8/4/2019 Maybe Pico Laser

1/7

192 IEEEOURNAL OF QUANTUMLECTRONICS, VOL. QE-18, NO. 2, FEBRUARY 198

Application of a Two-Wavele eto SemieoN. J. FRTGO, H. MAHR, AN D DAVID J . ERSKINE

Abstract-Wereporta wo-wavelength each of which s ndepen-dently tunable) ynchronouslypumped picosecond laserwhichhaslargespectralseparation,highconversion efficiency, andwide uningranges.The aserhasbeenused to find the time-resolved reflectivityof a photoexcited semiconductor n he bandgapregion.Unusuallyrapid relaxation of the screened excitonic reflectivity has been notedand a simple carrier diffusion model is proposed. The model also pre-dicts results whichagree with previously published data.

P I. INTRODUCTIONICOSECOND studies of condensed matter have beenasubject of inten se interest in th e last several years, and amajor research tool in the picosecond experiments has beenthe synchronously pumped mode-locked laser [11, [2] . Theselasers have several natur al adva ntages. The very high repe titionrates (lo8 Hz) allow sensitive detection techniques to be used,since high average powers do not require high peak powers.This permits heir use in low quantum efficiency systems,while their pulse reproducibility over long experimental timeallows signal averaging techniques to be exploited. The widetuning rangesavailable make possible the examin ation ofavariety of physical systems and, by tight focusing, the moder-ManuscriptreceivedAugust 31,1981. Thisworkwassupported nThe authors are with the Department of Physics and Materials Center,part by MSC/NSF Grant DMR-78-16751.Cornel1 University, Ithaca,NY 14853.

ate intensities can be elevated to the GW/cm2 range for higintensity experiments. Early experiments using such systemobtained their spectral and temporal resolution through a nolinear upconversion light gate [ 3 ] , [4] that analyzed thluminescence signal from aphotoexcited sample. The avantage of such measurements is that they probe the occupation of real energy levels in the relaxing system, but they havthe drawback that he efficiency and the resolution are inversely related. A technique that is complementary to thluminescence upconversion is the utilization of a second laset o probe the system after its ph otoexcitation by the first laseThe energy (spectral) resolution is the linewidth of the problaser. If the probe is a synchronized picosecond laser, ipulse width is the time resolution, while if the probe is a CWlaser, time resolution can be achieved by gating with the excitation pulse. Both types of lasers have been used, th e first iapump-probe echnique 151, and the second in a read-iread-out technique [ 6 ].This paper describes a laser tha t is o f th e first variety, but has several advantages that complement the earlier systemThese inherent advantages accrue from the basic design of thcavity, and they allow a larger spectral separation between thpump and probe laser, much higher average powers, and verlarge tunin g ranges. In th e next section we describe the lasitsel f its principles of ope ration, its cavity configuration, iperforman ce, and ts operating characteristics. In Section 1

0018-9197/82/0200-01,92$00.75 0 982 IEEE

8/4/2019 Maybe Pico Laser

2/7

FRIGO e t al.: TWO-WAVELENGTH PICOSECOND LASER 193

t ,GAIN DU E TO AMPLIFIER

F W XEQUIL.CAVITYFLUX

Fig. 1. Schematic epresentation of thenonsaturating oundtrip loss(dashed curve) and saturable gain (solid curve) experienced by a cir-culating ultrashort pulse, plotted as a func tion of normalized cavityflux j (see text). The laser will drive itself to th e flu x correspondingto the n tersect ion of the two curves.we describe the results of a preliminary experiment which illus-trates he lasers utility n the studyofphotoexcited semi-conductors and propose a simple model.

11. TH E TWO-WAVELENGTH INTERSECTING CAVITYLASERThe standard synch ronously pumped m ode-locked laser uses

a three-m irror cavity to focus the radiation tightly on to a free-flowing dye jet [7] . The cavity lengths of the dye laser andthe mode-locked pumping laser areapproximately equal sothat gain is presented periodically to a circulating pulse whosecavity roundtrip ime coincides with he pumping interval.This pulse arises from the cavity noise and adjusts itself inphase to m eet the pumping pulse at the dye jet [ 4] , [8] . Onemay estimate th e circulating pulse flux b y examining the over-all gain associated with pulse propagation through saturablemedia [9] . Fig. 1 plots the energy gain experienced by a pulsein traversing a saturable gain medium (e.g., a pumpe d dye jet )as a function of the pulses flux. A measure of the intracavityflux is j = nu/A,where n is the number of photons in the ulse,u is the stimulated em ission cross section, and A is the beamsarea at the medium. Thus j has an approximate physical de-scription as the number of photons in the pulse tha t atte mp tto stimulate a transition. It can be shown [9] , 16] that theultrasho rt p ulse, in traveling throug ha medium ofopticalthickness

Zi =I( x ) u d x , (11will have its flux amplified fro m j i to j f , where

Here, N ( x ) is the population inversion density, u s the stim u-lated emission cross section , and E is the thickness of the dyejet.Saturation effects become impo rtant when j x 1. Forsmall signal levels the gain exceeds the loss. The flux then in-creases on each round trip until he circulating pulse reachesthe steady -state flux for which the gain equals the loss, Le.,that j for which the gain and loss curves in Fig. 1 intersec t.The laser cavity ma y also include a saturable absorber. (Anonsaturable absorber presents a n intensity independent losswhich simply changes the magnitude of the cavity losscurve.) Appropriate choices of u and A allow the absorbing

G A I N

CAVITYI LOSS I

LOSS

..................... . . . ........GAIN WITH BOTH ...MEDIA PRESENT ...\ .......

INTRACAVITYFLUX?.O........................... -jobs- .O t 4.0......... EPUIL................... CAVITYFLUX

ABSORBER

(SATURABLE)SATURABLE) CAVITY LOSS

.Fig. 2. Representation of gain and loss as in Fig. 1 but with saturable

absorber also present (lower dotted line). Solid ine represents totalgain due to bo thaturable media. Inset: schematic of a two-wavelengthintersectingcavity aserwith womedia non ecavityan done nthe o ther .jet to saturate before the amplifying jet, since a given intra-cavity flux yields a larger j for the absorber tha n the corre-sponding j for the amplifier. Naturally, th e overall gain as afunction of intracavity flux changes (see Fig. 2 ) , bu t it is possi-ble t o saturate the absorber at relatively modest energy loss tothe circulating pulse. If th e saturable absorber is i tse lfa laserdye, however, the addition of feedback (mirrors) to make acavity completes that cavitys description as a synch ronou slypumped laser (see inset Fig. 2). Thus the second jet has tworoles: in the first cavity (solid line) it contrib utes t o the pulseforming process by being a saturable absorber [101, nd in thesecond cavity (dashed line) i t is a synchro nously pumpe d gainmedium. The wo cavities intersectata single spot in th esecond jet .An interesting fea ture of th e intersecting cavity laser is itsunique combination of intracavity and extracavity characteris-tics. It has characteristics of intracavity pumping in the sense

that th e dye jet for the second cavity is inside the first cavityand its exposure t o large cavity fluxes fully exploits he in-herent nonlinearity of saturation. But since the two intersect-ing cavities are almost en tirely distinct, th e laser has the char-acteristics of extracavity pumping in the sense that the twolasers are nearly independ ent; the beam s are distinct and canbe tuned, filtered, and manipulated independently. This com-bination of characteristics occurs precisely because the wocavities overlap at only one point, obviating the need for dis-persive separation.The configuration which we use is shown in Fig. 3. The mostobvious difference from he inset of Fig. 2 is that in bothcavities the jetsare surrounded by shortfocal length mirrors t oincrease j by decreasing the spot size. This laser has a num berof convenient features. The outpu t coupler of the first (Yor yellow) laser can be flat or nearly flat so that the length

8/4/2019 Maybe Pico Laser

3/7

1 9 4 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. QE-18, NO . 2 , FEBRUARY 19

R34-__-----------04\ v50-y

Fig. 3. Actual configuration of two-wavelength intersecting cavity laser.Solid line represents prima ry (yellow or Y)cavity with amplifyingand abso rbing media present. Dashed line repres ents second (red orR)cav i ty . Mirro rsRl , R 4 , an d Y5 are plane for convenience.a n be adjusted without the need to refocus at either j e t . Thezig-zag configuration reduces coma [ l l ] By using a four-mirror configuration for the second (R or red) laser, againcoma is reduced and t he R1 -to-je t distance can be adjusted toequal the Y,-to-jet distance, thus decreasing the jitter in thesynchronization between the wo pulses and decreasing thesensitivity of the red laser to cavity length mismatch. Qualita-tively, the pulse forming process in both asers is similar o thatfor the standard synchronously pumped laser [ 12 ], [4] , [ 8 ] .In Fig. 2 th e overall gain and loss s given for pulse passagethrough each jet. But relative to the overall gains, the yel-low pulse sees more loss on its eading edge from thesaturableabsorber and more loss on its trailing edge from he gainmedium. These two com pression processes [9 ] are balancedby a temporal diffusion due to the frequenc y dispersion in thecavity [4] , [I21 . The red cavity is almost identical to thestandard cavity but is pumped twice per period.The laser that has been described here has several advantagesover other ypes of two-wavelength picosecond pulse gener-ation. Compared to intracavity two-wavelength methods, theintersecting cavity lasers most obvious a dvantage is that thewavelengths and cavity lengths of th e two lasers can be tunedindependently of each other.That is, since the beams arephysically separate, each of the wo beams can encounterdistinct tuning elements and they can propagate in cavitieswithdifferent physical lengths [1 4] . Another advantage ofthe intersecting cavity laser is the fact tha t since the two cavi-ties are optically distinct as well, the mirrors do not have thesame stringent requirements that would be necessary foracavity that had mirrors exposed to bo thwavelengths.Compared to parallel pumping configurations (for instance,an ion laser synchronously pumping two ndependentdy elasers), the pre sent laser offers a more efficient use of hepump power, since only one threshold must be overcome, andhence higher average powers can be attained[I51 . In addi-tion, the spectral separations of the two outputs can be muchgreater for the intersecting cavity laser. For parallel pum ping,bo th lasers experience a single Stokes shift aw ay from hepump laser, while in our laser the second cavity suffers twoStokes shifts since it is pumped by the first. This extra Stokesshift has permitted us to achieve spectral separations as greatas 1500a (0.45 eV) between t h e two output wavelengths.Finally, we compare to a tandem pumping configuration inwhich the outp ut of the first laser is used to pump the secondlaser, and sketch an interesting feature of intracavity pumpedsystems which wecall negative spectral feedback . If theyellow laser is being tuned to a spectral region for which thered dye absorption cross section is dropping, the red dye pre-sents less loss to the yellow cavity. But if the loss in the yel-

3 O O r X. , , , / C O N F I G U R A T I O N30 % T ISTANDARD 3-MIRRORTANDARD 3-MIRROR

/- - x\ , /3O%T C ON FIG UR ATI ON+,/

\/ \ Y OUTPUT

I : \ \ / (8 %T )

W A V E L E N G T H ( n r n )Fig. 4. Comparison of wavelength dependen ce of standard and ntesecting cavity out put s. Bot h yield 8 ps pulses in yellow.) Dashecurve is outp ut fro m three-mirror configuration, upper solid curve

yellow ou tpu t rom two-wavelength configuration, lower socurve is 10 t imes concomitan t red output. Dotted curve is maxmum usable out pu t from three-mirror laser if as littleas 80 mW is dverted t o tandempum p a econd laser. Note the muchnarrowertuning range.low cavity decreases, then that cavitys flux (and hence the relaser pump ing rate) in creases. The red laser is then autom atically pumped harder at exactly those spectral locations wherit must be pumped harder. This negative spectral feedbacgreatly enhances the usefulness of the laser. In the andempumping configuration, the regions where the red lasers crosection is dropping require more yellow power t o pumpsteadily decreasing the power available foranexperiment.Additionally, the intersecting cavity configuration allows opeation in a higher j regime, which results in flatter outpupower characteristics due to more complete saturation I61as Fig. 4 shows. Both of the yellow o utp ut curves yielde8 ps pulses (we used a th ree-pl ate birefringent filter). Althougfor most of he uning range the hree-mirror configuratiohas a higher power out put, the usable yellow power for thetandem pumping case is the tota l power minus the thresholfor the second laser. Even assuming a constant red thresholof as low as 80 mW across the entire tuning range, one seethat the tuning range for th e intersecting cavity laser is severtimes wider than that for the tande m umped configuration.The data in Fig. 4 were taken oran Ar laser pum pinrhodamine 6G and cresyl violet, but there is nothing that re-stricts one to these components. The technique should worfor a variety of pum p laser lines (e.g., 4 88, 6 47 nm in the iolaserseries) and dye laser pairs (e.g., mos t rhodam ines anoxazines). We have used a variety of dyes for the second jeamong them are nile blue, oxazine 720 ,oxazine 725 , LD 690and various mixtures to tailor th e outp ut. Fig. 5 showsfew of th e possibilities to illustrate tradeoffs tha t are open tthe user. The yellow autocorrelation widths were approxmately 8 ps, the red autocorrelation widths were approxmately 4 ps (we used a two-plate birefringent filter in the recavity) and the cross correlations w idths varied with pow e

8/4/2019 Maybe Pico Laser

4/7

FRIGO e t al.: TWO-WAVELENGTH PICOSECOND LASER 195YELLOW REDOUTPUT(5-8 psec ACI (4 psec ACIOUTPUT

R h 6 G , , CV(I*,~T) OX725107%TI1 200mw5-8 psee A / C TGr- IOrnWO X 7 2 5 i0.17-T) _ _ _ _ _ 5 0 - 2 O O g WI , I , , I , , I / I I , I I I I I I , l I

550 60 0 650 700 750X (n rn l

Fig. 5. Spectral characteristicsof several differen tdye andcouplingoptions.

12 ps at 100 mW yellow power to 1 6 ps at 200 mW yellowpower. For high power uses, cresyl violet and oxazine 725span the range between 6200 A and 7000 A with 20 mWaverage pow er in CV and 10mW in OX 725. These powers arehigh enough tha t they hold the possibility of attaining non-linear optical effects using acombination of the wo wave-lengths. When a wide tuning range is desired, on heotherhand, lower o utp ut coupling can trade power for tuning range.For instance, OX 725 was tuned over an 800 A width, and theperiod of the uning filter was reached before he dye gaindropped off. This degree of tuning range is unprecedented insuch lasers.In short, the intersecting cav ity laser we are reporting herecan be characterized as having large spectral separations be-tween the two outputs, broad tuning ranges in both outputs,and flexibility in cavity, pump , and dye pair selection. Its highflux m akes no nlinear processes accessible, and the high repe-tition rate allows a variety of sensitive detectio n techniquesto beused.111. APPLICATION:REFLECTIVITYND THEDIFFUSIONOF CARRIERS

In thi s section we present the results of a preliminary experi-ment in which we have applied our laser to study CdSe. (Theexperiment is an example of a use of the laser in which theflux from th e shorter wavelength out put drives a system into anonlinear response and the second wavelength merely probesthe system.) We are interested in following the fast processeswhich occur in direct gap semiconduc tors such as CdSe afterintense photoex citation. A rich variety of physical processes(Mott transition, electron-ho le plasma, liquid,and droplets,etc.) have beenhypothesizedan dexperimentalsupportfo reach has been reported [17] . Since in some cases the physicalprocesses are expected t o be mu tually exclusive, the field is ofinherent nterestand not yet completely understood. Manyoptical experiments have been performed to ascertain whichrelaxation processes are taking place, and lasers with severalnanosecond pulse durations have figured prominently [171 .Picosecond and subpicosecond transmission [18] , lumi-nescence [19] , and gain [ 2 0 ] measurements have been per-forme d on materials such as CdS , CdSe, and G aAs. Each ofthese types of experiments can be performed with our lasersystem, and each answers different types of questions aboutthe relaxation processes occurring in the semiconductor. Wereport here an additional type of experiment, namely, whatwe believe s the first time resolved [21 ] reflectivity experi-men t perform ed i n the bandgap region of a direct gap semi-conductor under high photoexcitation [22] . The reflectivity

II

, ~ - - M O T T TRANSITIONI nWTT z O C ~ - ~

Fig. 6. Possible trajectory of photoexcited semiconductor in e-h den-sity (n ) nd temperature ( T ) plane. At t ~ ,ensity no is created andsystem relaxes through recombination, diffusion, internal conversion,etc. Phonon generation can change temperature as well. The reflec-tivity in excito nic region is featureless for densities greater tha nnMb u t recovers as system relaxes belowMott density .

measurem ent is of interest or several reasons: first, t is asurface^' probe (in the sense tha t only the properties within awavelength of the surface are usually interrogated); and sec-ond, it is an ideal test for th e existence of oscillators, takenin the Lorentz sense to be two quantum levels. The oscillatorwe observe (located just below th e band edge) is the Wannierexciton formed by the attraction of an electron in the con-duction band and hole in the valence band. This type of mea-surement complements others, since it does not integratethe entire optical de pth of th e sample as do transmission ex-periments and does not have the ambiguity of determining thesource of the photons as do luminescence experiments [23 ].The experiment uses the two-wavelength laser first to excitethe crystal with photons of energy above the bandgap, creatinga high density of carriers in th e conduction b and, and then toprobe the reflectivity of the relaxing crystal as a function oftime and spectrum. There is not universal agreement on whatshould occur at low (LHe) temperatures after the photoexcita-tion, but it is clear that at high enough electron-hole (e-h)densities there should be a plasma state, and at very low e-hdensities the system should condense into excitons. Betweenthese two regions is aMott ransition 24]between heconducting plasma state and the insulating exciton state[25 ]. Motts criterion for the transition is

n g a x 0.2where a, is the Bohr radius for an exciton in the solid, and IZ isthe num ber d ensity. For .CdSe, this yields a Mott density ofn~ = O I 7 cma 3. After intense picosecond pulse excitatio n, adense e-h plasma is created which screens out the formation ofexcitons; there are no excitons present, real or potential, sincethe oscillator (the two-level system) is no longer present in theexcited region. As time proceeds, diffusion and recombinationprocesses reduce the e-h density to values below nM so that atlater times the reflectivity of the excitonic oscillator will re-appear. Fig. 6 sketches the process evolving from the initialsystem poin t as created by a short pulse at to and possessingan initial temperature and density. As time progresses to t l ,the density decreases to the Mott density and then below. Thetemperature of the system can also vary as the system relaxes.We have not drawn in an ntersec tion with an electron-holeliquid (EHL) coexistence curve since a calculation shows that

8/4/2019 Maybe Pico Laser

5/7

196 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. QE-18, NO. 2 , FEBRUARY 198

YELLOWF I L T E R SBLOCKING

L HeXSTAT-1.8K($-$A S E R L A S E R

Fig. 7. Experimental setup. Pump and probe beams are spatially over-lapped after temporal delay is set by delay line. Correlator providesreal-time diagnostic auto- and cross correlations as experiment runs.Beams floodpinh ole which is imaged to crystalsurface,while r e dpower is mon itore d to normalize reflectivity signal. Probe laser wave-length is scanned to provide exc itonic reflectivity signature at eachdelay.the steady-state lattice temperature in the excitation region isequal to or greater than the suggested EHL critical temp era-ture [26] .

The experimental apparatus we have used to examine thisprocess is shown in Fig. 7. The pump and probe laser outputsare combined on a dichroic filter after a variable time delay isadded to the probe laser pulse. To ensure that the pulses re-main correctly spaced, we divert a small portion of the com-bined beams to acorrelationsetup so thatauto- and crosscorrelations can be performed while the experiment is inprogress. The combined beams flood a pinhole t o reducethe spatial inhomoge neity of the Gaussian profiles and hepinhole is imaged onto the surface of the crystal immersed insuperfluid helium. The light which is reflected from thecrystal surface is monitored and is electronically divided by aportion of the light tha t goes through he pinhole. This di-vided ignals proportional to the crystal reflectivity. BYscanning the probe laser wavelength through the excitonic re-gion, we can observe the reflectivity for each time delay set bythe delay line.An examp le of reflectivity curves tak en at a series of timedelays shows (see Fig. 8) that he qualitative processes de-scribed (Fig. 6) are occurring. At the earliest time delay theexciton is completely screened ou t. Since no 20 0 nM fo rthis case (where no is the density of absorbed photons) and

we have assumed a penetration depth of 0.1 pm [27], this ishardly surprising. What s quite nterestin g, howev er, is theunexpectedly rapid reappearance of he excitonic oscillator.Assuming a carrier diffusion of 1 pm in 1 ns [26] and a life-time as short as 300 ps [19], [23] ,[28 ], one expects thedensity to exceed nM for more than 1 ns, at which time the.excitonic oscillator should begin to recover. Thedata showan almost complete recovery of the oscillator after 1 ns. Weoffer as a tentativ e expla nation of his effect a carrier diffusioninto he bulk of the crystal that occurs much more rapidlythan has been assumed to date.We assume th at the carrier diffusion at these low tempera-

> -t2 -w -I-O

tRU N 8

I I II8225 1.8250 I8275ENERGY (eV)

Fig. 8 . Wavelength dependent reflectivityofCdSe at different timefollowing photoexcitation. The exciton is screened at 3 3 ps but recovers quickly.tures is dominated by mpurity scattering from he n;=loi6 cm-3 mpuritydensity . By treating he impurities aionized centers whose Coulomb potential is screened by thcarrier plasma, an effective diffusion coefficient can be determined by using elementary kinetic heory and the Borappro xima tion. We use the screened poten tial

~ ( r )- - h r2Kr (4where .K is the static dielectric constant and X is the ThomasFerm i screening wavevector, given by

a, is theexcitonic Bohr radius, and kF is the Fermi wavevector. For densities greater than n M , his approach yields density dependent diffusion coefficient of theapproximateform (see Fig. 9)

We have calculated Do 100 an d 01 = 3 taking ambipolar diffusion and full carrier screening into account [161 . At higdensities the potential is more effectively screened so that thcarriers diffuse rapidly away from the surface. As t h e densitydrops, however, the impurities become more efficient scatterers, and make the diffusion coefficient drop with density [29]A numerical solution of the nonlinear diffusion equationshows that after only 10 ps, the carriers have diffused almos2 pm into th e rystal with a co ncomitant reductionby a factoof 20 in density. The solutio n also shows a very rapid reduction in density to below theMott density. Adrift velocitdescription (1 pmlns) predicts a density that is everywhergreater than nM after 1 ns, while the diffusion model predicta density which is everywhere less than nM afteronly400 psat which point i t is an order of magnitude lower than the drifvelocity predic tion. The reflectivity data in Fig. 8 do not rulout eithera condensation to a n EH L or a coexistence oexcitons and plasma at densities below n M , but do indicat

8/4/2019 Maybe Pico Laser

6/7

FRIGO et al.: TWO-WAVELENGTH PICOSECOND LASER

101 110.29.34 Af7.6 1.33

BORN APPROXIMATIONGEOM 16.7 03 3 / / , BROOKS-HERRING

-GEOMETRIC

1001 / I/

I f I IIO IOI 1 0 ~ 10 IOn-

Fig. 9. Diffusion coefficients calculated for ambipo lar carrier diffusionagainst plasma-screened im purity scattering in various approxima -tions. Geometric refers to opaque scatterers.

tha t regardless of the ultimate fate of the e-h system, theremay be early diffusion processes which must be taken int oaccount.The diffusion mod el can easily be extend ed to give approx i-matesolutionsfor n(t), the imedependentdensity of theEHP afterultrashort pulse (USP) excitation nd nss, th esteady-state plasma density achieved under nanosecond excita-tion . We find th atn ( t )= no ex p ( - t / ~ ) [l t 1 t 2 / a ) no/nM)a!

. D o d d % )1 - exp ( - a m 1 1/(0(+2) (7)for the time dependent den sity [ 3 0 ]. In this expression, 7 sthe carrier lifetime, and no is the photon absorption density.Since no is inversely proportional to do,n ( t ) s independent ofdo after very short imes. The approximation to n ( t ) agreeswell with our numerical solution, since our fairly large excita-tion spot size (-40 m) makes the diffusion essentially onedimensional. A feature of the diffusion model which gives usincreased confidence is the fact that itcan be used to interpretother data which ave recently been published by Hoshida et al .Their luminescence measurements lead them to a calculateddensity as a function of time. Table I presents the data as eadfrom Fig. 3(b) of their publication [ 3 2 ] . Using our own valuesof DO nd a, and 7 = 300 ps, [23] we show in Table I densitiescalculated by (7). The agreement is quite good, especiallysince their no was nearly twice ours and their excitation wave-length was 600A closer to the bandgap. In fac t, themore gen-eral point tha t he peak density they observe is almost 15times smaller than the density one would expect (i.e., n o ) up -ports the fastdiffusion hypothesis. After ~1.50s their datashow aonstant ensity of *3 X ~ m - ~ ,eature ourmodel does not explain. However, the agreement at earlytimes with their data and the rapid recovery of the excitonicreflectivity that we rep ort ends credence to the possibilitytha t very rapid carrier diffusion effects must be taken in to ac-countat early times to describe the relaxation ofphoto-excited sem iconductors. The existence of such effects couldinfluence such seemingly disparate areas as laser annealing,

197

TABLE INORMALIZEDENSITIEST E A R L Y IMESFTER HOTOEXCITATIONT IME (psec) EXP ( R e f . 32 ) CALC (Eon . ( 7 ) )

20 8 8 .98@ 5 5. 0

12 0 4 L .015 0 3 3 . n

micro structure device design, and high-speed switching devices.1V. S U M M A R Y

We have described a new two-wave length picosecond laserwhich has he advantages of high output flux, independenttuning, broad uning ranges, and large spectral separations.The laser augments devices which are currently being used toprobe the relaxation of photoexcited semiconductors and hasbeen used to obtain he first time resolved reflectivity spec-trum near the bandgap of a photoexcited semiconductor. Wehave seen an unusually fast relaxation of the screening of theexciton and have proposed a carrier diffusion model that pre-dicts the rapid recovery. The model also predicts results th at,at early times, agree with previously reportedexperimentaldata.ACKNOWLEDGMENT

N. J. Frigo would like t o thank Prof. N. W. Ashcroft andDr . J. Oliva for a series of very fruitful discussions.REFERENCES

[ l ] C. V. Shank, E. P. Ippen,an d S . L. Shapiro, Eds., PicosecondPhenomena, vol. 4, Springer Series in Chemical Physics. Ne wYork: Springer, 1 978.[2 ] R. Hochstrasser, W. Kaiser, and C. V. Shank, Eds., PicosecondPhenomena II, vol. 14, Springer Series in Chemical Physics. NewYork: Springer, 1 980.[3] H. Mahr and M. D. Hirsch, An optical up-conversion ight gatewith picosecond resolution, Opt . Commun., vol. 13, pp. 96-99,1975.[ 4 ] N . J. Frigo, T. Daly, .and H. Mahr, A study of a forced modelocked CW dye laser, IEEE J. Quantum E lectron., vol. QE-13,[ 5 ] J. P. Heritage, Vibrational dephasingmeasurements with CWmode-locked dye lasers, Appl .Phys .Lett . , vol. 34,pp .470-4 7 2 , 1 9 7 9 .[ 6 ] E. P. Ippe n and C. V. Shank, Eds., Picosecond Phenomena, vol.

; 4 , Springer Series in Chemical Physics. New York: Springer,1978, p . 103 .[7 H. Kogelnik e t a l . , Astigmatically compensated cavities for CWdye laser, IEEE J. Quantum Electron. , vol. QE-8, pp. 373-379,1 9 7 2 .[ 8 ] C. P. Ausc hnitt, R . K. Jain, and J . P. Heritage, Cavity leng th de-tuning characteristics of the synchronously mode-locked CW dy elaser, IEEE J. Quantum Electron. , vol. QE-15, no. 9, pp. 912-917, 1979.[9] G.H.C. New, Mode locking ofquasi-continuous lasers, O p t .Cornmun., vol. 6 , pp,188-192,1972;and Pulse evolution inmode-locked quasi-c ontinu ous lasers, IEEE J. QuantumElec-tron. , vol. QE-10,pp .115-124,1974.Thesepaperspresentadescription ofpulse propagation in saturablemedia under he

[ 101 S ince m ost laser dyes can be viewed as ideal four-level media, thera te equa t ion approximat ion .saturation of the second jet is desirable but no t necessary for thelaser to operate.[ l l ] M. H. Dunn and A. I. Ferguson, Coma compe nsation in off-axislaser resonators, Opt . Commun. ,vol. 20, pp. 214-21 9, 1977.

pp . 101-109 ,1977.

8/4/2019 Maybe Pico Laser

7/7

198EEEO U R N A L OF QUANTUM ELECTRONICS, VOL. QE-18 , NO. 2 , FEBRUARY 198[ 121 H. A. Haus, A theory of forced mode locking,IEEE J. Quan-tum Electron. , vol. QE-11, pp . 323-330, 197 5.[ 13 1 N. Frigo, C. Hemenway, an d H. Mahr, Cavity leng th stabilizationtechnique for synchronously pumped mode-locked lasers, Appl.Phys. Lett. , vol. 37, pp. 981-984, 19 81.[14]Althou gh he physical engths of the wo cavities areequal inintracavity pumped lasers, it is the optical lengthswhich must bemade identical for synchronously pu mped systems. See [4 ] and

[8 1 .[ 15 ] This is equivalent to saying th at slope efficiencies are greater tha nthe overall efficiencies.161 This point will be amplified in a future communication.171 C. Klingshirn and H. Haug, Optic al prop erties of highly exciteddirec t gap semiconductors,Phys. Rep ., vol. 70, pp. 315-398,1 9 8 1 .18 1 C. V. Shank, R. L. Fork, R. F. Leheny, and J . Shah, Dynamicsof photoexcited GaAs band-edge absorption with subpicosecondresolution,Phys. Rev. Lett. , vol. 42, pp. 11 2-115 , 1979.191 H. Yoshida, H. Saito , and S. Shionoya, Time resolved spectra ofspontaneou s luminescence from high density electron-hole plasmain CdS,Solid State Commun., vol. 33, pp. 161-165 , 1980 .[ 2 0 ] K . Bohnert e t al. , Gain spec troscopy and plasma recombinationin CdS, Solid State Commun., vol. 27, pp. 295-299, 1978 .[2 1] By time resolved we mean that the experim ent was not carriedo u t in the steady-state (i.e., nano seco nd) time regime.[2 2] Sh an k e tal . have measured reflectivity (C. V . Shank et al., Pico-second time resolved reflectivity of direct gap semiconductors,Solid State Commun., vol. 26, pp. 567-570, 197 8), but on ly atfixed wavelength which was well above the bandg ap.[23] See T. Daly and H. Mahr, Time resolved luminescencespectrafrom highly photoexcited CdSe at 1 .8 K,Solid StateCommun.,vol. 25, p . 323, 1978, and [1 9 . Of course, we pay fo r this ad-vantage by not being able to determ ine the occupation numbersfo r the exciton.[ 2 4 ]The abruptnessof theMo tt ransit ion is stillunder investi-

[2 5 ] N . F. Mo tt,Meta l-Insu lator Transitions. New York : Barnes andgation.Noble, 1974.[26] Using scaling laws (see T. L. Reinecke and S . C. Ying, ScalingRelations for EHD condensation in semiconductors, Phys. Rev.Lett. , vol. 43, pp. 1054-1057 , 1979), and T, for CdS of 55 K(R . F. Leheny and J. Shah , Condensation of optically excite d

carriers in CdS, Phys. Rev. Lett ., vol. 38, pp. 511-514, 197 7one arrives at Tc = 28 K for CdSe. This agrees with a theore ticaprediction of 30 K given by M. Rosler andR. ZimmermannPhase diagram of EHL in polar semiconductors, Phys. StatuSolidi ( b ) ,vol. 83, pp. 85-91, 197 7.[27] R. B. Parsons, W. Wardzynskl, ana A. D. Yoffee, Theopticalproperties of single crystals of CdSe, Proc. Roy. SOC. Ser. A.[28 ] We assume that he luminescence ifetime is a lower boun d fothe carrier lifetime.[2 9] One can view this as a transp ort equivalent of the Zener diodwith density corresponding t o voltage and transport current coresponding to electrical current.[301 The developm ent of the expressions will be described mor e fullelsewhere.[ 3 1 ] Do calesasn;.[ 3 2 ] H. Yoshida, H. Saito ,an d S. Shionoya, Picosecond elaxationprocesses of high density electron-hole plasma in CdSe, PhyStatus Solidi (b),vol. 104 , pp. 331-340, 1981 .

V O ~ . 62, pp. 120-131, 1961.

N. J. Frigo, photographand biography not available at he ime opublication.

H.Mahr, photograph and iography not available a t he ime opublication.