Ultrafast Laser Technology and Spectroscopy · 2019. 5. 11. · Ultrashort pulses are generated by...

Ultrafast Laser Technology and Spectroscopy

Gavin D. Reid and Klaas Wynne

inEncyclopedia of Analytical Chemistry

R.A. Meyers (Ed.)pp. 13644–13670

John Wiley & Sons Ltd, Chichester, 2000

ULTRAFAST LASER TECHNOLOGY AND SPECTROSCOPY 1

Ultrafast Laser Technologyand Spectroscopy

Gavin D. ReidUniversity of Leeds, Leeds, UK

Klaas WynneUniversity of Strathclyde, Glasgow, UK

1 Introduction 1

2 Ultrafast Lasers and Amplifiers 22.1 Oscillators 22.2 Dispersion and Pulse Broadening 32.3 Chirped-pulse Amplification 62.4 Pulse Recompression 82.5 Saturation Effects 9

3 Wavelength Conversion 93.1 White-light Generation and the

Optical Kerr Effect 93.2 Generation of Ultraviolet and

X-rays 103.3 Optical Parametric Amplifier for

Infrared Generation 113.4 Noncollinear Optical Parametric

Amplification 123.5 Terahertz-pulse Generation and

Detection 123.6 Femtosecond Electron Pulses 14

4 Time-resolved Experiments 144.1 Auto- and Cross-correlation 144.2 Pump–Probe Techniques 17

5 Applications 185.1 The Study of Fast Chemical

Reactions 185.2 Imaging 205.3 Structure Determination: Electron

Beams and X-rays 21

Acknowledgments 22

Abbreviations and Acronyms 22

Related Articles 22

References 23

Ultrafast laser technology and spectroscopy involves theuse of femtosecond (10�15 s) laser and other (particle)sources to study the properties of matter. The extremelyshort pulse duration allows one to create, detect and studyvery short-lived transient chemical reaction intermediates

and transition states. Ultrafast lasers can also be usedto produce laser pulses with enormous peak powers andpower densities. This leads to applications such as lasermachining and ablation, generation of electromagneticradiation at unusual wavelengths (such as millimeter wavesand X-rays), and multiphoton imaging. The difficultyin applying femtosecond laser pulses is that the broadfrequency spectrum can lead to temporal broadening ofthe pulse on propagation through the experimental set-up.In this article, we describe the generation and amplificationof femtosecond laser pulses and the various techniques thathave been developed to characterize and manipulate thepulses.

1 INTRODUCTION

Ultrafast spectroscopy has become one of the most activeareas of physical chemistry. Rather than postulatingmechanisms for chemical and biological reactions, ultra-short laser pulses can now be used to observe and evencontrol the outcome of reactions in real time. Becauseof our improved understanding of reaction pathways,the ‘‘arrows’’ describing purported electronic motion inmechanistic organic chemistry are no longer sufficient..1/

A state-of-the-art laser system can generate 1-J ca. 20-fspulses and the peak fluence at the focus of these lasers canexceed 1020 W cm�2. In contrast, the total solar flux at theEarth is only 1017 W. An exciting new era is beginning,which will allow the possibility of using these intenseultrashort laser pulses as sources of short X-ray and elec-tron pulses. These will reveal the positions of atoms as afunction of time as reactants proceed to products throughthe transition states. More routinely, femtosecond laserscan be used to detect and monitor transient chemicalspecies in solution or the gas phase, to image living cellswith micrometer resolution, for laser ablation mass spec-trometry (MS) and micromachining applications, whichwill all be of immediate interest to the analytical chemist.

With the invention of flash photolysis in 1950,.2/ radicalintermediates were observed by light absorption (ratherthan fluorescence) during the progress of a chemicalreaction. When the pulsed laser followed, nanosecondexperiments derived from the flash-photolysis techniquewere to reveal the chemistry of singlet states in solution.However, it was not until the mode-locked ruby.3/ andNd : glass.4/ lasers were built in the mid-1960s that thepicosecond timescale became accessible and the field of‘‘picosecond phenomena’’ was born. When excited-stateprocesses were studied in the picosecond domain, such asenergy redistribution in molecules and proteins, protonand electron transfer reactions, photoisomerization anddissociation, and relaxation in semiconductors, many

Encyclopedia of Analytical ChemistryR.A. Meyers (Ed.) Copyright John Wiley & Sons Ltd

2 GENERAL ARTICLES

measured rate constants were found to be instrumentlimited. Nevertheless, important results such as theobservation of the ‘‘inverted region’’ in electron transferreactions.5 – 7/ and Kramers’ turnover in excited-statereactions in solution..8,9/

However, ultrafast spectroscopy was revolutionized inthe 1980s by the invention of the colliding-pulse mode-locked (CPM) dye laser, which generated 100-fs pulsesin its early form.10/ and 30-fs pulses as the technologywas perfected..11/ This ring laser, operating at about620 nm, coupled with improvements in dye–amplifierchains,.12/ allowed the exciting field of femtochemistryto be developed,.13/ which will be discussed briefly insection 5.1, and the generation of 6-fs probe pulses,.14/ arecord which stood until very recently. Self mode-lockingin Ti : sapphire-based lasers was discovered.15/ in 1990and the early 1990s brought a new revolution – simplicityof use – and, with it, the commercialization of ultrashortpulse technology. Ti : sapphire oscillators now produce10–20-fs pulses routinely and 4–5-fs pulses in optimizedconfigurations using mirrors designed to reverse the‘‘chirp’’ introduced by the Ti : sapphire rod. The limitingfactor on the exceptional stability of these oscillatorsis the pump source and here diode-pumped solid-statelaser sources are rapidly replacing large, expensive, low-efficiency ion lasers.

In parallel with improvements in oscillator technol-ogy, the technique of chirped pulse amplification.16/

using solid-state gain media in regenerative or multi-pass schemes has replaced the dye–chain amplifiers ofthe past. A typical amplifier for routine chemistry appli-cations produces 1 mJ per pulse at a 1-kHz repetitionrate or 100 mJ at 10–20 Hz with a duration between 20and 100 fs. Moreover, a Ti : sapphire laser oscillator andamplifier combination can be purchased in a single boxless than 1 m square, operating at mains voltages withno external water-cooling requirements. Total hands-offoperation is a reality and, in fact, the complete lasersystem can be computer controlled.

In the next section, we shall describe the technologybehind Ti : sapphire lasers and amplifiers and discuss howlight at almost any frequency from X-rays to terahertz canbe generated and employed by the chemist. A history ofthe field can be found in the papers submitted to the bien-nial conference ‘Ultrafast Phenomena’, the proceedingsof which are published in the Springer Series in ChemicalPhysics, which is now in its eleventh volume..17/

2 ULTRAFAST LASERS AND AMPLIFIERS

2.1 Oscillators

Ultrashort pulses are generated by mode-locked lasers.By constructive interference, a short pulse is formed

when many longitudinal modes are held in phase in alaser resonator. Various techniques have been employed,usually grouped under the terms ‘‘active’’ or ‘‘passive’’mode locking and descriptions of these can be found inmany standard texts.18,19/ and review articles..20/ Activemode locking uses a modulator in the laser cavity whereaspassive schemes use a saturable absorber, often a thinsemiconductor film, to lock the relative phases. Modernsolid-state mode-locked lasers use a different schemecalled self-mode-locking and titanium-doped sapphire(Ti : sapphire) has become by far the most commonlaser material for the generation of ultrashort pulses.Developed in the mid-1980s,.21/ Ti : sapphire has a gainbandwidth from 700 to 1100 nm peaking around 800 nm,the broadest of the solid-state materials yet discovered,high-gain cross-section and extremely good thermalconductivity. Mode locking is achieved through the actionof an instantaneous nonlinear Kerr lens in the laser rod(see section 3.1). The peak fluence of the laser approaches1011 W cm�2, which is enough to focus the beam as ittravels through the gain medium on each pass. This Kerrlens then couples the spatial and temporal modes andmaintains phase locking.

A basic oscillator–cavity configuration.22/ is shownschematically in Figure 1. The laser is pumped by about5 W from a continuous wave (CW) laser source, usuallynow an intracavity-doubled diode-pumped neodymiumlaser. This light is focused into the Ti : sapphire rod,collinearly with the laser axis, through the back of one ofthe mirrors. The cavity consists of a Brewster-angle cutTi : sapphire rod, 5 mm or less in length, doped to absorbabout 90% of the incident pump radiation, two concavefocusing mirrors placed around it, a high reflector andan output coupler. A pair of Brewster-cut fused-silicaprisms are inserted to control the spectral dispersion(chirp) introduced in the laser rod. Dispersion arisesfrom the variation of the refractive index of the materialacross the gain bandwidth of the laser, which can lead toa temporal separation of the resonant wavelengths and

Pump laser (~5W CW)

HROC

(10%)P1

P2

P3P4

λ/2

L

M1M2

Ti:sapphire

Figure 1 Diagram of a basic self-mode-locked Ti : sapphireoscillator showing the cavity layout. The pulse is coupled outfrom the dispersed end of the cavity, which requires a pair ofmatching extracavity prisms.


place a limit on the generated bandwidth (see section 2.2).The cavity dispersion, coupled to the Kerr lens effect, is anintrinsic part of the pulse-formation process. Ordinarily,the Kerr lens in the rod would contribute to the overallloss but this is overcome by a small adjustment to theresonator. Displacement of one of the curved mirrorsby only ca. 0.5 mm pushes the cavity into pulsed mode.Here the cavity is corrected for the nonlinear lens effectand CW operation is restricted. Pulsing is establishedby perturbing the cavity to introduce a noise spike,literally by tapping a mirror mount. This configurationdelivers 12-fs pulses centered at 800 nm with 5 nJ energyat an 80-MHz repetition rate. Using a shorter rod,shorter pulses have been obtained.23/ as the dispersion isbetter compensated and space–time focusing effects arecontrolled. The laser repetition rate can be adjusted bythe insertion of a cavity dumper in a second fold, withoutprejudice to the pulse duration..24/ The use of mirrors thathave dispersion opposite to that of the rod.25/ obviatesthe need for prisms entirely. Alternatively, a mixture ofprisms and mirrors can be used to generate pulses asshort as 5 fs..26/ At the time of writing, the use of mirrorswith well-defined chirp characteristics is complicated bythe demand for extreme tolerances in the manufacturingprocess. Many schemes have been proposed for self-starting oscillators, perhaps the best of which is the use ofa broadband semiconductor saturable-absorber mirror inthe cavity..27/ Advances in these areas will surely continue.

Other important solid-state materials include Cr : Li-SAF (chromium-doped lithium–strontium–aluminumfluoride), which can be pumped by red diode lasersand operates close to the peak Ti : sapphire wave-length, and Cr4C : YAG, which lasers at around 1.5 µm,an important communication wavelength. Cr : forsteritelases, operating at about 1.2 µm, can be frequency dou-bled to the visible region and have been used forimaging applications (see section 5.2). Furthermore, pas-sively mode-locked frequency-doubled erbium-dopedfiber lasers have been developed commercially. Theselasers operate between 1530 and 1610 nm and efficientfrequency doubling to 765–805 nm is possible in period-ically poled nonlinear crystals (i.e. these lasers can beused in place of Ti : sapphire for many applications)..28/

They have the advantage of being cheap and extremelycompact since they do not require complicated dispersion-compensation schemes, owing to the soliton natureof the pulses supported in the fiber. They can alsobe pumped using cheap large-area telecommunications-standard laser-diode sources. Unfortunately, the pulseduration is limited to a minimum of about 100 fs.

2.2 Dispersion and Pulse Broadening

A bandwidth-limited pulse has a spectral width givenby the Fourier transform of its time-domain profile.

(a)Propagation direction

(b) M Propagation direction

Figure 2 Schematic diagram of the electric field of (a) an undis-persed Gaussian pulse and (b) the same pulse after travelingthrough a positively dispersing medium, M. A frequency sweepfrom low to high frequency (right to left) can be observed onthe trace in (b).

Consequently, a 10-fs full width at half-maximum (fwhm)Gaussian pulse centered at 800 nm has a bandwidth of94 nm (1466 cm�1). When a short pulse travels througha dispersive medium, the component frequencies areseparated in time. Figure 2(a) and (b) shows the effect ofdispersion on a Gaussian pulse traveling through a pieceof glass. There are two points to note. First, the centerof the pulse is delayed with respect to a pulse travelingin air. This is usually called the group delay, which is nota broadening effect. Second, normally dispersive mediasuch as glass impose a positive frequency sweep or ‘‘chirp’’on the pulse, meaning that the blue components aredelayed with respect to the red.

In order to get a physical feel for the effect of the chirp,it is common to consider the phase shift as a functionof frequency w. The phase, j.w/ can be developed as apower series about the central frequency w0, assumingthe phase varies only slowly with frequency according toEquation (1):

j.w/ D j.w0/C .w� w0/j0.w0/C 12 .w�w0/2j00.w0/C 16 .w�w0/3j000.w0/C 124 .w�w0/4j0000.w0/C Ð Ð Ð

.1/where (Equation 2):

j0.w0/ D @j@j

∣∣∣∣wDw0

, j00.w0/ D @2j

@w2

∣∣∣∣wDw0

,

j000.w0/ D d3j

dw3

∣∣∣∣wDw0

, etc. .2/

j0 is the group delay, j00 the group delay dispersion(GDD) [or group velocity dispersion (GVD)] and j000

4 GENERAL ARTICLES

and j0000 are simply the third-order dispersion (TOD) andfourth-order dispersion (FOD).

For the sake of simplicity, consider a transform-limitedGaussian pulse with a central frequency w0 and a pulsewidth (fwhm) tin. Then its electric field, Ein, takes theform (Equation 3)

Ein.t/ D E0 exp[�(

2 ln 2t2

tin2

)C iw0t

].3/

The electric field after traveling through a dispersivemedium can be found by transforming Ein to the fre-quency domain and adding the components from thephase expansion j.w/ in Equation (1) before transform-ing back. If we assume only a contribution from the GDDterm, the electric field Eout is given by Equation (4):.18/

Eout.t/ D E0 exp[i.w0t � j/� .t � j0/2

].4/

where (Equation 5)

D(

t2in2 ln 2

C 2ij00)�1

.5/

The effects of this dispersion are twofold. First, byinspection of the Gaussian part of Eout, tout is analogousto tin from Ein and is broadened with respect to theinput-pulse width by a factor (Equation 6)

tout

tinD√

1C j002

t4in16.ln 2/2 .6/

Second, a frequency sweep is introduced in the outputpulse (because the expression in Equation (5) is complex)with a sign that is opposite to that of j00.

The GDD, j00m, due to material of length lm, is relatedto the refractive index of the material, n.l/, at the centralwavelength, l0, through its second derivative with respectto wavelength (Equation 7):

j00m D

l30lm2pc2

d2n.l/dl2

.7/

Figure 3(a) shows the variation of refractive index withwavelength for some common materials and Figure 3(b)shown the GDD. The data were obtained from glasssuppliers and the fits are to Sellmeier-type equations,which are then used to take the numerical derivatives foruse in subsequent calculations.

Using Equations (6) and (7) together with refractiveindex data, we can calculate values for the GDD arisingfrom a length of material. Figure 4 shows the effect of10 mm of fused silica on a short pulse. Silica is one of theleast dispersive materials available and 10 mm is chosento represent one or two optical components, which mightbe part of an experimental arrangement. If we consider

λ (nm)500 15001000 2000 2500 3000

n

1.5

1.6

1.7

1.8

A

B

D

C

(a)

λ (nm)500 1000 1500 2000 2500 3000

GV

D (

103

fs2 )

−0.2

−0.1

0.0

0.1

0.2

A

B

DC

(b)

Figure 3 (a) Refractive index versus wavelength data for somecommon materials: (A) fused silica, (B) Schott BK7, (C) SchottSF10 and (D) sapphire. The points are measured values and thelines are fits to Sellmeier equations. (b) The GDD for 1 mm ofmaterial derived from the fits.

Input pulse width (fs)

0 50 100 150 200

Out

put p

ulse

wid

th (

fs)

50

100

150

200

Figure 4 Gaussian pulse width before and after 10 mm offused silica (solid line), corresponding to one or two opticalcomponents. The broadening is due to GDD.

a pulse of around 100 fs in duration, the effect is minimalbut visible. However, a 10-fs pulse is broadened by morethan a factor of 10!


p1

p2

b

l p

ϕ2

αϕ1

r

(a)

p1

p2

r b

γlg

(b)

Figure 5 (a) Prism and (b) grating pairs used in the controlof dispersion; r and b indicate the relative paths of arbitrarylong- and short-wavelength rays. j1 is the (Brewster) angle ofincidence at the prism face. The light is reflected in the planep1 –p2 in order to remove the spatial dispersion shown.

A good understanding of dispersion is essential inorder to deliver a short pulse to the sample and carefulcontrol of the phase shift is necessary. Fortunately, anumber of designs using prism and grating pairs have beendevised whereby this can be achieved..29/ The two mostimportant schemes are shown in Figure 5(a) and (b). TheTi : sapphire oscillator we discussed above uses the prismpair..30/ This arrangement creates a longer path throughthe prism material for the red wavelengths compared withthe blue, introducing a negative dispersion. Providedthat the prism separation, lp (defined tip to tip), issufficiently large, the positive dispersion of the materialcan be balanced. The prism apex angle is cut such that atminimum deviation of the center wavelength, the angleof incidence is the Brewster angle. Here, the Fresnelreflection losses for the correct linear polarization areminimized and the system is essentially loss free. Thesecond scheme is the parallel-grating pair.31/ and, again,a longer path is created for the red over the blue. Gratingpairs (Figure 6) introduce negative GDD at very modestseparation leading to compact designs but suffer fromlosses of close to 50% in total. Both prism and grating

G1 G2

M

L1 L2

f f2f

γ

lglg

Figure 6 Schematic diagram of a grating-pair pulse stretchershowing the arrangement for positive dispersion. G1 and G2 arediffraction gratings, L1 and L2 are identical lenses separated bytwice their focal length, f , and M is a mirror acting to double-passthe beam through the system. The distance lg – f determines thetotal dispersion.

pairs are used in a double-pass arrangement to removethe spatial dispersion shown in the diagram.

Expressions for calculating the dispersion are givenin Table 1. The equations look a little daunting butthe dispersion can be modeled easily on a personalcomputer. To illustrate this point, Figure 7 shows thetotal GDD and TOD arising from 4.75 mm of sapphirebalanced against a silica prism pair separated by 60 cm.This is typical of a Ti : sapphire oscillator. The net GDDis nearly zero at 800 nm but the net TOD remainsnegative at the same wavelength. In fact, it is a generalobservation that prism compressors overcompensate thethird-order term. The greater the dispersion of the glass,the less distance is required, but the contribution of thethird-order term increases. Experimentally, there mustusually be a compromise between prism separation andmaterial.

Grating pairs are important in amplification and will beconsidered in more detail below. Significantly, however,the sign of the third-order contribution from the gratingpair is opposite to that of the prisms, allowing a combinedapproach to dispersion compensation, which has beenused to compress pulses in the 5-fs regime..14/ It can bemore useful to think in terms of the total GDD versuswavelength with a view to keeping the curve as flat andas close to zero as possible across the full bandwidth ofthe pulse.

Mirror coatings have been developed which canprovide second- and third-order compensation. Thisso-called ‘‘chirped’’ mirror reflects each wavelengthfrom a different depth through the dielectric coat-ing, which is made up of multiple stacks of varyingthickness. In combination with a prism pair, this tech-nique has been as successful as the grating/prismcombination without the associated losses. This typeof system will become more common as the mirrors,tailored to individual requirements, become availablecommercially.

6 GENERAL ARTICLES

Table 1 Expressions (Equations 8–17) for the dispersion formaterial, prism and grating pairs

The accumulated phase in a double-pass prism compressor (seeFigure 5a) is

j.w/ D 2wlpc

cos(jbluest2 � j2

).8/

where j2 is the (frequency-dependent) exit angle, jbluest2 Dj2.wbluest/ is the exit angle of the shortest-wavelength lighttransmitted by the prism pair:

j2.w/ D arcsinfn sin[a� arcsin.n�1 sinj1/]g .9/where n is the (frequency-dependent) refractive index of theprism material, j1 is the (frequency-independent) angle ofincidence on the first prism and a is the prism top angle. Ifthe prism compressor is designed for frequency wdesign:

a D 2 arcsin 1√

1C n2design

.10/j1 D arcsin

[ndesign sin

(a2

)].11/

where ndesign is the refractive index of the prism at the designwavelength. Expressions for the group delay, GVD, TOD andFOD can be obtained by taking derivatives of Equation (8).

The group delay in a grating compressor/stretcher (see Figures 5band 6) is

djdwD P

c.12/

where the optical pathlength is

P D L 1C cos qcos.g� q/ .13/

q.w/ D g� arcsin(

2pcwd� sin g

).14/

with g the angle of incidence on the first grating and d the groovefrequency. In the case of a grating compressor, L D lg. In thecase of a grating stretcher, L D 2.lg � f / cos g.

Expressions for the GVD, TOD and FOD can be obtained bytaking derivatives of Equation (12). For a double-pass gratingcompressor/stretcher, the analytical expression

d2jdw2D �l

3Lpc2d2

[1�

(l

d� sin g

)2]�3/2.15/

is found, where l is the wavelength.

The accumulated phase in material is

j.w/ D wnlmc

.16/

where lm is the length of the material. Expressions for thegroup delay, GVD, TOD and FOD can be obtained by takingderivatives of Equation (16). An analytical expression for theGVD is

d2jdw2D l

3lm2pc2

d2ndl2

.17/

Wavelength (nm)600 700 800 900 1000

GV

D (

fs2 )

TO

D (

fs3 )

−300

−250

−200

−150

−100

−50

0

50

−1500

−1000

−500

0

500

1000

Figure 7 The residual GVD and TOD arising from the balancebetween the dispersion of a 4.75-mm Ti : sapphire laser rod andthe intracavity silica prism pair separated by 60 cm.

2.3 Chirped-pulse Amplification

The amplification of nanojoule-level femtosecond pulsesto the millijoule level and above is complicated by theextremely high peak powers involved. A 1-mJ 20-fs pulsefocused to a 100-µm spot size has a peak fluence of5ð 1012 W cm�2. The damage threshold of most opticalmaterials is only a few gigawatts per square centimeter,1000 times lower. The problem is overcome by stretchingthe pulse in time using dispersion to advantage. This isfollowed by amplification and subsequent recompressionto the original pulse duration. This technique also has thebenefit of eliminating unwanted nonlinear effects in theamplifier materials. A diagram showing the principle ofchirped-pulse amplification (CPA) is shown in Figure 8.

The pulse stretcher is a variation of the grating pairdescribed above..32/ A unity-magnification telescope isplaced between two gratings in an antiparallel rather thanparallel geometry. This reverses the sign of the dispersion

O S A C

b r

b r

Figure 8 Diagram showing the principle of CPA. The oscillatoroutput (O) is stretched in the grating stretcher (S) such that thered frequency components (r) travel ahead of the blue (b). Thepeak intensity is reduced in the process. The stretched pulseis then amplified in a regenerative or multipass amplifier (A)before recompression in a grating-pair compressor (C).


of the grating pair but otherwise the mathematicalexpressions given in Table 1 are identical.

The stretching factor is defined by the effective gratingseparation L D 2.lg � f /, where f is the focal length ofthe lens and lg the distance from the lens to the grating.Typically, the pulse duration is increased to 100 ps ormore for efficient extraction of the stored energy. Whenlg is equal to f , there is no dispersion, and when lgbecomes larger than f , the dispersion changes sign. Inpractice, the lenses are replaced by a single spherical orparabolic mirror in a folded geometry, which eliminateschromatic aberration and allows gold-coated holographicgratings to be used near their most efficient Littrowangle of incidence, arcsin.lc/2d/, where lc is the centralwavelength and d the line separation of the grating. Othermore sophisticated stretcher designs, one for examplebased on an Offner triplet,.33/ have been made but areoutside the scope of this discussion. Ignoring the amplifierfor now, the pulse is recompressed using an identicalparallel grating pair separated by 2lg.

CPA technology developed rapidly during the 1990s.Solid-state materials usually have long upper-state radia-tive lifetimes compared with laser dyes. The largesaturation fluence (1 J cm�2) and long storage time (3 µs)of Ti : sapphire make it an ideal amplifier gain material.Here we shall consider two basic schemes, the regenera-tive and the multipass amplifier. These operate either at10–20 Hz, pumped by a standard Q-switched Nd : YAGlaser giving up to 100 mJ at 532 nm, or at 1–5 kHz pumpedby an intracavity-doubled acousto-optically modulatedCW Nd : YLF laser, which usually provide more than10 W at 527 nm in a 200-ns pulse. These pump lasers arenormally flash-lamp pumped but diode-pumped equiva-lents have appeared commercially in recent months. Agood spatial mode quality is essential and a clean top-hatprofile is ideal.

Figure 9(a) and (b) shows two arrangements for regen-erative amplification. The arrangement in Figure 9(a) isoften used at 1 kHz..34/ Briefly, a single vertically polar-ized pulse from the oscillator, stretched to ¾100 ps, isinjected into the amplifier using a fast-switching PC. Thisis performed by stepping the voltage in two stages, first bya quarter wave, in order to trap the pulse in the amplifiercavity, and then up to a half wave for ejection. Typically,the pulse makes around 12 round trips in the cavity beforethe gain is saturated. A FR is used to isolate the outputpulse from the input. The arrangement in Figure 9(b).35/

differs in two respects. First, the focusing in the cavityis relaxed in order to remain near the saturation fluencefor the more energetic pulses at 10 Hz. Second, the PC isused to switch the pulse in and out while it is travelingin opposite directions. This has two great advantages forshort pulses: (1) there is only one pass made through theFaraday isolator, which has extremely large dispersion

M1 Ti : sapphire M2

TFP

TFP

Input

Output

PC

M3FR

λ/2

Pump

(a)

M1 Ti : sapphire M2TFPTFP

Input Output

PCPump

(b)

Figure 9 Two schemes for regenerative amplification. Thedesign in (a) is often used for kilohertz repetition rate amplifiersand that in (b) at a 10–20-Hz repetition rate. The Ti : sapphirerod is usually ca. 20 mm long and doped for 90% absorption.TFP, thin-film polarizing beamsplitter; PC, Pockels cell; FR,Faraday rotator; l/2, half-wave plate. In (a), M1 is 150 mmradius of curvature, M2 is 1 m and M3 is flat. In (b) M1 is �20 mand M2 is C10 m.

and only a limited spectral bandwidth, and (2) it is onlynecessary to apply a half-wave voltage to the PC at themoment the pulse is switched in or out of the cavity.Again, this is to avoid bandwidth-limiting effects.

An alternative and perhaps more straightforwarddesign for amplification of femtosecond pulses is basedon the multipass scheme that has been used in the pastwith dye amplifiers. One of the best arrangements for useat kilohertz repetition rates.36/ is shown in Figure 10 andan example of a 10-Hz system can be found in a paper byChambaret et al..37/ A PC is used to inject a single pulsefrom the 80-MHz pulse train into the amplifier, where itis allowed to make about eight passes with a slight offsetat each cycle before being picked off and ejected. The

Ti : sapphire

M1

M3

M2

PC

Figure 10 Multipass-amplifier arrangement. M1, M2 are 1-mradius of curvature mirrors and M3 is flat and up to 15 cm wide.A PC and a pair of polarizers are used to inject a single pulseinto the amplifier.

8 GENERAL ARTICLES

pulse incurs significantly less loss in these arrangements,accrues much less chirp and only one pass is made throughthe PC. There is also no need for a Faraday isolator.

Additional power-amplification stages may be added toincrease the pulse energy further. The ring configurationcan be modified by arranging for the beams to cross awayfrom the focus to achieve a different saturation fluence.In this configuration, 4 W after recompression at 1 kHzhas been obtained..38/ At kilohertz repetition rates, thepresence of a thermally induced refractive index changeacross the spatial profile of the beam must be avoidedin order to achieve diffraction-limited output. This isachieved either by cooling to 120 K where the thermalproperties of sapphire are much improved.39/ or by usingthe lens to advantage..40/ At lower repetition rates, themedium has time to recover and a thermal lens is usuallynot established. In this regime, power amplifiers can beadded to the limit of available pump energy. An additionalcomplication requires that short pulses of more than a fewmillijoules in energy must be recompressed under vacuumto avoid nonlinear effects and ionization of the air.

2.4 Pulse Recompression

Clearly, the amplification process introduces extra dis-persion and one of the major considerations in system

λ (nm)760 780 800 820 840

GV

D (

103

fs2 )

0

2

4

6

8

A

B

C

Figure 11 Solid line (A): the net GVD due to the stretcher–amplifier–compressor combination using 1200 lines mm�1 diff-raction gratings. The difference between the angle of incidencein the stretcher compared to the compressor is 10.32° and theextra grating displacement is 69.4 mm. Dashed line (B): thesame using 1200 lines mm�1 gratings in combination with anSF18-glass prism pair. The difference between the angle ofincidence in the stretcher compared with the compressor is3.4° and the extra grating displacement is 26.2 mm. The prismseparation is 2.4 m. Dashed-dotted line (C): the same, usinga 1200 lines mm�1 diffraction grating in the stretcher and an1800 lines mm�1 grating in the compressor in combination withan SF10-glass prism pair. The angle of incidence in the stretcheris 13° and in the compressor 39°. Littrow is 41°. The prismseparation is 1.65 m.

design is the recompression process. The naive approachis to add additional separation between the gratings inthe pulse compressor and this is how the first systemswere built. Unfortunately, the stretcher and compressorcombination is the most dispersive part of the system anda mismatch between the two introduces vast third- andfourth-order contributions to the phase expansion. Theeasiest way to correct the TOD is to adjust the angle ofincidence between the stretcher and compressor, whichchanges the third-order contribution. Figure 11 (line A)shows the net group-delay dispersion versus wavelengthfor the kilohertz regenerative amplifier discussed above.The GDD curve is essentially flat over only a narrowwavelength range although the GDD and TOD are zerosimultaneously at the center wavelength. Table 2 showsthe bandwidth (fwhm) of Gaussian pulses of differentdurations. Ideally, the GDD curve should be flat overperhaps twice the bandwidth to avoid phase distortions.

Recall that the third-order contribution from prismpairs has the opposite sign to gratings..41/ This fact canbe used to null the GDD, TOD and FOD terms andthis is illustrated in Figure 11 (line B). The difference isdramatic and this system will support much shorter pulsesat the expense of 2.4 m of pathlength between the SF18prism pair.

Another method in the recent literature.42/ uses grat-ings of different groove density in the compressorcompared with the stretcher balanced against additionalround trips in the amplifier. This method, while bet-ter than the angular adjustment technique, is not aseffective as the grating–prism combination approach,although it has found favor in commercial applicationowing to its inherent compactness. Typical parametersare a 1200 lines mm�1 grating in the stretcher at an angleof incidence of only 6° and 2000 lines mm�1 in the com-pressor at 57°, which is reasonably close to Littrowgeometry (55°). Gratings with 2000 lines mm�1 are sig-nificantly more efficient than those with 1200 lines mm�1,giving improved throughput in the compressor. However,a combination of mixed gratings and a prism pair as shownin Figure 11 (line C) is a little better than matched grat-ings and prisms with the benefit of extra throughput andreduced prism separation without the need to balance the

Table 2 Pulse duration versus bandwidth(fwhm) for Gaussian-shaped pulses centered at800 nm

Gaussian pulse Gaussian bandwidthduration (fwhm) (fs) (fwhm) (nm)

100 9.450 18.830 31.310 94


total dispersion with extra amplifier material..43/ This sys-tem will support 20-fs pulses with little phase distortion.

2.5 Saturation Effects

The gain cross-section, sg, is not constant as a functionof wavelength. Since this appears as an exponent incalculating the total gain, successive passes throughthe amplification medium can lead to pulse spectralnarrowing and a shift in the central wavelength. This limitsthe maximum bandwidth to 47 nm in Ti : sapphire..38/ Asthe gain approaches saturation, the leading red edge of thepulse extracts energy preferentially and the spectrum willred shift. The maximum gain bandwidth can be achievedby seeding to the blue of the peak, allowing the gain toshift towards the maximum on successive passes. Second,by altering the gain profile by discriminating against thepeak wavelengths using an étalon or a birefringent filter,termed regenerative pulse shaping, the theoretical limitcan be overcome..44/

3 WAVELENGTH CONVERSION

Ultrafast lasers and amplifiers typically operate at a verylimited range of wavelengths. For example, Ti : sapphire-based ultrafast lasers are tunable in the near-infrared(NIR) region from about 700 to 1000 nm but typicallywork best at about 800 nm. The high peak power of theselasers can be used, however, to convert the laser light todifferent wavelengths. In fact, in some cases ultrafast lasersystems may be the ideal or only route to make radiationat certain wavelengths. Below, a series of techniques aredescribed to convert femtosecond laser pulses at visiblewavelengths to other wavelengths.

3.1 White-light Generation and the Optical Kerr Effect

At high intensities such as on the peak of an ultrashortlaser pulse, the refractive index of any medium becomesa function of the incident intensity. This effect, which isoften referred to as the optical Kerr effect (OKE),.45/ canbe described by Equation (18):

n.I/ D n0 C n2I C Ð Ð Ð .18/where n0 is the normal refractive index of the mediumand n2 is the nonlinear refractive index. The nonlinearrefractive index is very small, for example, in fusedsilica n2 ³ 3ð 10�16 cm2 W�1. A laser pulse with centerfrequency w traveling through a medium of length Lwill acquire an optical phase wLn/c and therefore theeffects of the nonlinear refractive index will becomeimportant when this phase factor becomes comparable to

a wavelength. As an example, consider the propagation offemtosecond pulses through an optical fiber. With a 9-µmfiber-core diameter (typical for communications-gradefiber), 10-nJ pulse energy and 100-fs pulse width, thepeak power is 100 kW, corresponding to a power densityof 1.5ð 1011 W cm�2. If the length of the fiber is 1 cm, theoptical pathlength changes by Ln2I D 472 nm or half awavelength. From this calculation, it can be seen that theOKE can have a significant effect on a femtosecond pulsetraveling through a medium. For pulses with energiesin the order of millijoules or higher, even the nonlinearrefractive index of air becomes important.

To understand how the OKE can modify the spectralproperties of an ultrashort pulse, one has to consider howthe nonlinear refractive index modifies the optical phaseof the pulse. The electric field of a laser pulse traveling inthe x direction can be written as Equation (19):

E.t/ cos.wt � kx/ .19/where k D wn/c is the wavenumber. Since the wavenum-ber depends on the (nonlinear) refractive index of themedium, the pulse will acquire a time-dependent phaseinduced by the Kerr effect. Inserting Equation (18)into Equation (19) and performing a Taylor expansionaround the peak of the ultrashort pulse, one finds(Equation 20)

E.t/ cos[.wC xt/t � kx] .20/where x depends on the nonlinear refractive index, thepulse width and peak power, and the distance traveled.Consequently, the nonlinear refractive index inducesan approximately linear frequency sweep (or chirp, seesection 2.2 and Figure 12) on the pulse. In other words,the spectrum of the pulse has broadened owing to thenonlinear interaction. If a single pulse modifies its owncharacteristics in this way, the effect is often referredto as self-phase modulation. If one pulse modifies theeffective refractive index causing a second pulse tochange its characteristics, this is referred to as cross-phasemodulation.

The spectral broadening induced by the nonlinearrefractive index is extremely useful in spectroscopicapplications. For example, an 800-nm femtosecond pulsecan be sent through a short length of fiber or through a fewmillimeters of glass or sapphire to produce a broadbandoutput pulse. Often there will be significant power atwavelengths ranging from 400 nm to 1.6 µm. For thisreason, such spectrally broadened pulses are referred to aswhite-light continuum pulses. The white-light continuumgenerated in a fiber has been used to generate some of theworld’s shortest pulses of around 5 fs..46,47/ A white-lightcontinuum pulse is an ideal seed for an optical parametricamplifier (see section 3.3).

10 GENERAL ARTICLES

Time−2 0 2

I(t)

0

1

ω(t

)

−0

(a)

(b)

Figure 12 (a) Chirp on an ultrashort pulse induced by the non-linear refractive index of a dielectric medium. The input pulsehas a sech2 envelope and the figure shows the instantaneous fre-quency within the pulse. A Taylor expansion around the peak ofthe pulse shows that the frequency sweep is approximately lineararound time zero. (b) Photograph of a femtosecond white-lightcontinuum beam generated in a piece of sapphire. (Picture cour-tesy of the Center for Ultrafast Optical Science, University ofMichigan.)

An implication of the nonlinear refractive index isself-focusing or defocusing. As a laser beam is typicallymore intense in its center, the nonlinear change of therefractive index will be strongest in the center. As a result,the medium will act as an intensity-dependent lens. In aset-up in which the sample is translated through the focusof a beam, this effect can be used to measure the nonlinearrefractive index of a sample quickly. Self-focusing is thebasis of the Kerr lens mode locking (KLM) effect usedin ultrashort lasers (see section 2.1). Self-focusing canbecome a run-away process leading to beam distortionand catastrophic damage to optical components. Inwhite-light generation, self-focusing can result in thebeam breaking up into multiple filaments that make thewhite-light output extremely unstable. It is therefore ofthe utmost importance to choose the incident power suchthat white light is generated without producing multiplefilaments. For a 100-fs pulse, this usually means that thepulse energy should be limited to approximately 1 µJ.

3.2 Generation of Ultraviolet and X-rays

The very high peak power that can be achieved withfemtosecond pulses means that in principle nonlin-ear frequency conversion should be very efficient. Itshould be straightforward to use second-harmonic gen-eration (SHG), third-harmonic generation (THG) andfourth-harmonic generation (FHG) to produce fem-tosecond pulses in the near- to deep-ultraviolet (UV)region. However, the group velocity of the pulses(see section 2.2) depends on the center wavelength andchanges significantly as the UV region is approached. Forexample, in a 1-mm b-barium borate (BBO) crystal (suit-able for harmonic generation down to about 180 nm) thedifference in group delay between the fundamental andthe fourth harmonic is 3.3 ps (see Table 3). Dependingon the set-up, this implies that the conversion efficiencyis very low or the pulses produced are very long..48/

Therefore, when UV pulses are produced, it is extremelyimportant to use the thinnest possible nonlinear crystals.As a rough guide, one should choose the thickness ofthe crystal such that the group-delay difference betweenthe fundamental and the harmonic is about equal to orless than the width of the pulse. An efficient harmonic-generation set-up will also use multiple conversion stepsand between steps readjust the relative time delaybetween the laser pulses at different wavelengths..49/

Most nonlinear crystals used for harmonic generation[BBO, lithium triborate (LBO), potassium dihydrogen-phosphate (KDP), etc.] are opaque in the deep-UVregion. Very high harmonic generation in low-pressuregases has been used successfully to generate deep-UV andsoft X-ray pulses. It was recently shown.50/ that a glasscapillary could be used to modify the phasematchingcondition for coherent soft X-ray generation. Using thisset-up, femtosecond pulses at 800 nm were converted tothe 17–32-nm wavelength range (¾30th harmonic) withabout 0.2 nJ energy per harmonic order. A similar set-upwas used.51/ to mix 800- and 400-nm pulses to produce 8-fspulses at 270 nm. Extremely short (5 fs) amplified laserpulses have been used.52/ to generate X-rays (¾4 nm) inthe water window by harmonic generation in a gas jet.

Table 3 Group delays calculatedfrom the refractive index of BBO,of femtosecond pulses at variouswavelengths traveling through a1-mm crystal (ordinary polarization)

Wavelength tgroup tgroup(nm) (ps) (ps)

800 5.62 –400 5.94 0.32267 6.74 1.12200 8.97 3.34


The advantage of very high harmonic generation is thatthe X-rays are generated in a well-collimated beam. Thedisadvantage is that it has not yet been shown to be pos-sible to generate hard X-rays with wavelengths smallerthan a molecular bond length.

Electron impact sources could generate femtosecondhard X-rays if high-charge, high-energy femtosecondelectron bunches were available. Even so, electronimpact sources have the disadvantage that the X-raysare emitted in a 2p solid angle, which makes theirbrightness typically very low. Therefore, these sourcesare difficult to use in diffraction experiments althoughnot strictly impossible. Very high-power laser pulses[peak powers of the order of 1 TW (1012 W)] can beused to generate laser-produced plasmas..53/ Typically,a high-power laser pulse is used to evaporate a (metal)target and produce a plasma by stripping electrons off theatoms with multiphoton ionization..54/ Recombination ofthese electrons with the ions results in the emission ofhard X-ray pulses (wavelengths of the order of 1 Å).Very recently, it has been shown that reverse Thompsonscattering of terawatt laser pulses off a high-energy(50 MeV) electron beam can be used to produce hardX-rays (0.4 Å)..55/ However, only 104 X-ray photonswere generated per laser shot, resulting in about onediffracted X-ray photon per shot in diffraction offSi h111i.

3.3 Optical Parametric Amplifier for InfraredGeneration

The infrared (IR) region of the spectrum is very importantfor the sensing of a great variety of (transient) molecularspecies. Femtosecond IR pulses can be used to determinewhich bonds in a molecule break or form. The mid-IR fingerprint region is ideally suited to determine thepresence of specific molecules in a sample. Therefore,a great deal of effort has been invested over the lastdecade to produce femtosecond pulses tunable in thenear- and mid-IR regions. Most techniques in use noware based on parametric difference-frequency processes(see Figure 13a and b)..56/ In difference-frequency mixing,a strong femtosecond pulse at frequency w1 C w2 mixesin a nonlinear crystal with a (weaker) pulse at frequencyw1, to produce a new beam of femtosecond pulses atfrequency w2. If the incident power at frequencies w1and w2 is zero, a nonlinear crystal can produce thesefrequencies spontaneously in a process referred to asoptical parametric generation (OPG). If the incidentpower at frequencies w1 and w2 is small but nonzero,the pump pulse at frequency w1 C w2 can amplify theformer frequencies in what is referred to as OPA. Sincethe peak power of a femtosecond pulse can be extremelyhigh while the pulse energy is relatively low, one can

produce enormous parametric gain without destroyingthe nonlinear crystal.

The frequencies or wavelengths that are produced inOPG or OPA depend on the phasematching condition,group velocity walk-off and the type of crystal used.Figure 13(b) shows materials that are commonly used forparametric generation in the IR region. BBO has a limitedtuning range in the IR range (approximately 1.2–2.8 µmwhen pumped at 800 nm) but is very efficient owing to thesmall group-velocity walk-off and high damage threshold.KTP and its analogs rubidium titanyl phosphate andcesium titanyl phosphate (RTA and CTA) are not asefficient as BBO but allow the generation of femtosecondpulses at wavelengths as long as 3–4 µm. There is avariety of crystals suitable for generation of pulses inthe mid-IR region such as AgGaS2 and GaSe. However,when these crystals are used to convert directly fromthe visible to the mid-IR, they suffer from enormousgroup velocity walk-off, (two-photon) absorption of thepump and very poor efficiency. Therefore, generatingmid-IR pulses is typically performed in a two-stage

ω1+ ω2

ω1

ω2

(a)

Frequency (cm−1)

10 100 1000 10 000

Terahertz methods

GaSe

AgGaS2

KTP

BBO

Translations

Librations

Fundamentalvibrations Overtone

vibrations(b)

Figure 13 (a) Difference-frequency mixing. A strong fem-tosecond pulse at frequency w1 Cw2 can mix in a nonlinearcrystal with a (weaker) pulse at frequency w1, to produce anew beam of femtosecond pulses at frequency w2. (b) Diagramshowing the various femtosecond IR tuning ranges that canbe obtained using an optical parametric amplification (OPA).Using the common crystals BBO and potassium titanyl phos-phate (KTP), tuning between 1 and 3 µm can be obtained. Withthe more unusual crystals AgGaS2, AgGaSe2 and GaSe, onecan obtain radiation to wavelengths as long as 20 µm.

12 GENERAL ARTICLES

process:.57/ an OPA generates two NIR frequencies(e.g. 800 nm! 1.5 µmC 1.7 µm, for example, in BBO)followed by a difference frequency mixing stage (e.g.1.5–1.7 µm! 12 µm, for example, in AgGaS2).

All known materials suitable as a nonlinear difference-frequency mixing crystal absorb strongly in the far-IRregion. GaSe and AgGaSe2 have the longest wavelengthcutoff of about 18 µm. In order to produce longerwavelengths, different techniques have to be used (seesection 3.5). It has recently been shown that periodicallypoled crystals such as periodically poled KTP.58/ can beused with great success to generate femtosecond IR pulsesefficiently.

When femtosecond IR pulses are generated, theyinevitably have a very large bandwidth, e.g. about100 cm�1 for a 100-fs pulse, which is clearly much largerthan the line width of a typical vibrational transition. Thisdoes not mean that femtosecond IR pulses are uselessfor vibrational spectroscopy – quite the contrary! The IRpulse can be spectrally resolved after the sample. Therecent availability of IR diode arrays and IR charge-coupled device (CCD) cameras means that an entireIR spectrum can be taken in a single laser shot..57,59/

However, in time-resolved experiments, the broadbandIR pulse can excite multiple transitions at once and onehas to take account of this carefully in the theoreticalanalysis of experiments..60/

3.4 Noncollinear Optical Parametric Amplification

Noncollinear optical parametric amplification (NOPA)is a technique used to generate sub-20-fs tunablevisible and NIR pulses..61/ In a collinear geometry, thetemporal output of parametric generators and amplifiersis restricted by group-velocity mismatch between thepump and the generated signal and idler fields. In anoncollinear arrangement, this effect can be overcomesince only the projection of the idler group velocity on tothe seed is important. By arranging the pump and seedincidence angles with respect to the phase-matching anglecorrectly, this group-velocity mismatch can be zeroed insome nonlinear crystals. A seed pulse, which is a singlefilament of white-light continuum generated in a 1-mmthick piece of sapphire, is amplified by the frequency-doubled output of a Ti : sapphire amplifier, in type I BBOcut at 31°. The sapphire must be cut such that the opticalaxis runs perpendicular to the cut face. Type I LBO isused to generate the second harmonic of the Ti : sapphirearound 400 nm. The pump beam focused on to the BBOgenerates a cone of parametric superfluorescence (insetof Figure 14). When the angle of incidence at the crystalis correct, there is no appreciable spatial divergence ofthe superfluorescence. By directing the continuum seedbeam along the cone axis, a large spectral bandwidth from

Sapphire

10%

90%800 nm

Variabledelay

LBO

BBO

10 fs

Signal

Pump

Parametric super-fluorescence

Figure 14 Schematic diagram of a noncollinear OPA. The insetshows the arrangement of the seed beam (the signal) relative tothe pump and the generated superfluorescence.

the white light can be simultaneously phase matched.Adjustment of the relative delay between pump andseed and some control of the chirp on the continuumtogether change the center wavelength and bandwidthof the amplified light. One great advantage of thisscheme is that relatively thick crystals can be employed(typically 2 mm), which results in high single-pass gain.The amplified output is then recompressed using aprism pair (BK7 separated by ¾60 cm) yielding sub-20-fsvisible pulses continuously tunable from 480 to ¾700 nm.Pulses as short as 5 fs have been generated.62/ usinga prism–double chirped mirror recompression scheme,although the mirrors are unavailable commercially at thetime of writing. Pumping with only 10 µJ of blue light,2 µJ can be generated at the signal wavelength. If higherenergy is available, a second amplification stage can beadded and 10 µJ can be obtained for a 75-µJ pump. Usingthe same technique, extremely short NIR light can begenerated in type II phase-matched BBO pumped at theTi : sapphire fundamental.

3.5 Terahertz-pulse Generation and Detection

As described above, NIR and mid-IR pulses can begenerated using parametric down conversion. However,down conversion cannot produce pulses with a wave-length longer than about 18 µm. Long-wavelength pulsescan be generated (and detected) using so-called tera-hertz techniques. There are effectively two methods forgenerating subpicosecond terahertz (1012 Hz) pulses: pho-toconduction or optical rectification. In photoconduction,a laser pulse incident on an absorbing semiconductorcreates (real) charge carriers in the conduction band.Acceleration of these carriers in an electrical bias fieldgives rise to a transient photocurrent that radiates elec-tromagnetic waves. In the far field the radiated electricfield is given by ER.t/ / dJS.t//dt, where JS.t/ is the time-dependent surface current. This method is typically used


HV

VIS input

THz output

THz

outp

ut

GaAs

(a)

Delay (ps)

E(t

) (a

rb. u

nits

)

−0.4

−2 −1 0 1 2 3 4

−0.2

0.0

0.2

0.4

0.6

0.8

0 20 40 60 80 100Frequency (cm−1)

|E(ω

)| (

arb.

uni

ts)

(b)

Figure 15 (a) Schematic diagram illustrating the generation ofterahertz pulses. A visible femtosecond input pulse irradiates asemiconductor antenna and creates conduction electrons. Theacceleration of these electrons in an external DC field results inthe emission of two beams of terahertz pulses. (b) A terahertzpulse generated and detected in a 1-mm long ZnTe crystal cutperpendicular to the h110i akis by a 150-fs pulse at 800 nm.The inset shows the amplitude spectrum. The oscillations in thepulse are due to the finite crystal thickness. (1 THz ³30 cm�1).

in conjunction with an antenna structure (see Figure 15aand b), which allows an external bias field to be applied.An antenna structure ideally suited to be used with low-power mode-locked lasers was developed in the 1980s atBell Laboratories.63/ and IBM,.64/ and is now the mostcommon method for generating and detecting terahertzpulses. In such a set-up, two metal electrodes are laiddown on a silicon or GaAs substrate, typically with aseparation of ¾100 µm. A beam of femtosecond laserpulses is focused between the electrodes, in a spot witha diameter of a few micrometers. On the generationside, the metal electrodes are biased with a few tens ofvolts and the excitation by the pump laser triggers theemission of terahertz radiation. On the detection side,

the incident terahertz beam accelerates carriers createdby another visible beam, resulting in a measurable pho-tocurrent. Since the visible beam has to be focused toa very tight spot in this method, only unamplified ultra-fast lasers can be used. There is no overriding reason,however, why one should use such closely spaced elec-trodes. Large-aperture photoconducting antennas workvery well for the generation of terahertz pulses whenpumped by amplified pulses. The conversion efficiencyis about 0.1%. With low repetition rate (10–1000 Hz)ultrafast laser systems, far-IR pulses with energies as highas 1 µJ have been generated..65/

An external bias field is not strictly necessary for photo-conductive generation of terahertz pulses, as real carriersgenerated by a visible laser pulse can be accelerated inthe field of the depletion layer of the semiconductor.This surface field will accelerate the carriers perpendic-ular to the surface of the semiconductor and hence theterahertz oscillating dipole will be perpendicular to thesurface. Therefore, terahertz radiation generated throughthis effect is only observed if the angle of incidence ofthe exciting visible laser beam is nonzero. Typically, theeffect maximizes at the Brewster angle.

Optical rectification is distinct from photoconduction,in that the visible exciting beam creates virtual rather thanreal carriers. A more appropriate way to describe this isthat the second-order susceptibility, c.2/, of the crystal isused for difference-frequency mixing. Thus, the second-order polarization can be written in the time domain asEquation (21):

P.2/THz.t/ D e0c.2/EVIS.t/EŁVIS.t/ .21/

which shows that the electric field of the terahertz pulsehas the same shape as the intensity envelope of thevisible exciting pulse. In the last few years, it has beendiscovered that optical rectification is an efficient methodfor generating terahertz pulses if used appropriately.Since a subpicosecond terahertz pulse has a spatial lengthcomparable to its center wavelength, it travels througha material at its phase velocity. Therefore, for optimumconversion from visible to far-IR wavelengths, one hasto match the group velocity of the visible pulse with thephase velocity of the terahertz pulse..66,67/ This conditionis met in some zinc blende, large band-gap semiconductorssuch as ZnTe and GaP when the exciting laser has a centerwavelength of ca. 800 nm.

The inverse of optical rectification is electroopticsampling: a terahertz pulse incident on an electroopticcrystal such as ZnTe will induce a birefringence throughthe Pockels effect. An ultrafast visible probe pulse witha variable delay copropagating through the same crystalwill experience a retardation that can be retrieved withbalanced detection. Scanning the relative time delay of

14 GENERAL ARTICLES

the probe pulse, one can record a time-domain traceof the electric field of the terahertz pulse. Using thismethod, signal-to-noise ratios, defined as the ratio of theterahertz pulse peak to the noise background, as highas 107 have been reported..68/ However, the signal-to-noise ratio with which one can measure the peak ofthe terahertz pulse is typically of the order of 102 –103

in 100 ms. An exciting new variation on this techniqueis the use of a chirped probe pulse..69/ A femtosecondpulse at 800 nm can be stretched and chirped to tens ofpicoseconds using a grating pair. If this chirped pulse isused in the electrooptic sampling process, there will be arelationship between wavelength and relative time delay.Thus, detection of this probe pulse with a spectrometerand diode-array detector allows one to measure the entireterahertz pulse shape in a single laser shot.

As rectification and electrooptic sampling are nonres-onant effects, the minimum duration of the terahertzpulses that can be generated or detected is limited onlyby the thickness of the crystal scaled with the differencein phase and group velocity. Thus, with ca. 10–15-fs excit-ing pulses at 800 nm, it was shown that terahertz pulsescould be generated with detectable frequencies as highas 70 THz..70/ At these large bandwidths, it is unavoid-able that the t-ray spectrum will overlap with a photonabsorption band in the generating and detecting crystals,leading to large oscillations in the terahertz field trailingthe main peak.

The current record highest detectable frequency fora terahertz pulse is ¾70 THz, but there is no reason tobelieve that this could not be improved upon. Usingthe simple time–bandwidth relation, nt D 0.32, itfollows that with the shortest visible pulses achievable,ca. 4–5 fs, usable power at frequencies from 0 to 160 THz(l D 1.8 µm) could be achieved. As femtosecond laserscontinue to shrink in size, it may be expected thatultrafast terahertz devices may well take over fromFourier transform infrared (FTIR) spectrometers asgeneral-purpose IR spectrometers. As an entire terahertztime-domain trace can be acquired in a single shot,.69/

these devices would combine the reliability and accuracyof FTIR spectrometry with real-time speeds. The mostsignificant aspect of ultrafast terahertz pulses, however,is that they are synchronized with visible or UV pulses,allowing time-domain spectroscopy.

3.6 Femtosecond Electron Pulses

Very short (picosecond to femtosecond) electron pulsesare useful for a variety of applications. For example,picosecond electron pulses have been used as aprobe pulse for determining the time-dependent struc-ture of molecules undergoing chemical reactions (seesection 5.3). However, such pulses might also be used

as a seed for electron accelerators or for the genera-tion of femtosecond X-ray pulses. Current technology forgenerating femtosecond electron pulses is based on exper-iments done in the past with picosecond and nanosecondlaser pulses..71 – 73/ A UV laser beam is used to irradiate ametal target. If the photon energy is higher than the workfunction of the metal (typically 4–5 eV for common tran-sition metals such as gold, silver or tungsten), electronsare ejected into the vacuum through the photoelec-tric effect. These emitted electrons are electrostaticallyextracted and accelerated into a narrow beam. In recentexperiments (see section 5.3), this technique has beenbrought into the subpicosecond domain. The main prob-lem in maintaining the time resolution is the space-chargeeffect: nonrelativistic electrons repel each other throughCoulomb repulsion. It is therefore of the greatest impor-tance to accelerate the electrons as quickly as possibleand to keep the number of electrons per pulse as low aspossible. Thus, it was seen in an experiment.74/ that for a100-µm laser spot size on the photocathode, the electronpulse would broaden to about 15 ps when there were1000 electrons in the pulse. When the number of elec-trons per pulse was reduced to 100, the pulse width wasless than 1 ps. There is no fundamental reason why onecould not work with ten or even one electron per pulseand therefore it should be possible to achieve electron-pulse durations in the order of tens of femtoseconds. Ofcourse, to achieve a reasonable signal-to-noise ratio in anexperiment, the pulse repetition rate should be high. Suchpulses will be of great value in time-dependent molecularstructure determination.

4 TIME-RESOLVED EXPERIMENTS

Most electronic devices cannot measure transients muchfaster than about 1 ns. Although there are specializedelectronic devices such as streak cameras that may be ableto resolve picosecond or even hundreds of femtosecondtransients in real time, in most cases it makes moresense to look for alternative detection techniques. Thetechniques that are used most frequently are based onauto- or cross-correlation of two beams of femtosecondpulses (see Figure 16a). If the sample is a nonlinear crystalused for sum-frequency generation, this technique can beused to determine the shape and relative arrival timeof two short pulses. If the sample contains molecules oratoms that resonantly absorb the incident radiation, theexperiment is a pump–probe experiment.

4.1 Auto- and Cross-correlation

In an autocorrelator, an incoming beam of pulses is splitin two. One beam travels through an optical path with


Input (ω1)

Variable delay

Compensation plate

SHG Crystal

Detector

Beamsplitter

Fixed delay

(a)

τ (fs)−60 −40 −20 0 20 40 60

I cro

ss-if

0

2

4

6

8

(b)

Figure 16 (a) Schematic diagram illustrating the layout of anautocorrelator. Two laser beams of femtosecond pulses atfrequency w1 are overlapped in a nonlinear crystal such asBBO. The sum-frequency signal at frequency 2w1 as a functionof relative time delay is proportional to the shape of the pulse.(b) Interferometric autocorrelation of a 25-fs fwhm laser pulseat 800 nm.

a fixed length, the other through a path that includesan optical delay line. An optical delay line consistssimply of a pair of mirrors or a retro-reflector mountedon a motorized translation stage or a sine-wave-drivenloudspeaker. In such a set-up, the spatial position of themirrors on the translation stage is related directly to therelative time delay between the two beams of pulses.For example, if the optical delay line is translated byL D 1 µm, this corresponds to a change in relative timedelay of t D 2L/c ³ 6.6 fs. Both beams are focused ina nonlinear crystal such as BBO or KDP in order toproduce second-harmonic radiation. Phase matching.56/

in the crystal is used to produce a beam at the second-harmonic frequency in which one photon has been takenfrom one beam and one from the other. Alternatively,

two-photon absorption in a photodiode may be usedto provide the required second-order response..75/ Theaveraged measured auto- or cross-correlation signal thenhas the form (Equation 22)

Icross.t/ /∣∣c.2/∣∣2 ∫ Iw1.t/Iw2.t � t/ dt .22/

where c.2/ is the second-order susceptibility of thenonlinear crystal and t is the relative delay time t1 � t2between the two pulses. Of course, the cross-correlationsignal consists itself of a train of femtosecond pulsesbut since one is only interested in the average signal asa function of the relative time delay, no fast detectoris required. Since the nonlinear crystal is chosen suchthat it does not exhibit any time-dependent processesof its own, the cross-correlation signal as a function oftime delay is proportional to the shape of the incomingpulses. For example, in the case of an autocorrelationof a pulse with a Gaussian envelope, the autocorrelationsignal as a function of delay has itself a Gaussian shape.In this example, one can measure the fwhm of theautocorrelation signal and find the width of the intensityenvelope of the pulse by multiplying by 0.71. The valueof the conversion factor depends on the pulse shape anda list of conversion factors can be found in Table 4. Inpractice, it may be wise to use nonlinear curve fitting todetermine the pulse shape and corresponding conversionfactor.

Clearly, the auto- or cross-correlation signal containslimited information about the pulse shape. For example,an asymmetric pulse shape will go undetected in an auto-correlation. More serious is that an autocorrelation willprovide almost no information about possible chirp onthe pulse (see section 2.2). If the pulse is chirped, theautocorrelation will be broader than might be expectedfrom the pulse spectrum. Table 4 has a column withtime–bandwidth products, that is, the product of thefwhm of the intensity envelope of the pulse in the timedomain and the frequency domain. However, checkingthat the time–bandwidth product is close to that expectedfor a given pulse shape is not a very good method ofmaking sure that the pulse is chirp free.

A better method for detecting chirp is the measurementof an interferometric autocorrelation and is taken byoverlapping the two input beams. The correlation signalis now much more complicated.77/ and oscillates atfrequencies corresponding to the laser fundamental andsecond harmonic. Since the second-harmonic intensity isproportional to the square of the incident intensity, thedetected second-harmonic intensity as a function of delayis (Equation 23)

I2w.t/ D 1T∫ T/2�T/2

∣∣[E.t/C E.t � t/]2∣∣2 dt .23/

16 GENERAL ARTICLES

Table 4 Second-order autocorrelation functions and time–bandwidth products for various pulse-shape models,.76/ wheretp D pulse width (fwhm), tG D autocorrelation width (fwhm) and n D spectral width (fwhm)

I.t/ (x � t/T) ntp tp/T G20.t/ (y � t/T) tG/T tp/tGGaussian I.t/ D e�x2 0.4413 2pln 2 e�y2/2 2p2 ln 2 0.7071

Diffraction function I.t/ D sin2 x

x20.8859 2.7831

32y2

(1� sin 2y

2y

)3.7055 0.7511

Hyperbolic sech I.t/ D sech2 x 0.3148 1.7627 3.y coth y� 1/sinh2 y

2.7196 0.6482

Lorentzian I.t/ D 11C x2 0.2206 2

11C .y/2/2 4 0.5000

One-sided exponential I.t/ D{

e�x ^t½00 ^t


bandwidth of that pulse would be resolved and thatthe instantaneous frequency remains the same at eachpoint in time. However, for a chirped pulse, where lowerfrequencies lead higher ones or vice versa, the frequency-resolved trace will be considerably different, since theinstantaneous frequency is a function of time. Since thephase of the signal pulse is contributed only by E(t)[E.t � t/ appears as the square, so all phase informationis lost], the phase can be retrieved from a FROG trace.This is achieved using an iterative Fourier-transformalgorithm.

Ultrashort pulse characterization techniques generallyrequire instantaneously responding media. The polariza-tion gate geometry FROG technique uses the electronicKerr effect, which is accompanied, however, by a Raman-ringing effect. The slower nuclear motion of the materialmust therefore be considered in the iterative algorithmused to retrieve the pulse phase and intensity. The pulse-retrieval algorithm can be modified.80/ by including termsdue to the slow response of the medium in the signal-field equation. Such problems with a slow response of thecorrelating medium can be avoided by using two-photonabsorption in a diode..75/

4.2 Pump–Probe Techniques

Most ultrafast spectroscopy experiments use the pump–probe technique, which is very similar to the cross-correlation technique described above. In pump–probespectroscopy the pump beam is typically much strongerthan the probe beam, the two beams have a differentcenter wavelength (or the probe may not even be a laserbeam), and the sample tends to be more interesting.As in the cross-correlation technique, the femtosecondtime resolution is obtained by sending one of the beamsthrough a motor-driven optical delay line. The (relatively)strong pump beam initiates some process of interest, e.g.a chemical reaction. The probe beam, entering the samplelater, will be amplified, attenuated or refracted becauseof the changes taking place in the sample. There are somany variations of this scheme and literally thousands ofexperimental examples that it would be pointless to listthem all. Therefore, two examples of the pump–probetechnique will be described in some detail here to conveythe general idea.

Figure 18 shows a very typical pump–probe spec-troscopy set-up. A relatively strong pump beam is sentthrough a (motorized) optical delay line and focused intothe sample where it initiates some chemical reaction. Inmany cases, the pump beam will be modified, e.g. by dou-bling or tripling its frequency through SHG or THG. A(small) fraction of the pump beam is split off by an opti-cal beamsplitter and converted to another wavelength.In this example, a white-light continuum is generated as

WL

DL1

DL2

S

SP

DPump

Probe

Figure 18 ‘‘Classical’’ pump–probe spectroscopy set-up. Arelatively strong pump beam is sent through an optical delay line(DL1) and focused into the sample (S). A small fraction of thepump beam is split off and converted to another wavelength. Inthis example, a white-light continuum is generated as a probe,which is sent through another optical delay line (DL2) and intothe sample. After the sample, the white-light probe is spectrallyresolved by a spectrometer (SP) before being detected by a‘‘slow’’ detector (D).

a probe but one could also use other conversion tech-niques to make probes at widely varying wavelengths.In any event, the probe pulse is sent through anotheroptical delay line and focused into the sample. One maytemporarily replace the sample by a nonlinear crystal todetermine at which setting of the optical delay lines thepulses overlap in the sample. In Figure 18, the white-light probe is spectrally resolved by a spectrometer afterthe sample in order to measure the transient transmissionspectrum of the sample. The signal measured as a functionof the pump–probe delay time reflects the creation anddestruction of chemical species in the sample. However,on short timescales (¾

18 GENERAL ARTICLES

Pump

Probe

Scanningtunnelingmicroscopy

Figure 19 Unconventional pump–probe technique. In thisexample, the pump beam excites electrons in the conductionband of a semiconductor, thereby creating a femtosecondvoltage pulse in the metal transmission line deposited ontop of the semiconductor sample. The voltage pulse can bemeasured by an scanning tunneling microscopy (STM) tip. Ifthe current flowing through the STM cantilever is itself gatedby a probe pulse, time- and space-resolved measurements canbe performed.

and spatial resolution. There are many other examples ofunconventional pump–probe techniques. The probe mayconsist of X-ray pulses, electron pulses or any other kindof pulsed particle beam. The only critical requirement isthat the pulses in the pump beam are synchronized tothose in the probe beam.

5 APPLICATIONS

As ultrafast lasers are becoming smaller and easier to use,they will find increasingly down-to-earth applications. Forexample, IR generation using ultrafast lasers may becomeso simple and cheap that its advantages can be used: spa-tially coherent beams (resulting in better focusing anddirectionality), coherent detection (allowing one to mea-sure refractive indices directly without resorting to theKramers–Kronig relations), broadband (allowing single-shot detection of an entire spectrum) and more power at‘‘odd’’ wavelengths (especially in the far-IR region). Oneof the main advantages of ultrafast lasers is, of course, thatthey allow time-resolved experiments with which one canobserve transient species. Another advantage is that shortpulses with modest energy can have huge peak power.This makes femtosecond pulses very suitable for laserablation of materials, multiphoton absorption (for imag-ing of biological materials), fragmentation (e.g. of DNAinto fragments that may be analyzed using MS), etc. Thehigh peak power also permits the efficient conversionto other wavelengths using nonlinear crystals. A slightlyunexpected recent observation is that when femtosecondlasers are used for machining the resulting cuts are muchcleaner because the laser pulses turn the material into aplasma rather than melting it. The number of applications

of ultrafast lasers is already large and will only grow. Itwould be impossible to describe all these applications inthe limited space available here. Therefore, a few keyapplications will be described.

5.1 The Study of Fast Chemical Reactions

In principle, there is no difference in the informationthat can be obtained from a frequency-resolved ora time-resolved experiment. In a frequency-resolvedspectrum, a vibronic transition may show up as a series ofsharp absorption lines. In the equivalent time-resolvedexperiment, one will observe quantum beats whoseperiods correspond to the inverse of the spacings betweenthe absorption lines. In practice, however, there may bedifferences. For example, even in the gas phase, thespacing between the absorption lines may be so smallthat it is hard to resolve them. More importantly, in thesolution phase, the molecule under study will coupleto the degrees of freedom of the surrounding bath.Strictly, the Schrödinger equation for the liquid could besolved, which would show that the dynamics in the liquidin fact correspond to about one-trillion-trillion (1024)well-defined quantum states. Most of these bath stateswill be coupled to the vibronic states in the molecule,resulting in the broadening of the transition. In sucha case, a spectrally resolved experiment will providelittle information about the dynamics of the moleculeor the dynamics of a chemical reaction that one wouldlike to study. Even hole-burning spectroscopy will notprovide much more information in most cases. Onlytime-resolved pump–probe techniques can elucidate themolecular dynamics.

In the 1980s and 1990s, a series of experiments wereperformed by a variety of groups which came to beknown as ‘‘femtochemistry’’ or ‘‘femtobiology’’. Theseexperiments exploited the property that if a moleculeis excited with a laser pulse shorter than the oscillationperiod of relevant vibrations in the molecule, a coherentvibrational wavepacket is created in the excited state (seeFigure 20a and b). Vibrations with a period shorter thanthe pulse width are simply not coherently excited and donot give rise to quantum beats.

The ‘‘hydrogen atom’’ of femtochemistry is thediatomic molecule NaI that was extensively studied inthe gas phase..13/ When NaI is excited by a femtosecondUV pulse (see Figure 21a and b), a wavepacket is createdon the repulsive excited state, which (at large interatomicdistances) corresponds to the ion pair NaC and I�. How-ever, this repulsive potential forms an avoided crossingwith the ground-state potential, which (at large inter-atomic distances) corresponds to the radical pair Na C I.If the system is probed in the excited-state potentialwell, it is seen that the wavepacket coherently oscillates


(a)

Delay (ps)0.0 0.2 0.4 0.6 0.8

∆OD

(m

OD

)

−80

−60

−40

−20

0

(b)

H2N S

N

NH2+

Figure 20 (a) Schematic diagram of a vibronic transitionexcited by a pulse whose width is smaller than the vibrationalperiod. The pulse creates a coherent vibrational wavepacket inthe excited electronic state that will oscillate in the excited-statepotential well. (b) Time-resolved 600-nm pump, 700-nm probesignals in the dye molecule thionine studied with 42-fs timeresolution. The signal is stimulated emission from the excitedelectronic state and the oscillations correspond to a vibrationalmode at 443 cm�1 in the excited-state potential well.

in the bound state. However, if the sodium radical isprobed by inducing fluorescence with the probe pulse, itis seen that the population of the radical increases in astepwise fashion. Therefore, such an experiment showsthat the chemical reaction (a dissociation in this case)is a quantum-mechanical process in which a fraction ofthe bound wavepacket tunnels to the state of dissoci-ated radicals each time the wavepacket travels throughthe crossing region. Interestingly, it is possible to usequantum mechanical interference of wavepackets to steera reaction in a desired direction and away from undesireddirections. This is referred to as coherent control and hasbeen applied on small molecules with varied success..85/

A study, such as that on NaI described above, becomesinteresting if one can compare the behavior in the gas

AB

A + B

(AB)*(AB)**

Fluorescence

A++B−

fs-p

robe

fs-p

ump

(a)

6

4

2

0−2 0 2 4 6 8

A

B

C

Sig

nal

Time delay (pico secs)(b)

Figure 21 (a) Simple diagram depicting a typical coherentdissociation reaction. The pump pulse excites a small moleculeto its first excited state. If the pump pulse is shorter thanthe vibrational period, it may create a coherent wavepacketthat will oscillate in the excited-state potential well. In thisdiagram, the molecule splits into two fragments consisting ofeither two radicals or two ions. A probe pulse excites themolecule to a third state, from which it fluoresces back to theground state. The total fluorescence is measured as a functionof pump–probe delay. (b) Pump–probe results.86/ from NaIwith lpump D 310 nm. (A) lprobe D 580 nm; (b) lprobe D 589 nm(on resonance); and (C) lprobe D 612 nm. (Reproduced fromRosker et al..86/ by permission of Elsevier Science. ElsevierScience BV, 1988.)

phase with that in the condensed phase..87/ Variousmolecules that had been studied in the gas phase havenow been studied in solution where again one couldobserve quantum beats due to vibrational wavepackets.Examples are HgI2.88/ and I2..89,90/ Vibrational quantumbeats have now been observed in a large variety ofmolecules in the condensed phase, including proteins..91/

In these large, complicated systems, quantum beatsprovide a unique opportunity to determine the potentialsrelevant for chemical and biological reactions. Not least,the femtochemistry technique may be used to detect

20 GENERAL ARTICLES

short-lived intermediates that would be invisible whenordinary spectrally resolved techniques were used. Arecent experiment.1/ has shown that femtochemistry canbe combined with MS: pump and probe laser beams werecrossed with a molecular beam and radical fragmentswere detected with MS as a function of pump–probedelay. The technique was used to study Diels–Alderreactions and the concept of concertedness and maywell find more general use in analytical chemistry. Nowthat high-repetition rate, high-power lasers are available,ultrafast lasers may be used to make a variety of elusivemolecules that normally occur only in the atmosphere orin space.

5.2 Imaging

Nonlinear ultrafast optics can be of immense value for(biological) imaging studies. Femtosecond lasers canbe used to perform multiphoton absorption confocal-imaging studies. Using this technique, one can image thespatial distribution of one specific molecule inside a livingcell..92/ Tunable femtosecond NIR pulses are ideal forthis purpose as scattering and damage to the cell arereduced compared with UV radiation. A new alternativeinvolving THG at the focus of a microscope has beenused recently in imaging applications..93/ At an interface,giving rise to a slight change in refractive index orthird-order nonlinear susceptibility, THG becomes phasematched..94/ The UV light generated can be detectedusing a photomultiplier tube or CCD camera. Theconversion efficiency is low (10�8), but at the tight focusof a high numerical-aperture objective lens, a fluenceof 100–300 GW cm�2 (a few nanojoules per pulse) isenough to generate a detectable third-harmonic signalwithout damage to the sample. The technique benefitsfrom being background free. NIR light at 1.2 µm has beenemployed,.95/ giving a third-harmonic signal at 400 nmaway from potentially harmful UV wavelengths, whichwould damage delicate (possibly living) specimens. Thechirp induced by the lens is also much smaller in the NIRregion. In distinct contrast to multiphoton absorptionof samples tagged with fluorescent probes, no reductionin signal is observed over time since the sample is notrepeatedly bleached. Scanning mirrors are used to providetraveling Lissajou patterns giving a nearly uniform sampleillumination and the image is recorded on a CCD camera.An example image.95/ is shown in Figure 22(a). Here, arhizoid (a tubular single cell) tip from chara plants (greenalgae) is shown. The bright spots are stratoliths, vesiclescontaining BaSO4 crystals, which flow within the cell andare necessary for the gravitational response of the alga.The CCD camera detects the motion of these stratolithsover time. This example shows that the technique isapplicable to the same systems as more conventional

(a)

150

200

250

Del

ay (

fs)

300

2120

1918

1716

1514

1716

1514

1312

1110

98

y (mm)x

(mm

)

(b) 350

Figure 22 (a) THG image.95/ at root tip showing motion of stra-toliths. The image is approximately 75ð 75 µm2. (Reproducedfrom J.A. Squier, M. Muller, G.J. Brakenhoff, K.R. Wilson,Opt. Express, 3(9), 315–324 (1998), by permission of the OpticalSociety of America, 1998.) (b) THz image of a bonsai leaf takenby plotting the transmission time as a function of position..99/

phase-contrast microscopy and will surely be developedfurther as techniques for optimizing the duration of thepulse at the objective are developed..96 – 98/

The frequency range between ca. 100 GHz and a fewterahertz has not been studied very well, as not manylight sources are available. FTIR spectrometers typicallypeter out at frequencies below about 50 cm�1 (1.5 THz),even when equipped with bolometric detectors and far-IR optics. Microwave devices may go to frequenciesas high as 1 THz but usually have poor tunability.However, this frequency range is of great interest as manylow-frequency vibrational and rotational modes absorbhere. The pseudo-band gaps of superconductors and inter-band gaps of semiconductor heterostructures are also inthis range. An exiting new application of terahertz pulsesis t-ray imaging. T-ray imaging was first performed atBell Laboratories:.100,101/ a beam of terahertz pulses wasfocused to a tight spot and a sample was scanned through


the beam. Owing to the long wavelengths at ca. 1 THz,spatial resolution was limited to about 1 mm. However,because the transit time of subpicosecond terahertz pulsescan be measured with an accuracy of a few femtoseconds(see Figure 22b), it is possible to make tomographicimages..100/ Thus, by measuring the internal reflectionsin a sample, for example, the various surfaces in afloppy disk, it is possible to detect hidden features with adepth resolution much higher than the wavelength. Veryrecently, several attempts have been made to improvethe lateral resolution by applying near-field techniquessuch as using small apertures in front of the sample.102/ orterahertz pulse generation in subwavelength regions..99/

It was shown recently.103/ that electrooptic sampling canbe performed in parallel using a large-area electroopticcrystal and an unfocused probe beam, thus allowing theacquisition of t-ray images in real time.

Using a technique analogous to ultrasound, optical-coherence tomography utilizing femtosecond lasers haspermitted micrometer resolution in real-time imag-ing applications, particularly in biomedicine..104/ Cross-sectional images are made in a similar manner to theterahertz-imaging application by measuring the ‘‘echo’’time of backscattered light using interferometric meth-ods. Since the axial resolution is limited by the coherencelength of the light, short-pulse Ti : sapphire and partic-ularly NIR Cr : forsterite lasers are seen as attractivesources. An image is measured by building up thebackscattered pattern at several transverse positions andthese high average-power lasers are ideal for imaging ata few frames per second.

5.3 Structure Determination: Electron Beams andX-rays

Time-resolved pump–probe spectroscopy has been usedfor a long time to study chemical reactions. Often suchspectroscopy relies on excitation and probing at visiblewavelengths and transient visible spectra have to becarefully analyzed and interpreted to find out what thereaction products are. More recently, several groups havestarted to use femtosecond IR pulses in the hope thattransient IR spectra will give more direct informationabout which chemical bonds are broken or formed.However, neither visible nor IR spectroscopy providesdirect information about the spatial atomic structure of agiven reaction intermediate.

X-ray diffraction has been used for close on acentury to determine the atomic structure of crystals.Especially in the life sciences this has resulted in a muchbetter understanding of the structure of proteins andother biomolecules and hence to a better understandingof the fundamentals of biochemistry. Because of thegreat absorption of electrons by materials, time-resolved

electron-diffraction experiments have so far only beenperformed in the gas phase and on surfaces. However,as steady-state electron diffraction has also been used todetermine the structure of proteins in the solid state,.105/

femtosecond time-resolved electron diffraction in thesolid state may also become a possibility. Electronsat present provide the most structural informationfor a given amount of radiation damage..106/ Theatomic cross-section of carbon for (elastic or inelastic)scattering of electrons is more than six orders ofmagnitude larger than that of X-rays. Furthermore,radiation damage by 80–500-keV (

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