n. bloembergen- from millisecond to attosecond laser pulses

8/3/2019 N. Bloembergen- From Millisecond to Attosecond Laser Pulses

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D < r v ,f1 11,e/t,v" Ul, Ot lf,\-ttluFrom Millisecond to AttosecondLaser Pulses

N. BloembergenCollegeof Optical Sciences, niversity of Arizona

Tucson, AZ. 85721, USA

1. From millisecond o nanosecondpulses.Maiman [960] achieved he first operating aser, utilizing a ruby crystal pumped by axenon flash lamp. The light flash lasted about one millisecond and the laser ouutfluctuated during this time interval. The population inversion in the fluorescent evels ofthe chromium ion changedby the competition between he pumping mechanismand the. stimulated emission processes nto various laser modes. This led to relaxation typeoscillationsand fluctuations n the laser output.Hellwarth fl96la and 1961b1achievedQ-switchedpulsesof less than one microsecondduration within the first year of ruby laser operations. The quality factor Q of the lasercavity was kept low by the use of a polarization-switching cell with nitrobenzene,subjected o an electric field causingbirefringenceby the Kerr effect. A largepopulationinversion in the ruby was established,as the light with orthogonal polarization wasswitchedout of the lasercavity with a Nicol prism. When the electric field on the Kerrcell was suddenlyswitched off, a powerful laserpulsewas createdby the high gain fromthe large inverted population. Reproduciblepulseswith a duration between en and onehundred nanosecondwere obtained. In this early period Q-switching was also obtainedby mounting a mirror or a cubic totally reflecting glassprism on a turbine-driven dentistdrill. The laser oscillation could only build up, when the rotating minor was nearlyparallel to the fixed mirror of the laser cavity. Clearly this mechanical method had nomode control and became rapidly obsolete, although it survived longer for the Q-switching of high-power COz aser operatingnear lOrmwavelength.This cursory overview is intended for non-specialists,who wish to become acquainted\with the remarkable developments in time-resolved optical techniques. Morecomprehensiveeviews may be found in the references.The next sectionoutlines the evolution from the nanosecond o the femtosecond egime.It is based on familiar nonlinear optical processes, ncluding saturable absorption,intensity-dependentndex of refraction, self-focusing and self-phase modulation. Thetransition to the attosecond egime is described n the third, final section. It requires"extreme" nonlinear processes, ncluding tunneling and the creation of quasi-freeelectrons,which enablea transition from the visible to the (soft) x-ray spectral egion.


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2. From nanosecond o femtosecondpulses.This section is based on an earlier brief overview (Bloembergen U999]) and on acomprehensiveeview by Brabec and Krausz [2000]. Mode-locking of a large numberoflongitudinal modes all activated by the gain profile of the laser medium can lead to oneshort pulse traveling back and forth in the laser cavity of lenglh l. The frequencyspacingbetween he modes is cl2l and the output is a train of pulses,separated y thetime interval2llc. Active mode-locking was first achieved or a helium-neon laser byHargrove, Fork and Pollack 119641.They acousticallymodulated he index of refractionat the frequency c/21. Since the gain-bandwidth profile of the gas-laser ransition israthersmall, thepulsedurationremainedmuch longer than ten nanoseconds.Passive modeJocking of a ruby laser was first demonstratedby Mocker and Collins[1965]. They used a saturable absorber in the form of a liquid film or jet with ableachabledye near one of the mirrors in the laser cavity. The generationof a shortpulseoutput may be qualitatively understood as follows. Initially, spontaneousemissionprocessesare amplified and lead to a stochastic ight intensity. A peak in this output issubsequentlyamplified the most, as it causesmore initial bleaching of the saturableabsorber. Thus, intervals of higher intensity are attenuated ess on passagehrough thebleachabledye film. Thus, after many round trip passagesn the laser cavity the energytransfer of the stimulated emissionprocessess concentrated o a shorter time interval,which is eventually limited by the inverse of the gain-bandwidth product of the laser.For the ruby laser his product was not large enough o break the nanosecond arrier.Pulsesshorter han a nanosecond,marking the entrancento the picoseconddomain,werefirst obtainedby DeMaria, Stetserand Heinau U966} They used a neodymium glasslaser. This material as well as neodymium-yttrium-aluminumgarnet (Nd - Yag) havesufficient gain-bandwidth product to permit the generation of laser pulses of 10psduration. These lasers, operating near 1.06rm wavelength, were widely used forexperiments in time-resolved spectroscopy. Other frequenciescould be obtained byharmonic generation,stimulated rrmanscattering and selphasemodulation. Shapiroll977l hasedited an early review dedicated o picosecondpulsegeneration.The first entry into the sub-picosecondor femtosecondregime was accomplished byShankand Ippen U9741. They used a broad gain dye-lasermedium in combinationwitha saturabledye-absorber ilm. An analysis by New U9721had shown that it is possibleto obtainpulsesshorter han the characteristic elaxation imes of the dye media, since hepulse duration is determinedby the time that the saturablegain exceeds he saturableabsorption. The use of a ring dyeJaser systemwith counter-propagatingaser pulses,which crosseach other in the passagehrough a saturabledye film, only a few micronsthick, led to even shorter pulses. A limit is then set by the dispersion in the groupvelocity which causesdifflerentFourier components of the short pulse to propagateatdifferent speeds. This produceschirping and stretchingof a short pulse. The chirpingproducedby self-phasemodulation is often more important. As the intens rises during


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the leading edge, he index of refraction rises, and the light frequency s shifted towardthe red. A blue shift occurs at the trailing edge of the pulse. Chirping can becompensated by introducing negative group velocity dispersion. This may beaccomplishedby prism or grating configurations which increase he optical path lengthfor red-shifted ight relative to that for blue-shifted ight. Fork, Britto-Cru2, Becker andShank [1987] reportedpulsesof 6fs dtnation by a prism configuration in the lasercavity.The linearly po\anzed ight beamswere incident near Brewster's angle o avoid reflectionlosses at the prism surfaces. These femtosecond dye laser systems required frequentadjustmentsand alignment of the componentswas critical. Ippen U9941has reviewedthe theory and experimentsof passivemode ocking of laserpulses.A true revolution in femtosecondgenerationoccurred,when Spence,Kean and Sibbett[1991] discovered hat a titanium-aluminum oxide (Ti-sapphire) aser crystal would yieldvery shortpulseswithout the useof a saturableabsorber. Self-focusing of the laser beamin the Ti-sapphirecrystal occursbecauseof its intensity-dependentndex of refraction. Incombinationwith a suitableplacedaperture, he self-focusing can cause alarger fractionof the pulseenergy o pass hrough the apertureat higher intensity. Thus, less absorptionand more gain occurs for more intense parts of the stochastic amplified spontaneousemission. This so-called Kerr-lens self-focusing is a purely dispersive effect. It isindependentof materialrelaxation times and can be as fast as he inverse of the frequencydetuning from the absorption edge of the material. Compensationof group velocdispersion in the laser crystal and the chirping by self-phase-modulation s againessential. Besidesprism and grating configurations, negative group velocity dispersionmay also be obtained from chirped mirrors. These are layered dielectric films in whichred-shiftedcomponentspenetratedeeper han blue-shifted components,as the thicknessof alternating films causing Bragg reflection increases with increasing depth. Thecompensationof self-phase-modulation y negativegroupvelocity dispersion eads o theformation of soliton-like optical pulsesNonlinear effects are essentialnot only in the generationof picosecondand femtosecondpulses,but also in their measurementand evaluation. The short pulse is split into twopulsesand a variable time delay is introduced between he first (or pump) pulse and thesecond or probe) pulse. The two pulsesare recombined n a thin nonlinear crystal andthe second harmonic generated n the crystal by the combination of the two pulses isobservedas a frmction of the time delay. Armstrong U9671first used his technique orpicosecondpulses. Note that one femtosecondcorresponds o a differential of 0.3prmnthe path lengths of the two pulses. The intensity of the secondharmonic as a function ofpath length differential yields the autocorrelationof the intensity of the laserpulse.For acomplete characterizationof the pulse the temporal behavior of the phaseof the lightfield must also be determined. This information may be obtained by analyzing thetemporal behavior of individual Fourier components n the generatedsecond harmonicsignal. It is spectrally analyzedas a function of time delay. Trebino and Kane [1993]introduced this technique, which they called Frequency Resolved Optical Gating orFROG. Other variations were subsequently ntroduced but they are all based on acomparisonof spectrally resolved componentsof the pulse and its delayed or advancedreplica.


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Conversely,pulsesmay be generatedwith prescribedamplitude and phasevariation. Afemtosecondpulse is spectrally resolved by a grating and different Fourier componentsmay be reflectedby different segmentsof piezoelectriccrystals. Voltages applied to thesegmentswill producedifferent path lengths or phases o individual Fourier componentson reflection. These componentsmay be recombined by the samegrating to produce amodified pulse with a different temporal phase variation. The different Fouriercomponentsmay, of cowse, also be attenuated y adjustable actors. Thesechangesmayalso be induced by passage hrough a liquid crystal array with a configuration ofelectrodes. The latter technique has been used by Shverdin, Vy'alker,Yavuz, Yin andHarris [2005] to generateahalf-cycle optical wave form of about 1.5fs duration. A 5fspulse of Ti-sapphire laser is used to generateseveral orders of antistokesand stokescomponentsof vibrational and rotational Raman transitions n hydrogen gas (H2 or D2).The componentscover a frequency range of more than two octaves. By adjusting theamplitudesand phasesof these componentsbefore recombining them it was possibletoobtain constructive interference over one half cycle, and nearly complete destructiveinterferenceoutside hat time interval.Femtosecondpump-probe techniqueshave led to many applications in time-resolvedspectroscopy n chemistry, biology and solid state physics, but their discussion fallsoutside the scope of this review. Zewail [2000] received the 1999 Nobel Prize forchemistry for this work on femtochemistry , the time-resolved spectroscopyof a largevariety of chemical reactions. Lobastov, Shrinivas and Zewail [2005] have recentlyextended emtosecond ime resolution to the field of electron diffraction. They call it 4Dulftrafast electronmicroscopy. A weak femtosecond "probe"pulse s used o liberate onthe averageabout one photoelectron rom the cathode of a standardelectronmicroscopewith a de Broglie wave length of 0.335nm at l2}kev energy. Distortion of the electronorbits due to spacecharge effects by a Coulomb repulsionbetween electronpairs is thusavoided. A pulse train of ten million pulses per second,builds up the diffraction of atargetthat has beenexcited by a femtosecond'ump" pulseat an adjustableearlier time.Thus, the variation in the diffraction pattern with sub-nanometerspatial resolution and1Ofsemporalresolution can be observed.The output of a Kerr-lens mode-locked abletop Ti-sapphire aser with a crystal volumeof a few cc. typically producesa train of lOfs pulseswith about one nanojouleper pllsewith a repetition rate of l0Mhz. Such a pulse train can be amplified by a factor of 10' or104by the chirpedpulse amplification (CPA) technique describedby Mourou, Barty andPerry' [1998]. The pulse is first deliberately engthenedby a factor of l0' to 10* by anantiparallel grating configtration before being amplified. This is necessary o avoiddamageby light induced dielectric breakdown n the ampliffing medium. The amplifiedpulse is then re-compressedby a matching configuration of grating pairs. The CPAtechnique can generatea frain of lOfs pulseswith a pulse energy of one microjoule, o.revenhigher. If sucha pulse is focused by a.microscopeobjective to an areaof 10-o m',the resultingpoWer lux density would be l0'o watts/cm', with a correspondingight fieldamplitudeof lO'volts/cm. This is approximately equal to the Coulomb field at the Bohrorbit in the ground stateof the hydrogenatom, or the field responsible or the binding of


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a valenceelectron n a molecule. It is physically obvious that any material subjected osucha field is immediately transformed o a fully ionized plasma. f thg light intensity islowered by one or two ordersof magnitude, n tire rangeo 10to o 101swatts/cm2, hereis still a probability for ionization by tururelingrather than by multi-photon ionization.The first xperimenton two-photon inducedphotoelectricemissionfrom an alkali-metalcathodewas carriedout by Teich, Schoerand V/olga U9641with a ruby laser. The effectof thermionic emission due to heating during the long laser pulse had to be carefullyeliminated. Bechtel, Smith and BloembergenU9751demonstratedour-photonemissionfrom tungstenby a picosecondNd-glass aser. The ionization of Kr atomsby an eleven-photon pio""rr at l.06prmwas reportedby Mainfray [978]. The ionization rate and theiormation of Kr* ions increasedas the eleventh power of the laser intensity. Thisprobably represents the limit of high-order nonlinear optical perturbation theory.i


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pulse. Phasematching between he harmonicsand the infrared pulse is possiblebecausethe generated lasma owers the optical index of refraction. The energydistribution overthe harmonic spectrumdependssensitively on the intensity and phase variation in theincident laser pulse. The generation of particular harmonics may be optimized bycontrolling the phasevariation as describedpreviously (Kaptein, Murnane and Christov[2005]).The classical picture also predicts that the recollision mechanism s not operative forelliptical or circular polanzation of the laser pulses. In this case he electron doesnotreturn to the ion along a linear path. Experimentally Dietrich, Burnett, Ivanov andCorkum ll994l have demonstrated hat a ten percentellipticity largely suppresses ighharmonic generation. Corkum, Burnett and Ivanov l99al have proposed a sub-femtosecondswitch by using two orthogonally polarized laser pulse trains with wowavelengths differing by ten percent. Linear polarization of the resultant light fieldwould only occur during a faction of an optical cycle and so would the recollisions.The classical model is substantiated by a fully quantum mechanical calculation(Lewenstein, Balcou, Ivanov, Yu, L'Huiller and Corkum U9941). The laser fieldadmixes a quasi-freeelectron wave-packet, oscillating coherently with the laser field.The radiation emittedby the motion of the electron,describedby the solution of the time-dependentSchroedingequation, s determinedby the second ime derivative of the largeinduced oscillating dipole moment.While the spectrumof odd harmonics s indicative of a seriesof sub-femtosecond oft x-ray pulses, it does not represent a measurementof their duration. Unfortunately, thetechniqueof secondharmonic generationused or femtosecondpulsedurationscannotbeused here becausehe intensity of the soft-ray pulses s much too weak. Itanani, Qur,Yudin, Yu, Ivanov, Krausz and Corkum 120021have escribedan alternativemethod, heattosecond streak camera. Attention is focused on the high energy tail of emittedharmonics by filtering out harmonics with lower energy by filters of metal foils. Thehigh energy end, generatedn a fraction of a complete optical cycle, is used to liberatephoto-electrons n another gas jet exposed simultaneouslyto the frrndamental opticalpulse. Photo-electronsare collected in a direction perpendicular to the linear laserpolarization, which causesa deflection and a change in energy of the emitted photo-electrons, (Henschel, Klenberger, Spielmann, Reider, Milosevich, Brabec, Corkum,Heinzmann,Drescherand Krausz [2001]).Reproduciblequantitave esults require the use of a very short reproducible emtosecondpulse. Such a pulse contains only a few optical cycles n the wavelength range of 0.7 tolpm wavelength from a Ti-sapphire laser. The relative phasebetween he carrier fieldand the envelopebecomes mportant (Brabec and Krausz [2000]). When this phase szero, the laser field maximum coincideswith the maximum in the envelope.At the twoadjacentfield extrema, ahalf optical cycle away, the envelope s already substantiallyreduced. If the intensity is carefully chosen,significant tunneling and emission of thehighest energy harmonics may be limited to a fraction of the optical cycle around themaximum. In this case, he high frequency ail drops smoothlyto zero. When the carier-


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Spence,. E.,Kaen,P.N.,Sibbett,W. , 1991,Opt.Lett.16,42.Shverdin, . Y., Walker,D. H., Yavtsz, .D., Yin, G. Y., Harris,S.E.,2005,Phys.Rev.Lett.94,033904.Teich,M. C.,Schoer,.M., Wolga,G.J.,7964, hys. ev.Lett.13,611.Trebino, .,Kane,D. J.,1993, .O.S.A, l0, 110.Zewul, A. H., 2000,Femtochemistryn Les Prix Nobel 1999,Almquist,Wiksell lnt.Stockholm,p 110-203.

n. bloembergen- from millisecond to attosecond laser pulses

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