450 OPTICS LETTERS / Vol. 21, No. 7 / April 1, 1996

Time-resolved studies of stimulated emissionfrom colloidal dye solutions

Masood Siddique and R. R. Alfano

New York State Center for Advanced Technology for Ultrafast Photonic Materials and Applications,Institute for Ultrafast Spectroscopy and Lasers, Department of Physics and Department of Electrical Engineering,

The City College of New York of the City University of New York, New York, New York 10031

G. A. Berger, M. Kempe, and A. Z. Genack

New York State Center for Advanced Technology for Ultrafast Photonic Materials and Applications,Department of Physics, Queens College of the City University of New York, Flushing, New York 11367

Received October 19, 1995

The temporal profiles of the emission from titania particle suspensions in Rhodamine 640 perchlorate dyesolutions excited by 10-ps pulses of 527-nm radiation were measured over a wide range of particle and dyeconcentrations and laser powers. The dynamics of stimulated emission from random media is modeled by arandom walk of photons within the colloid and rate equations for molecular excitations. The pulse width andthe dependence of the threshold for laser action on dye and scatter concentration are computed by a MonteCarlo simulation of the model and are found to be in qualitative agreement with experiment. 1996 OpticalSociety of America

Lasing action in random amplifying media1 has beenobserved in powdered phosphors2 and in colloidal sus-pensions in dye solution.3 The radiation followingpulsed excitation is emitted in a short burst with anarrowed spectrum compared with those from spon-taneously emitted radiation.3,4 Because stimulatedemission is induced at a pumping level below thatrequired for the observation of signif icant amplif iedstimulated emission in a neat dye solution, such sys-tems may find applications as novel displays, switches,and sensors.

In this Letter we explore the mechanism for lasingby comparing ultrafast emission measurements ona time scale comparable with the residence time ofthe pump photons in the medium and much shorterthan the excited-state lifetime to a Monte Carlosimulation of photon migration and level occupation.The 10-ps excitation pulse used in these experimentswas an order of magnitude shorter than in previousmeasurements. The temporal profile of emissionwas measured with a resolution of 10 ps in a seriesof samples of titania particles suspended in solutionsof Rhodamine 640 perchlorate in which lasing wasobserved by Lawandy et al.3 Suspensions are particu-larly useful because they allow one independently tochange the transport mean free path l, in which thedirection of propagation at the pump frequency israndomized, and the small-signal absorption lengthat the pump wavelength la, by varying the density ofscatterers and the dye concentration, respectively.

We produced the colloid by mixing DuPont R960 pow-der of alumina-coated titania particles with an aver-age diameter of 0.25 mm with Rhodamine perchloratedye in methanol solution. The dye concentrations var-ied between 1024 and 2.5 3 1023 M, corresponding toabsorption lengths la between 1400 and 50 mm. Thedensity of scatterers was varied between 5 3 109 and5 3 1011 cm23. The highest concentration studied hada volume fraction of 0.4%. The values of l that cor-

0146-9592/96/070450-03$6.00/0

respond to these concentrations were measured to bebetween 16 mm and 1.6 mm for the emitted light and10 mm and 1 mm for the pump light.

A 10-ps pulse at 527 nm, obtained from a frequency-doubled single-shot Nd:glass laser, was focused ontothe colloid contained within a 1 cm 3 1 cm 3 3 cmglass cuvette to a spot size of 0.5 mm. The incidentbeam made an angle of ,5 deg with the normal to thesample surface. We varied the pump pulse intensityfrom . 400 to ,1 mJ by inserting neutral-densityfilters in the beam. A portion of the laser pulse wascollected by an energy meter to monitor the incidentpulse energy. The light that was backscattered fromthe front surface of the sample surface was collectedand collimated by a lens. We removed light at thepump frequency by passing the collected light throughthree long-pass filters, which cut off wavelengthsbelow 540 nm. This light was focused onto the slitof the streak camera along with a small portion ofthe incident pulse to provide a time reference. TheHamamatsu C979, with a silicon intensified targettube (C1000) and a temporal analyzer streak camera,had a temporal resolution of ,10 ps.

In the neat 1024-M dye solution a short pulse onthe picosecond time scale was observed only for pumppulse energies above 25 mJ . The threshold for las-ing action is defined as the pump energy for whichthe duration of the emitted pulse is 100 ps. As scat-terers are added to the solution, laser action ceasesup to the highest energies available with our laser forscatterer densities of 5 3 109 and 5 3 1010 cm23. Asthe density of the scatterers is further increased, laseraction reappears at higher thresholds than in theneat dye solution. At higher dye concentrations lasingaction requires a higher incident power in the neat so-lution, but the addition of scatterers lowers the thresh-old for lasing action significantly below the valuein the neat solution, and pulses with widths compa-rable with that of the incident pulse are observed.

1996 Optical Society of America

April 1, 1996 / Vol. 21, No. 7 / OPTICS LETTERS 451

Fig. 1. Time-resolved emission from Rhodamine 640 dyein methanol (1023 M, la ­ 140 mm) with titania particles(5 3 1011 cm23, l ­ 16 mm). (a) Spontaneous emissionafter excitation with 7 mJ of pump light. (b) Emissionat threshold of ,13-mJ pump energy. (c) Short pulse ata pump energy above threshold (16 mJ ). The referencepulse shown in each figure indicates the input pulseduration and the time resolution of the detection system.Its timing with respect to the onset of the emission variesfrom (a) to (c). EpyEthr is the ratio of pump to thresholdenergies.

Examples of the change in the emission profile as thepump energy increases are shown in Fig. 1. Table 1gives the pulse width, uncorrected for the temporal res-olution of the streak camera, as well as the thresholdenergy for lasing for a wide range of values of l and la.

In the weak-scattering regime in which the trans-port mean free path is much larger than the wave-length, one can therefore ignore wave interference incomputing average transport within the medium. Theenergy f low of pump and emitted photons can then bemodeled by a random walk of photons.1,5 The neglectof wave coherence is in accord with the observation thatlocal intensity f luctuations in ref lection from powderedsamples are small.2

The random walk of photons is computed with a tem-poral step size equal to the mean free time t ­ lyv,where v is the phase velocity in the solution. The val-ues of l at the incident and the emitted frequencies are

Table 1. Threshold Pump Energies and Measured FWHM of the Emission for VariousParticle Densities and Dye Concentrationsa

Dye Concentrations (molyL)yla smmd at the FollowingThreshold Energies (mJ )yEmission FWHM (ps)b

Particle densityscm23dy1 smmd 1024y1400 1023y140 2.5 3 1023y50

0 25y56 45y30 50y305 3 109y1600 NL 35y16 15y181018y800 NL 25y16 10y185 3 1010y160 90y80 17y26 8y181011y80 50y50 15y22 12y185 3 1011y16 50y24 13y20 6y20

aThe transport mean free path given is for the emitted light. The duration of the emitted pulse was the shortest obtainedat pump energies up to 400 mJ . In most cases the shortest pulse width was reached well below this pump energy.

bNL, Lasing was not observed for pump energies as high as 400 mJ .

taken to be the same. The incident beam is assumedto be random after penetrating a distance l into thesample. We further assume that the incident beamis a plane wave with incident intensity equal to thef luence of the incident pulse divided by the equiva-lent area of the beam at the laser surface, which istaken to be pw0

2, where w0 is the beam waist. Thusthis model focuses exclusively on the evolution of thesample along the longitudinal direction normal to thesurface. The average magnitude of the projection ofthe displacement of diffusing photons along the lon-gitudinal dimension during one mean free time isly2. After each mean free time, photons that are notabsorbed and that do not pass through the sample sur-face have moved either to the right or to the left by ly2with equal probability. The internal ref lectivity of thesample boundaries is 0.15. The sample thickness istaken to be 1 mm, which is much larger than the inten-sity attenuation length La ­ s1/3llad1/2 for the range ofparameters considered.

The dye molecule is modeled as a four-level system.Because the relaxation times from the terminal levelsof the pumped and emitting transitions, levels 4 and2, respectively, are generally on a subpicosecond timescale, we assume that only ground state, level 1, andthe emitting state, level 3, have significant population,n1 1 n3 ­ n, where n is the density of dye moleculesand ni is the density of molecules in the ith level. Thelevel populations and the emission and absorption ofphotons are governed by rate equations that involvethe cross sections for absorption of the pump radiationand for emission as well as the level populations andthe densities of pump and emitted photons.

In the Monte Carlo computation we keep track ofthe density of incident and emitted photons and ofthe population density n3 at points with depths in themedium that are multiples of ly2 at time intervalsthat are multiples of t. The emission spectrum ofRhodamine 640 (Ref. 4) is divided into 20 segmentsof equal area. The spatial and temporal evolutionof the photon density of each of these segments ofthe spectrum is followed separately. We take thethreshold to be the pump energy at which the ratioof the total number of stimulated and spontaneouslyemitted photons is unity. At this point we findthat the emission spectrum has narrowed to a fewnanometers and the emission has a width of less than

452 OPTICS LETTERS / Vol. 21, No. 7 / April 1, 1996

Fig. 2. Emission profiles from the Monte Carlo simula-tions for l ­ 18 mm and la ­ 140 mm. Emission for apump energy (a) below threshold (0.12 mJ ), (b) at threshold(0.47 mJ ), (c) slightly above threshold (0.59 mJ ), and (d) farabove threshold (2.8 mJ ).

Fig. 3. Calculated threshold pump energy versus (a) la forfixed l ­ 30 mm and (b) l for fixed la ­ 120 mm.

100 ps. Thus the transition in temporal and spectralfeatures of emission appears to occur at the samepump energies, and our criterion for the thresholdin consistent with that used in this and previousexperiments.3,4

The Monte Carlo simulation allows use to study thedynamics of molecular excitation and deactivation andwave transport in the medium on the same footing andis equivalent to solving the coupled nonlinear photondiffusion and molecular rate equations when diffusiontheory is applicable.

The temporal profile of the total number of emittedphotons at all frequencies is shown in Fig. 2 for a10-ps incident pulse for incident power levels thatcorrespond to excitation below, at, and above thresh-old in a sample with values of l and la similar tothose in Fig. 1. At low pump energy the emergingphotons are produced predominantly by spontaneousemission with the molecular lifetime of 4 ns (Ref. 4)[Fig. 2(a)]. At the threshold for laser action we findan emission pulse of width 40 ps, which reaches itspeak 60 ps after the arrival of the leading edge of thepump pulse [Fig. 2(b)]. Above threshold the emissionshortens dramatically and reaches its peak valueat earlier times. At pump energies six times abovethreshold the peak of the pulse is delayed by 10 ps

and its width narrows to 3 ps, which is shorter thanthe incident pulse [Fig. 2(d)]. The emission spectrumnarrows from the width of 40 nm associated withspontaneous emission below threshold to 7 nm abovethreshold. The temporal profiles in the experimentand in the simulations are similar. The principaldifference is that the lasing thresholds found in thesimulations are an order of magnitude lower thanobserved experimentally. This difference cannotbe explained by absorption of the emitted light inthe medium, which was omitted in the above cal-culations. We find that including the absorptiontypically raises the threshold by only 40%. However,the difference in the thresholds between experimentand our model may be due to the neglect of thetransverse excitation profile. Because this omis-sion results in a f lat transverse gain profile, theemitted photons cannot escape the gain region bytransverse diffusion. The difference between the ex-periments and the simulations should diminish whenl and la become significantly smaller than the beamdiameter.

In Fig. 3 the results of the computation of thethreshold energy as a functions of l with la heldconstant at 120 mm and as a function of la with l heldconstant at 30 mm are shown. In these calculationsthe actual spectral distribution of the spontaneousemission was represented by an effective cross sectionof se ­ 4.2 3 10216 cm2. The threshold dependsonly weakly on l and la. This can be anticipatedby considering the limit in which bleaching of thepump transition is negligible.4 In the absence ofgain or loss for the emitted photons the averagepath length of photons that are spontaneously emittedin the excited region of depth La is ksl , La

2yl ~

la. The small-signal gain in the medium is inverselyproportional to la. Thus the pump energy threshold,which depends on the gain–path length product, wouldbe independent of l and la.

In the present measurements, as well as in previousreports of lasing in random media, the lasing thresh-old is reached at the point at which the pump transi-tion is bleached. Such bleaching increases the pene-tration of the pump and consequently leads to longerpath lengths for emitted photons within the gain re-gion, which results in a reduced threshold in these sys-tems. This effect is taken into account in the presentMonte Carlo simulation, which we find is in qualitativeagreement with measurements of pulsed emission.

This research is supported by the U.S. Air ForceOffice of Scientific Research and the National ScienceFoundation.

References

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and N. M. Lawandy, Nature (London) 368, 436 (1994).4. W. L. Sha, C.-H. Liu, and R. R. Alfano, Opt. Lett. 19,

1922 (1994).5. A. Z. Genack and M. J. Drake, Nature (London) 368,

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