October 1, 1996 / Vol. 21, No. 19 / OPTICS LETTERS 1603

Understanding bichromatic emission fromscattering gain media

R. M. Balachandran and N. M. Lawandy

Department of Physics and Division of Engineering, Brown University, Providence, Rhode Island 02912

Received April 24, 1996

Intense optical pumping of solutions of high-gain laser dyes and TiO2 nanoscatterers in methanol is found toresult in narrow-linewidth bichromatic emission. Experimental studies of the long-wavelength emission peakshow that weak pumping of the scattering gain medium by the primary lasing emission results in a randomsystem that lases at longer wavelengths. Measurements with other dyes show that the bichromatic emissioneffect is very general. 1996 Optical Society of America

Since the first demonstration of laser action in scatter-ing gain media,1,2 there have been a growing number ofinvestigations into the spectral, spatial, and temporalproperties of the emission.3 – 8 Studies with variablescatterer concentrations have shown that the scatter-ers provide the requisite feedback necessary to initi-ate laser action in these systems.4,8 Models based onamplified spontaneous emission have been put forth inan attempt to explain the observed narrow-linewidthemission.9,10 This approach, however, predicts thresh-olds that are independent of the scatterer density,in disagreement with experimentally observed behav-ior. Furthermore, the amplified spontaneous emis-sion models do not provide the necessary gain–lengthproduct to account for the observed linewidth col-lapse.4 A laser model based on scatterers’ providingthe requisite feedback for the system to behave as alaser in random phase limit was recently developedthat accurately predicts the threshold gain and theemission characteristics of this system.

In the earliest reports on high-gain dye scatteringsystems, Lawandy et al.1,2 observed bichromatic emis-sion in Rhodamine 640 perchlorate dye solution with250-nm-diameter TiO2 scatterers. At very high pumpf luences, the emission spectrum consisted of two nar-row peaks—the main peak at 617 nm and a secondpeak at 648 nm. More recently, Zhang et al.11 ob-served bichromatic emission in a binary dye mixturein the presence of scatterers. The dye molecules wereof the donor–acceptor type, and the observed bichro-matic emission was due to energy transfer through theoverlap of the absorption and emission characteristicsof the dyes. The main difference between these twoexperiments was that in the former a single dye wasused to observe the bichromatic emission. In this Let-ter the dependence of the second emission peak is stud-ied as a function of dye concentration, pump f luence,and available volume. The behavior of this emissionis explained by a laser model with scattering providingthe requisite feedback.

We carried out the bulk of the experiments usingRhodamine 640 perchlorate dye with various scattererconcentrations. Similar results were obtained fromother dyes such as Rhodamine 6G, Rhodamine 590tetraf luoroborate, and DCM. The scatterers, which

0146-9592/96/191603-03$10.00/0

consist of 250-nm-diameter nanoparticles (R-900 TiPure, Du Pont), were ultrasonically dispersed intothe dye solution. These samples were pumped with7-ns pulses at 532 nm from a frequency-doubled andQ-switched Nd:YAG laser, and the incident pump en-ergy was controlled with a pair of Glan laser polar-izers. Spectral analysis of the emitted radiation wasperformed by an optical multichannel analyzer with aliquid-nitrogen-cooled CCD detector.

The first set of experiments consisted of studyingthe absorption and emission properties of the pure dyesolutions. The dye absorption and f luorescence prop-erties were studied and found to scale with the dyeconcentration up to the maximum dye concentrationof 1022 M. Small red shifts with increasing dye con-centrations, which can be attributed to increased re-absorption and reemission, were observed in these dyesolutions. These measurements indicate that dye doesnot undergo any spectral transformation that may haveresulted from the formation of new species such asdimers.

The output intensity and linewidth of the emissionfrom a 2.5 3 1023 M solution of Rhodamine 640 per-chlorate mixed with 1.5 3 1011ycm3 TiO2 scattererswere measured as a function of pump f luence (Fig. 1).As the f luence was increased, the initially broad emis-sion spectrum was observed to split into two narrowpeaks, at l ­ 617 nm and l ­ 648 nm. Complete nar-rowing of the main peak takes place at ,50 mJycm2

and signals the onset of linewidth collapse of the sec-ond laser emission peak. Furthermore, both emis-sion peaks showed linear input–output characteristicswith well-defined thresholds that correspond to the f lu-ences for linewidth collapse. The narrowing of the sec-ondary peak immediately after the rapid growth of themain short-wavelength peak suggests that the two areclosely related and the first is required to drive thesecond.

An examination of the absorption and f luorescencecurves of Rhodamine 640 perchlorate shows that theyoverlap enough to permit energy transfer by reabsorp-tion. We confirmed this mechanism by using the dyeDCM as the gain medium. The emission and absorp-tion spectra of DCM overlap when methanol is used asthe solvent, whereas when DMSO is used as the solvent

1996 Optical Society of America

1604 OPTICS LETTERS / Vol. 21, No. 19 / October 1, 1996

Fig. 1. Linewidth and input–output characteristics ofthe main peak (617 nm) and the longer-wavelength peak(648 nm) for a 2.5 3 1023 M solution of Rhodamine 640perchlorate with 1.5 3 1011ycm3 TiO2 particles.

the spectra have almost no overlap. The introductionof scatterers results in two peaks in the methanolic so-lution, whereas the DMSO solution produces only onepeak even at the highest pump energies. This clearlyshows that the primary emission peak pumps the dye,which then produces a second longer-wavelength peak.This experiment also clearly rules out other sugges-tions for the bichromatic spectrum based on triple-state transitions.

To test the self-pumping hypothesis further, wetransversely pumped a 1-cm-long cell containingRhodamine 640 perchlorate in methanol s5 3 1024 Mdby a 15-mJ pulse at 532 nm, focused by a 15-cmfocal-length cylindrical lens. This simple dye laser,which gets feedback from ref lections off the cell walls,produced an intense 4-nm-wide emission at 617 nmwith a total output energy of 3.5 mJ. This outputwas collected and focused into a 1.1-mm-diameter spoton a cell containing 8.6 3 1011ycm3 scatterers in a5 3 1023 M Rhodamine 640 perchlorate solution inmethanol. As shown in Fig. 2, the resulting emissionspectrum consisted of the 652-nm peak along with thescattered 617-nm pump light. We verif ied the factthat the resulting emission consisted of only these twofeatures by measuring the 617-nm pump off a purelyscattering solution. Figure 2 also shows the emissionspectrum of the solution for pumping by 532-nmradiation with emission peaks at 617 and 648 nm.This result suggests that the primary lasing emissionpumps the surrounding unpumped volume, which inturn lases at 648-nm, with scattering again providingthe requisite feedback.

One can use this model, shown schematically inFig. 3, to estimate the threshold gain required for ob-serving spectral narrowing of the second peak. Refer-ring to Fig. 3, volume V1 is the region pumped by the532-nm pump light and lases at 617 nm. A fractionof the 617-nm light travels farther into the mediumand is distributed in volume V2, creating a weak inver-sion that results in gain at longer wavelengths. Feed-back is provided by the surrounding volume, whichtends to confine the light within V2. The transport

length sItd of the 617- and 648-nm emissions is 60 mm,and the absorption length sa21d of the 617-nm emis-sion is 2.6 mm. The 617-nm light travels a distanceof ,3

psIty3ad, creating volume V2 and resulting in

an area that is approximately 2.5 times the originalpump area.

The feedback that is due to the scatterers canbe quantified by a Monte Carlo simulation of thismultiple-scattering problem, which can be completelycharacterized by the scattering cross section and theHenyey–Greenstein phase function.12 One set of pho-tons (P1 in Fig. 3) was launched at random directionsfrom random positions on the back surface of the gainvolume defined by the 617-nm emission, and the re-turn probability sR1d to gain volume V2 through thesame surface was calculated. Another set of photons(P2 in Fig. 3) was launched inward and gave the frac-tion that escaped from the gain volume through thesame surface sR2d as well as the corresponding aver-age total path length sLd traveled within the volume.The main loss mechanism for P1 and P2 was photonsscattering out of the sample. The threshold gain sgthdobtained from the usual round-trip resonator condition

Fig. 2. Bichromatic emission from a 5 3 1023 M solutionof Rhodamine 640 perchlorate with 8.6 3 1011ycm3 TiO2scatterers (solid curve). The spectrum shown by thedashed curve is from the same solution pumped by 617 nm,which has a peak at 652 nm. This spectrum also includessome of the scattered 617-nm light off the sample.

Fig. 3. Theoretical model used to describe the bichromaticemission. V1 is the volume pumped by the 532-nm lightthat lases at 617-nm. The 617-nm light in turn pumpsvolume V2, which produces the 648-nm emission.

October 1, 1996 / Vol. 21, No. 19 / OPTICS LETTERS 1605

Fig. 4. Effective gain spectrum resulting from the 617-nmemission pumping the scattering gain medium in vol-ume V2.

was given by

expsgthLdR1R2 ­ 1 , (1)

with the values of R1, R2, and L, gth , 3.7 cm21.This threshold gain can now be used in the two-level

dye laser equations for the laser intensity sI1d and theinversion sn2d:

dn2

dt­ s1 2 n2dfBpIpstd 1

ZdlBabssldIlsl, tdg

2 n2

"ZdlBlsldIlsl, td 1 G

#, (2)

dIl

dt­ chg0sldn2std 2 asldf1 2 n2stdg 2 gthj

3 Ilsl, td 1 hsldn2std , (3)

where Bp, Bl, and Babs are the Einstein coefficientsfor the pump, lasing, and reabsorption transitions, re-spectively, obtained from the experimentally measuredabsorption and emission cross sections; G is the sponta-neous emission rate; and hn2 is the spontaneous emis-sion seed necessary to initiate the laser action. Whensolved in the steady-state approximation for the 7-nspump pulse, the threshold inversion reduces to

n2 ­BpIp

BpIp 1 G. (4)

The experimentally determined threshold 532-nmpump f luence for the long-wavelength emission wasfound to be , 50 mJycm2. Approximately 20% ofthis incident pump light gets scattered out and doesnot pump the medium. The fraction of the remain-ing 40 mJycm2 of the 532-nm pump converted to617-nm light is emitted in both forward and back-ward directions and has been measured to be ,50%.This implies that at least 25% of the 532-nm pumpenergy gets converted into 617-nm emission lightthat pumps the surrounding volume while the restescapes.13 Since the 10 mJycm2 of 617-nm light isspread over an area that is 2.5 times the 532-nmpump area, the equivalent f luence incident upon themedium is ,4 mJycm2. Substituting this into Eq. (4),we can estimate the threshold inversion that is dueto the 617-nm emission to be 0.016. This thresholdinversion can be used to calculate the gain spectrum ofthe dye, including the ground-state absorption, which

is given by

geff sld ­ g0sldn2 2 aabsslds1 2 n2d . (5)

This gain spectrum is shown in Fig. 4 and peaks at,640 nm and remains approximately constant until,660 nm. This gain spectrum is at the heart of thereason that the emission appears at the wavelengthsobserved.

The fact that the lasing at 648 nm takes place involume V2 surrounding V1 was further confirmedby a series of experiments with cylindrical cavitiesof different diameters and variable depths made ofabsorbing black acrylic. A scattering gain mediumconsisting of a 5 3 1023 M solution of Rhodamine 640perchlorate and 2.8 3 1011ycm3 of TiO2 in methanolfilled this volume. The incident beam diameter waskept fixed at 3 mm, and the bichromatic spectrafrom a volume 3 mm in diameter was measured as afunction of cavity depth. The second peak disappearedcompletely at a depth of ,1 mm. When the sameexperiment was repeated with a 5-mm-diameter cavitywhile a beam diameter of 3 mm was retained, thesecond peak could still be observed at a depth of 1 mm.Clearly, increasing the volume of the cavity resultedin an additional volume that could be pumped by theprimary lasing emission. The increased average pathlength traveled in this larger gain volume produced alower threshold for lasing at the longer wavelength,and hence the second peak could still be observed.

The authors thank Spectra Science Corporationfor funding this research and J. A. Moon for usefuldiscussions.

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