 2nd harm

onic

Plasma ext. Field

Plasma (Hamster et al.)

GaAs 10.7 kV/cm(You at al.)

2 mm ZnTe

GaAs 1 kV/cm

Max

imum

Foc

used

Fie

ld A

mpl

itude

(kV/

cm)

1E–4

1E–3

0.01

0.1

1

10

100

1000 (b)


THz P

ulse

Ene

rgy (

nJ) Estimated based on measured

saturation properties of ZnTe

JTHz ∝ Jopt2

Plasma 2

nd harmonic

Plasma ext. field


GaAs 10.7 kV/cm (You et al.)

2 mm ZnTeGaAs 1kV/cm

1 10 100 1000 10000 1000001×10–9

1×10–8

10–7

10–6

10–5

10–4

10–3

10–2 (c)

η ∝ Jopt

η ∝ J opt

η ∝ J opt


Pulse

Ene

rgy C

onve

rsio

n (η

)

Estimated based onmeasured saturationproperties of ZnTe

Optical Pulse Energy (µJ)

Plas

ma 2

ndHar

mon

ic Plasma ext. Field


GaAs 10.7 kV/cm (You et al.)

2 mm ZnTe

GaAs 1 kV/cm

FIgure2.2 ComparisonoftheTHzemissionefficacyofa2-mmZnTecrystalwithothertypesofTHzemitters:(a)thefocusedpeakelectricfield,(b)theTHzpulseenergy,and(c)theenergyconversionefficacyaredisplayedasafunctionoftheenergyperpulseofthefemto-secondnearinfraredpumplaser.(FromLoefflerT.,Semicond. Sci. Technol.20,S140,2005,IOPPublishing.Withpermission.)

7525_C002.indd 55 11/15/07 10:47:14 AM


However,thelargesizeoftheselaserspreventsthemfrombeingusedinportableTHzsystems.Tobuildacompact,integrated,andsensitiveTHzspectroscopyorTHzimagingsystem,ithasthusbecomecrucialtodevelopaTHzwavegenerationanddetectiontechniquecoupledtoanopticalfibercable.Theerbium(Er)-andytterbium(Yb)-dopedfiberlasersoperatingat1,550nmand1,000nm,respectively,areespe-ciallyattractivefromthisviewpoint.Thelargevelocitymismatchandconsequentlyasmallcoherentlength,however,makeZnTeunsuitableforapplicationatthesewave-lengths. Although GaP and CdTe have been suggested as potentially compatiblesemitters for Yb-doped laser systems operating at 1,000 nm, GaAs is an excellentcandidateforTHzwaveemissionwitherbium-dopedfiberlasers.Calculations17showthatthephasematchingconditionissatisfiedat1,050nmand1THzinCdTecrystalsresultinginanenhancementofcoherencelength,whereasGaAscrystalphasematch-ingoccursat1,330nm.Thisopticalwavelength inGaAsis the longestamongallbinarysemiconductors.14Evenat1,550nm,thecoherencelengthstillretainsalargevalue, thus enablingGaAs tobeused a suitable emitter in thiswavelength range.GaAsalsohastheaddedadvantageofhavingitslowestphononresonancelyingathigherTHzfrequencies(10THz)andconsequentlyincreasedbandwidthcapability.ThecoherencelengthofsomeorganiccrystalssuchasBNAisalsoquitelargeinthelongwavelengthregime;however,becauseofthedifficultieshighlightedpreviously,organiccrystalshavenotgainedpopularityasTHzemitters.

2.3.2 recenTDevelopmenTS

TheincreasinginterestinthedevelopmentofnovelTHzsourceshasstimulatedin-depth studies of microscopic mechanisms of THz field generation in conventionalsemiconductors,38–53electroopticmaterials,55–63andanextensivesearchfornewmate-rialstobeemployedinTHzgenerationanddetection.WeconcludeourdiscussiononTHzemittersbyhighlightingsomerecentdevelopmentsinTHzemitterresearch.

The THz emission from nonresonant optical rectification discussed in earliersectionsresultedfromdipolarexcitationsfromsuchmaterialsasGaAs,ZnTe,andLiNbO3.THzemissionmayalsoresult fromnondipolarexcitations.EmissionviaopticalrectificationoffemtosecondlaserpulsesinYBa2Cu3O7,65singlecrystalsofiron (Fe),66andfilmsconsistingofnanosizedgraphitecrystallites67wasobservedandwasfoundtohaveresultedfromquadrupolemagneticdipolenonlinearities.

ForFe,whichcrystallizesinabody-centeredcubiclattice,opticalrectificationis forbiddenby latticesymmetry.Anonvanishingsecond-orderopticalnonlinear-itycan,however,resultfromanelectricquadrupolemagneticdipolecontribution,surface nonlinearity or sample magnetization. Each of these contributions to thesecond-order nonlinear electric susceptibility has a characteristic dependence onsampleazimuthandopticalpumppulsepolarizationforagivencrystalorientation.TheTHzemissionreportedfromFewasfoundtobeapproximatelythreeordersofmagnitudeweakerthanthatfroma1-mmthick<110>ZnTecrystalunderthesameopticalexcitationconditions.

THz emission from metals such as gold and silver has also come to lightrecently.20,21Althoughsecondharmonicgenerationhadbeenreportedfrommetalsurfaces as early as the 1960s, optical rectification of laser light had not beenreporteduntilrecently.Kadlecetal.20,21generatedintenseTHzemissionbyoptical

7525_C002.indd 56 11/15/07 10:47:15 AM


rectificationofp-polarized810-nmlaserpulsesatafluenceof6mJ/cm2ingoldfilms.TheTHzamplitudewasfoundtoscalequadraticallywithopticalfluenceforvaluesupto2mJ/cm2.Thes-polarizedopticalpumpbeamresultedinTHzradiationemis-sion,whichwasapproximatelythreetimesweakerthanthesignalobtainedfromap-polarizedopticalpumpbeam.THzemissionfromsilvershowedadifferentbehav-ior.At thehighestopticalpumpfluence, theemittedTHzradiationwas15 timesweakerthanforgoldandshowedalineardependenceonincidentpumpfluence.20Theserecentexperimentalfindingsreveal thepossibilityofaccessingawealthofnew information about nonlinear optical properties and electronic structures ofmetalsurfacesviafemtosecondopticallyexcitedTHzemissionmeasurements.

2.4 experIMentalresultsoFterahertzeleCtrooptICdeteCtIon

MuchresearchactivityhasbeendevotedtoincreasingthesensitivityandbandwidthofelectroopticdetectionofTHz-frequencyradiationpulses.Otherthanthedurationoftheopticalprobepulse,thebandwidthoffree-spaceelectroopticsamplingisonlylimitedbythedielectricpropertiesoftheelectroopticcrystal.ElectroopticsamplingofTHz-frequencyradiationisapowerfultoolfordetectionofelectromagneticradia-tionpulsesinandbeyondthemid-infraredrange.Avarietyofelectroopticmaterials,includingsemiconductorsandinorganicandorganicelectroopticcrystals,havebeentestedfordetectorapplicationsinTHzspectroscopy.Inthissection,wepresentabriefoverviewoftheexperimentalresultsofbroadbandTHzelectroopticdetectionwithvariousmaterials.

2.4.1 maTerialS

2.4.1.1 semiconductorsandInorganicCrystals

In 1995, Wu and Zhang27 first demonstrated free-space electrooptic sampling ofshortTHz radiationpulses. In their experiment, aGaAsphotoconductive emittertriggeredby150-fsopticalpulsesat820nmradiatedelectromagneticwavesofTHzfrequency.A500-µmthickLiTaO3crystal,withitscaxisparalleltotheelectricfieldpolarization,wasusedastheelectroopticsamplingelement.Toimprovedetectionefficacy,theTHzradiationbeamwasfocusedontothedetectorcrystalbyahigh-resistivitysiliconlens.Thetemporalresolutionof thedetectedTHztransientwaslimitedbythevelocitymismatchbetweenopticalandTHzfrequencies.LaterworkbyWuandZhang68,69addressedthisshortcomingbycarefulgeometricdesignoftheradiationemitterandaspecialcutdetectorcrystal.Asignal-to-noiseratioofabout170:1wasobtainedwitha0.3-secondlock-inintegrationtimeconstant.

WuandcoworkersalsotestedZnTefordetectorapplicationsinanovelexperi-mentalgeometryinwhichtheopticalandTHzbeamsweremadetopropagatecol-linearlyintheelectroopticcrystal.68Inthissetup,a1.5-mmthick,<110>-orientedZnTecrystalwasusedasthedetectorwiththeopticalprobeandTHzbeamsetparal-leltothe<110>edgeoftheZnTecrystalforoptimalelectroopticphasemodulation.Asignal-to-noiseratioofabout10,000:1wasobtainedforasinglescanusingagainalock-inamplifierwithtimeconstantof0.3seconds.Nahataetal.11demonstrateda

7525_C002.indd 57 11/15/07 10:47:16 AM


broadbandtimedomainTHzspectroscopysystemusing<110>-orientedZnTecrys-tals forgenerationofTHzradiationbyoptical rectificationanddetectionofTHzradiationbyelectroopticsampling.

AnimportantconditionforgenerationanddetectionofTHzradiationbynon-linearopticaltechniquesistheappropriatephasematchingbetweentheopticalandTHzpulsesinthenonlinearopticalcrystal.Foramediumwithdispersionatopticalfrequencies,phasematching isachievedwhen thephasevelocityofTHzwave isequaltothevelocityofopticalpulseenvelope(ortheopticalgroupvelocity).11Thedata inFigure2.8showtheeffective indexof refractionofZnTeatopticalwave-lengthsnopteffandTHzfrequenciesnTHz.ThecoherencelengthlcofZnTeatTHzfre-quenciesforanopticalwavelengthl= 780nmdecreasesasillustratedinFigure2.3.ThetemporalwaveformofthemeasuredTHzelectricfieldanditsFourieramplitudeandFourierphasearedisplayedinFigures2.3,2.4,and2.5,respectively.ThepeakoftheTHzpulseamplitudeshowsathree-foldrotationalsymmetrywhentheZnTedetectorcrystalisrotatedby360°aboutanaxisnormaltothe<110>surface.Thisresultisinherenttoall<110>and<111>zincblendecrystals.40Thebroadbanddetec-tioncapabilityofZnTeisobviousfromtheFourieramplitudespectrum(Figure2.4),whichextendswellbeyond2THz.TherolloffinsensitivityforhigherfrequenciesfromphasemismatchandtheshortercoherencelengthareinagreementwithdatapresentedinFigures2.6,2.7,and2.9.Athinnercrystaldetectshigherfrequenciesbetter than a thicker crystal. However, the detector sensitivity of a thinner crys-talisreducedcomparedtoathickercrystal.Inadditiontolimitationsimposedby

2 4 6 8 10

–4

–2

0

2

4

Elec

tro-

optic

Sig

nal (

arb.

uni

ts)

Time (ps)

FIgure2.3 Timedomainmeasurementof aTHzpulsebyelectrooptic samplingwith aZnTecrystal10mm×10mm×1mminsize.TheTHzpulseandtheopticalprobepulseareincidentontothesurfaceoftheZnTecrystalparalleltothe<110>plane.Theopticalaxisofthecrystalisinthe<001>direction.ThelinearpolarizationoftheTHzradiationpulseisperpendiculartotheopticalaxis.Thelinearpolarizationoftheincidentopticalprobepulseisparalleltotheopticalaxis.(AdaptedfromSelig,H.,Elektro-optischesSamplingvonTera-hertzPulsen,Hochschulschrift:Hamburg,Universitaet,FachbereichPhysik,Diplomarbeit,7,2000.Withpermission.)

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phasemismatch,theabsorptioncausedbyatransverseopticalphononresonanceat5.4THz11inZnTeisexpectedtoattenuatethehigh-frequencycomponentsofTHzradiation.LaterexperimentsbyHanandZhang70reportedadetectionbandwidthupto40THzusinga27-µmZnTedetectorcrystal.

0.5 1.0 1.5 2.0 2.5 3.0100

101

102

103

104

Four

ier-

ampl

itude

(arb

. uni

ts)

Frequency f (THz)

FIgure2.4 Fourieramplitudeof the timedomainmeasurementdisplayed inFigure2.3.The bandwidth of the signal is approximately 2.75 THz. The dynamic range of the mea-surement is 500:1. (Adapted from Selig, Hanns, Elektro-optisches Sampling von Tera-hertzPulsen,Hochschulschrift:Hamburg,Universitaet,FachbereichPhysik,Diplomarbeit,7,2000.Withpermission.)

0.0 0.5 1.0 1.5 2.0 2.5 3.01.3×104

1.4×104

1.5×104

1.6×104

1.7×104

1.8×104

1.9×104

2.0×104

Four

ier-

phas

e (ar

b. u

nits

)

Frequency f (THz)

FIgure2.5 Fourier phase of the time domain measurement displayed in Figure2.3.(AdaptedfromSelig,H.,Elektro-optischesSamplingvonTerahertzPulsen,Hochschulschrift:Hamburg,Universitaet,FachbereichPhysik,Diplomarbeit,7,2000.Withpermission.)

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AlthoughZnTedeliversexcellentperformanceinthe800-nmwavelengthregime,itsefficacyisinherentlylimitedbylargegroupvelocitymismatch(GVM)of1ps/mm68betweenoptical andTHz frequencies.An idealmaterialwouldbeonewith largerelectroopticcoefficientand lowerGVM.At886nm,GaAshasbeen found topos-sessamoderateelectroopticcoefficient(25pm/V),butalowGVMof15fs/mm.TheelectroopticcoefficientofLiTaO3was found tobecomparable to thatofZnTe,butLiTaO3hasalargeGVM(>14ps/mm),whereasfororganiccrystalssuchasDAST,theelectroopticcoefficientisverylargebutGVMiscomparabletoZnTe.68Asubstantialimprovementinbandwidthdetectionandsensitivitymaybeobtainedbyusingmateri-alswithphonon resonanceoccurringathigherTHz frequencies.Among inorganicmediawithcomparablenonlinearopticalpropertieszincselenide(lowestTOphononresonanceat6THz),11GaAs(TOphononresonanceat8THz),andGaP(TOphononresonanceat11THz)71areexcellentcandidates.Toverifytheperformanceofelectro-opticsamplingwithGaAs,Vosseburgeretal.72performedtime-resolvedexperimentsofTHzradiationdetectionusingbulkGaAsastheelectroopticsamplingelement.Anexcitationwavelengthof900nmwaschosentoavoidphotoexcitationofcarriersbyinterbandabsorptionintheGaAs.ThemeasuredTHzradiationpulsehadacomplex

0 1 2 3 4 5 6 7 8–6

–4

–2

0

2

4

6

ZnTe 0.5 mmZnTe 1.0 mmEl

ectr

o-op

tic S

igna

l (ar

b. u

nits

)

Time (ps)

FIgure2.6 TimedomainmeasurementsofTHzpulsesbyelectroopticsamplingwithZnTecrystalsofdifferentthickness.Forbothmeasurements,theopticalprobebeamandtheTHzpulsebothincidentontothesurfaceofthecrystalsparalleltothe<110>plane.Thesurfaceofthecrystalsis10mm×10mm.ThelinearpolarizationsoftheincidentTHz-pulseandprobepulseareperpendiculartoeachother.Thepolarizationoftheprobebeamisparalleltotheopticalaxis(<001>direction).Theratioofthepeak-to-peakamplitudeoftheTHzpulsesmeasuredbythe1-mmcrystalandthe0.5-mmcrystalis2.3andscalesapproximatelywiththethicknessofthetwocrystals(1mm/0.5mm=2).ThethickerZnTecrystalexhibitsalargersignalthanthethinnercrystalbecausethephaseretardationG∝l islinearlyproportionaltothethicknessloftheelectroopticcrystal.(AdaptedfromSelig,H.,Elektro-optischesSam-plingvonTerahertzPulsen,Hochschulschrift:Hamburg,Universitaet,FachbereichPhysik,Diplomarbeit,35,2000.Withpermission.)

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0.0 0.5 1.0 1.5 2.0 2.5 3.0100

101

102

103

104

ZnTe 0.5 mm ZnTe 1.0 mm

Four

ier A

mpl

itude

(arb

. uni

ts)

Frequency (THz)

FIgure2.7 FourieramplitudesofthetimedomainmeasurementsdisplayedinFigure2.6.ThethinnerZnTecrystalhasaslightlylargerbandwidththanthethickerZnTecrystal.Thecalculatedbandwidthsofa0.5-mmanda1.0-mmZnTecrystalare2.86THzand2.62THz,respectively. (Adapted from Selig, H., Elektro-optisches Sampling von Terahertz Pulsen,Hochschulschrift:Hamburg,Universitaet,FachbereichPhysik,Diplomarbeit,35,2000.Withpermission.)

0

1

2

3

4

5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

0.5 0.6 0.7 0.8 0.9 1.0

nTHz

Inde

x of

Ref

ract

ion

n

Frequency f (THz)

nopt eff

Optical Wavelength (Nm)

FIgure2.8 IndexofrefractionofZnTeatopticalwavelength(nopteff)andTHzfrequencies(nTHz).Optical radiationat760-µmwavelengthpropagates at the same speedas2.6THz-frequencyradiationinZnTe.Theeffectiveindexofrefractionatl=780µmisnopteff=3.27.(AdaptedfromSelig,H.,Elektro-optischesSamplingvonTerahertzPulsen,Hochschulschrift:Hamburg,Universitaet,FachbereichPhysik,Diplomarbeit,33,2000.Withpermission.)

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temporalstructureandwassmallerbyafactorofapproximately20comparedwiththesamepulsemeasuredbyaZnTecrystal.ThereductioninamplitudehaditsoriginsinthesmallerelectroopticcoefficientofGaAsthanthatofZnTeandpoorphasematchingofGaAsat900mmand1THz.

Amongzincblendecrystals,GaPisanexcellentalternativetoZnTeforelectroop-ticsamplingofTHz-frequencyradiationbecauseofitshigh-frequencyphononbandat11THz,71 thehighestavailableamongallzincblendecrystals.TheelectroopticcoefficientofGaP(r41≈0.97pm/V30),however,isonefourththatofZnTe.In1997,WuandZhang73firstdemonstratedelectroopticsamplingofTHzradiationwithaGaPcrystal.UsingaGaAsemitterexcitedby50-fspulsesanda150-µmthick<110>GaP crystal, they demonstrated a bandwidth resolution up to 7 THz. BroadbandTHzelectroopticsamplingwithGaPcrystalswasfurtherdevelopedbyLeitenstorferetal.74Theycarefullyevaluatedthefrequencydependenceoftherefractiveindex,theelectroopticcoefficientandtheresponsefunctionoftheGaPelectroopticTHzdetector.Usinga13-µmthickcrystaland12-fstitanium–sapphirelaserpulsesthedetectedspectralbandwidthofGaPwasestimatedtobe~70THz.

Oneoftherecentlyreportedmaterialsusedforfree-spaceelectroopticsamplingof THz radiation is ZnSe in crystalline and polycrystalline form.75 Although theelectrooptic coefficient of ZnSe (r41≈ 2pm/V75) is only half of that of ZnTe, theTOphononresonancefrequency(6THz)11ishigherthanthatofZnTe(5.4THz),11thuspromisingahigherdetectionbandwidthpotentialfortheformer.TheGVMforZnSe(0.96pm/V75)iscomparabletothatforZnTe.Usinga10-fstitanium–sapphirelaser pulse to excite a 100-µm GaAs photoconducting antenna and a 0.5-mm,<111>-orientedZnSesinglecrystalasdetector,aspectralbandwidthof3THzwas

Cohe

renc

e Len

gth l c

(mm

)

0.010 1 2 3 4 5

0.1

1

10

Frequency (THz)

FIgure2.9 Calculated coherence length lc of ZnTe as a function of THz frequency forl= 780 µm. (Adapted from Selig, H., Elektro-optisches Sampling von Terahertz Pulsen,Hochschulschrift:Hamburg,Universitaet,FachbereichPhysik,Diplomarbeit,7,2000.Withpermission.)

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measured.Inthisexperiment,thebandwidthdetectedbytheZnSecrystalwaslim-itedonlybythegenerationoftheTHzradiation.Itwasfoundthatforthicker(1mm)polycrystalline electrooptic ZnSe samples, the random nature of crystallographicorientations within the interaction length distorted the phase of THz waveform.However, a reduction of the thickness to 0.15 mm minimized the distortion andextendedthebandwidthupto4THz.Becausepolycrystallinesemiconductorsofferpracticaladvantagesintermsofeaseoffabrication75overtheirsinglecrystalcoun-terparts,thesuccessfulapplicationofpolycrystallinematerialsforfree-spaceelec-troopticsamplingpermitsthepossibilityofutilizingnon-latticematchedthinfilmintegratedelectroopticdetectorsofTHzradiation.

As discussed previously, the mismatch between THz phase velocity and thegroup velocity of the optical probe pulse limits the detection bandwidth of zinc-blende electrooptic crystals such as ZnTe and GaP. However, this limitation canbe eliminated by using a novel detection scheme, taking advantage of the typeII phasematching in a naturallybirefringent crystal such asGaSe.53,76Thephasematchingconditioncanbesatisfiedbyangletuningwherebytheelectroopticcrystal

0.0

0.2

0.4

0.6

0.8

1.0

0

30

6090

120

150

180

210

240270

300

330

0.2

0.4

0.6

0.8

1.0

φ (°)

Elec

tro-

optic

Sig

nal (

arb.

uni

ts)

FIgure2.10 Measurementsof thepeakelectrooptic signal as a functionof theangleΦbetweenthe<001>directionofa<110>ZnTecrystalandthedirectionoflinearpolarizationoftheopticalprobebeam.ThepolarizationoftheTHzpulseisperpendiculartothepolariza-tionoftheopticalprobepulse.Duringthemeasurements,theorientationsofthepolarizationoftheopticalandtheTHzpulsesarefixedandthecrystalisturnedinstepsof10°.AnangleΘ=90°correspondstothesituationinwhichthepolarizationoftheopticalprobebeamispar-alleltothe<001>directionoftheZnTe.TwomajormaximaatΘ=90°andΘ=270°andfourminormaximaatΘ=30°,Θ=150°,Θ=210°,andΘ=330°areobserved.TheamplitudeofthepeakTHzelectricfieldisestimatedtobe5V/m.(AdaptedfromSelig,H.,Elektro-optischesSampling von Terahertz Pulsen, Hochschulschrift: Hamburg, Universitaet, FachbereichPhysik,Diplomarbeit,47,2000.Withpermission.)

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(z-cut GaSe crystal) is tilted by an angleqdet (the phase matching angle) about ahorizontalaxisperpendiculartothedirectionoftime-delayedprobebeam.76IntheexperimentsconductedbyKublerandcoworkers,76aTHzradiationpulsewasgener-atedbyopticalrectificationof10-fstitanium–sapphirelaserpulsesina20-µmthickGaSecrystal(qem =57°)anddetectedwithaGaSesensor(qdet =60°)ofthickness30µm.qdet/em=0signifiesnormal incidence.Theamplitudespectrumof theTHzpulsepeakedat33.8THzandextendedfrom7THztobeyond120THz.Comparedwitha12-µmthickZnTecrystalthatdisplayedalocalminimumat34THzunderthesameexcitation,theGaSespectrumshowedanearlyflatresponsefrom10THzupto105THz.TheenhancedperformanceofGaSecrystalsoverZnTecrystalsisattributedmainlytoagreaterinteractionlengthbecauseofbetterphasematchingandalargerelectroopticcoefficientofGaSe(Table2.4).

2.4.1.2 organicCrystals

InthequestfornovelmaterialsforelectroopticsamplingofTHzradiationpulses,organicelectroopticcrystalshaveattractedattentionowingtotheirveryhighelec-troopticcoefficients.Hanandcoworkers55firstdemonstratedtheapplicationoftheorganicionicsaltcrystalDASTasafreespaceelectroopticdetectorofTHzradia-tion.TheelectroopticcoefficientforDASTis160pm/Vat820nm68andisalmosttwo orders higher than that found in ZnTe (Table2.4). However, DAST exhibitstwoconfirmedphononabsorptionpeaksat1.1THzand3.05THz.77Recently,non-linear optical generation and detection of THz radiation pulses was investigatedtheoreticallyandexperimentallybySchneideretal.77Theydemonstrated that theTHzradiationspectrumgeneratedanddetectedusingDASTcrystalsextendedfrom0.4THzto6.7THz,dependingon the laserexcitationwavelength in the700-nm

table2.4propertiesoftypicalelectroopticsensorMaterials*

MaterialCrystal

structurepoint

group

electroopticCoefficient

(pm/V)

groupVelocity

Mismatch(ps/mm)

surfaceorientation

experimentaldetectionbandwidth

(thz)†

ZnTe Zincblende(30)43 30m( ) r41=3.90(30) 1.1(68) 110(11) 2.5(11)

GaP Zincblende(30)43 30m( ) r41=0.97(30) — 110(73) 7(73)

ZnSe Zincblende(30)43 30m( ) r41=2.00(30) 0.96(75) 111(75) 3(75)

LiTaO3 Trigonal(30) 3m(30) r33=30.3(30)

r13=5.70

14.1(68) — —

GaSe Hexagonal(53)

62 53m( ) r22=14.4(76) 0.10(76) — 120(76)

DAST — — r11=160(68) 1.22(68) — 6.7(77)Poled

polymers— — — — — 33(78)

*Amorecomprehensivelistingmaybefoundinreference68.

†Thebandwidthreportedhereissubjecttoexperimentalconditionsandnottheabsolutebandwidthforaparticularemitter/sensormaterial.

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to 1,600-nm wavelength range. Furthermore, they found that the technologicallyimportantwavelengthsaround1,500nmarevelocitymatchedtoTHzfrequenciesbetween1.5THzand2.7THz.

Amongotherorganicmaterials,poledpolymershavebeenreportedtoexhibitexcellentbroadbandelectroopticdetectioncapability.78Thesematerialsdemonstratelargeelectroopticcoefficients,79lowdispersionbetweentheTHzandopticalrefrac-tive indices,57,80easeof fabrication in largearea thinfilms,andeasilymodifiablechemicalstructuresforbetterTHzandopticalpropertiesbecauseoftheirorganicnature. Using poled polymers for free-space electrooptic detection, Nahata andcoworkers78recentlymeasuredanamplitudespectrumuptofrequenciesof33Hz.

2.5 applICatIonoFeleCtrooptICsaMplIngoFthzeleCtrICFIeldtransIents

Nonlinear techniques for the generation and detection of short pulses of THz-frequencyradiationhavefoundimportantapplicationssuchastimedomainTHzspec-troscopyandtimedomainTHzimaging.34Here,wediscussbrieflytheapplicationof electrooptic sampling of THz radiation pulses to longitudinal electron bunchlengthmeasurements.

Theelectroopticdetectionofthelocalnonradiativeelectricfieldthattravelswitharelativisticelectronbunchhasrecentlyemergedasapowerfulnewtechniqueforsubpicosecondelectronbunchlengthmeasurements.81–84Themethodmakesuseofthefactthatthelocalelectricfieldofahighlyrelativisticelectronbunchthatmovesin a straight line is almost entirely concentrated perpendicular to its directionofmotion.Consequently,thePockels’effectinducedbytheelectricfieldofthepassingelectronbunchcanbeusedtoproducebirefringenceinanelectroopticcrystalplacedinthevicinityofthebeam.Specifically,thebirefringenceinducedbyasingleelec-tronbunchismeasuredbymonitoringthechangeofpolarizationofthewavelengthcomponents of a chirped, synchronized titanium–sapphire laser pulse. When theelectricfieldofanelectronbunchandthechirpedopticalpulsecopropagateintheelectroopticcrystal,thepolarizationsofthevariouswavelengthcomponentsofthechirpedpulsethatpassesthroughthecrystalarerotatedbydifferentamountsthatcorrespondtodifferentportionsofthelocalelectricfield.Thedirectionanddegreeofrotationareproportionaltotheamplitudeandthephaseoftheelectricfield.Thusthetimeprofileofthelocalelectricfieldoftheelectronbunchislinearlyencodedtothewavelengthspectrumoftheopticalprobebeam.Ananalyzerconvertsthemodu-lationofthepolarizationofthechirpedopticalpulseintoanamplitudemodulationofitsspectrum.Thetimeprofileoftheelectricfieldoftheelectronbunchismeasuredasthedifferenceofthespectrumwithandwithoutacopropagatingelectronbunch.Thewidthofthetemporalprofilecorrespondsdirectlytotheelectronbunchlength,andtheshapeofthetemporalprofileisproportionaltothelongitudinalelectrondis-tributionwithintheelectronbunch.Thelengthandtheshapeofindividualelectronbunchesaredeterminedbymeasuringthespectraofsinglechirpedlaserpulseswithanopticalmultichannelanalyzerequippedwithananosecondshutter.Themethodallowsdirectinsituelectronbunchdiagnosticswithahighsignal-to-noiseratioandsubpicosecondtimeresolution.

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Theexperimentalarrangementsfortheelectroopticelectronbunchlengthmea-surements are schematically illustrated inFigure2.11.Theelectronbunch sourceistheradiofrequencylinearacceleratorattheFELIXfreeelectronlaserfacilityintheNetherlands.85TheelectronbeamenergyofFELIXwassetat46MeV,anditschargeperbunchataround200pC.Themicropulserepetitionratewas25MHz,andthemacropulsedurationwasaround8µwitharepetitionrateof5Hz.Atitanium–sapphireamplifier,producing30-fsFWHMpulsesat800nmwitharepetitionrateof1kHz,wasusedasaprobebeam.The30-fsopticallaserpulsesarechirpedtopulsesofupto20ps(FWHM)durationwithanopticalstretcherwhichconsistsofagrating,alens,andaplanemirror.86ThedurationofthechirpedpulseshasbeenmeasuredwithanopticalautocorrelatorbasedonsecondharmonicgenerationinaBBOcrystal.

The electron bunch length is measured inside the accelerator beam pipe attheentranceoftheundulator.A0.5-mmthick<110>ZnTecrystal isusedasan

Ti: SapphireAmplifier

Accelerator

rf-clock

OpticalStretcher

(a)

SpectrometerIntensifierccd

Polarizer Analyzer

ZnTe

FEL Cavity

Undulator

PulseGenerator

Dump

Fiber

e-beam

FEL

Signal

Reference

f

f + ∆z

(a) Optical Stretcher

MirrorLensGrating

FIgure2.11 Experimental setup for electron bunch length measurements by electroop-ticsamplingwithchirpedopticalpulses.Theelectronbunch length ismeasuredbyusinga ZnTe crystal placed inside the vacuum pipe at the entrance of the undulator. The fem-tosecond near infrared laser repetition rate is synchronized with the repetition rate ofthe electron bunches. The inset (a) exhibits a two-dimensional optical stretcher for laserpulse chirping. (Adapted figure with permission from I. Wilke, A. M. McLeod, W. A.Gillespie,G.Berden,G.M.H.Knippels,A.F.G.vanderMeer,Phys. Rev. Lett.88,124801-1(2002).Copyright2002bytheAmericanPhysicalSociety.)

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electroopticsensorandisplacedwithits4×4mm2frontfaceperpendiculartothepropagationdirectionoftheelectronbeam.Theincomingchirpedlaserbeamislinearlypolarized.Theoutgoingchirpedbeamissplitintoasignalbeamanda reference beam used to monitor possible laser power fluctuations. The signalbeam passes through an analyzer (a second polarizer), which is crossed withrespecttothefirstpolarizer.Subsequently,thespectraofthechirpedlaserpulsesaredispersedwithagratingspectrometerandthelinespectraarefocusedontoacharge-coupleddevice(CCD)camera.TheCCDcameraisequippedwithaninten-sifier,whichactsasananosecondshutterwithagatewidthof100ns.Single-shotmeasurements are performed by actively synchronizing the titanium–sapphireamplifier87withboththerepetitionrateoftheelectronbeamandthegateoftheCCDcamera,andthereforerecordingonlythespectrumofonechirpedlaserpulseatatime.Thetemporaloverlapbetweentheelectronbunchandchirpedlaserpulseiscontrolledbyanelectronicdelay.

Figure2.12ashowsmeasurementsof thechirped laserpulsespectrawithandwithoutacopropagatingelectronbunch.ThesignalspectraarelabeledbySandS′.Thecrossedpolarizersexhibitafinite transmissionof1.7% if theelectronbunchdoesnotoverlapwith thechirpedlaserpulse.This isattributedtoasmall intrin-sic stress birefringence of the ZnTe. The transmission of the crossed polarizerschangessignificantlywhentheelectronbunchandthelaserpulsecopropagate:inthesecircumstances,alargepeak,whichcorrespondstoastrongenhancementofthetransmission, isobservedin thecenterof thespectrum.Thestrongchangeofthespectrumisattributedtothewavelength-dependentchangeinpolarizationofthechirpedlaserpulsebecauseoftheelectricfieldoftheelectronbunch.Thelengthand shapeof the electronbunch isobtainedby subtracting the spectrumwithoutcopropagatingelectronbunch,whichhasbeencorrectedforlaserpowerfluctuationsby multiplication with the ratio of the reference spectra R/R′ from the spectrumwithcopropagatingelectron bunch. This difference S-(S′R/R′) is corrected forthewavelength-dependentvariationsinintensityinthespectrumbydividingbythespectrumS′R/R′.Thepixelsareconvertedtotimebymeasuringthelengthofthechirpt, thespectral resolutionof thespectrometerandCCDsetup,Dl/pixel,andthebandwidthofthechirpedlaserpulsesDlbw.Then,thetimeintervalperpixelisgivenby(Dt/pixel) = (Dl/pixel)/(t/Dlbw).ForthespectraofFigure2.12a,thechirpwas4.48psFWHM,whichresultsinanelectronbunchmeasurementasdisplayedinFigure2.12b.Thewidthof theelectronbunchis(1.72±0.05)psFWHM.Thesignal-to-noiseratiodependson theposition in thespectrum; in thecenterof thespectrum,itisbetterthan200:1.Themeasuredwidthandshapeofasingleelectronbunchagreeverywellwiththeelectronbunchmeasurementsaveragedovermorethan8,000electronbunches88andCTRmeasurements.89

Linear accelerators used as drivers for new femtosecond x-ray free-electronlasers or employed in new teraelectron volt linear electronpositron colliders forhigh-energyphysics,requiredense,relativisticelectronbuncheswithbunchlengthsshorterthanapicosecond.Precisemeasurementsoftheelectronbunchlengthanditslongitudinalchargedistributionareimportanttomonitorthepreservationofthebeamquality,whereas theelectronbunch train travels through thebeampipe,aswellastotuneandtooperatealinearcollideroraFEL.

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100 200 300 400

0

1×104

2×104

3×104

4×104

5×104

(a)

SS´

Coun

ts

Pixel

FIgure2.12 Fig.2.12(a)Measurementsofthechirpedlaserpulsespectrawith(s)andwith-out(s′)acopropagatingelectronbunch.(b)singleshotelectronbunchlengthmeasurements.Thewidthoftheelectronbunchis(1.72± 0.05)psFWHM.

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