October 15, 1996 / Vol. 21, No. 20 / OPTICS LETTERS 1685

Coherent backscattering from high-gain scattering media

Paulo C. de Oliveira,* A. E. Perkins, and N. M. Lawandy

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

Received April 29, 1996

We report on experimental observations of coherent backscattering signals from high-gain scattering mediain the regime where significant amplification takes place over one transport length. Our samples consistof polymer sheets containing optically pumped dyes as the amplifying medium, with TiO2 nanoparticlesproviding the scattering. The width of the backscattering cones narrows with increasing amplification, whilethe enhancement factor remains unchanged. 1996 Optical Society of America

The phenomenon of weak localization of photons inpassive random media was demonstrated more than adecade ago1,2 and remains a subject of great interest.Recently new features of this phenomenon were uncov-ered in the cases of partially coherent incident light3

and of amplifying scattering media.4,5

Constructive interference between a wave followinga certain multiple scattering path and its counterprop-agating wave traversing the time-reversed path resultsin coherent light emitted in the backscattering direc-tion, which enhances the intensity of the scattered lightin that direction. A phase difference will exist be-tween the counterpropagating waves when the outgo-ing wave does not emerge in exactly the backscatteringdirection, and after averaging over all light paths theangular distribution of scattered-light intensity willexhibit a sharp peak in the backward direction. Thepeak of the backscattering cone will be approximatelytwice as intense as the incoherent background, andits angular width is given by u ø lys2pld, where l isthe wavelength of the scattered light and l is the pho-ton transport mean free path.1,2 In the case of scat-terers immersed in an amplifying medium, the longerlight paths will experience greater amplif ication thanthe shorter ones. Because the major contribution tothe backscattered light at small angles arises from thelarger path lengths, there will be a change in the shapeand the amplitude of the backscattering cone, as pro-posed by Zyuzin4 in 1994 and verified by Wiersmaet al.5 in 1995, in a weakly amplifying sample ofTiO2O3-doped Ti:sapphire powders.

In this Letter we report on the observation ofcoherent backscattering from amplifying polymersheets containing dyes and randomly distributed TiO2nanoparticle scatterers.6 Our sample is criticallydifferent from that used by Wiersma et al.5 In oursystem the random scatterer and the amplifyingmedium are distinct, and the available gain canbe 2 orders of magnitude higher. In addition, thegain–length product over one transport length in thesystem of Wiersma et al. is of the order of 3 3 1023,whereas in our samples it is larger than 1. This isa new regime where signif icant amplif ication occursover one scattering length. Finally, in our system thegain is a maximum at the sample face and morphology-dependent resonances are eliminated, unlike for thesample described in Ref. 5.

0146-9592/96/201685-03$10.00/0

Optical pumping of polymer sheets containing dyesand TiO2 nanoparticle scatterers6 results in emis-sions that exhibit laser behavior with linewidths aslow as 4 nm.7 – 12 We used these types of sampleto study the enhancement of coherent backscatter-ing at small angles when the samples were opti-cally pumped by a Nd:YAG laser and probed by adye laser. The samples used in this experiment con-tained Pyrromethene 567 dye s2 3 1023Md and TiO2nanoparticle scatterers (.250-nm-diameter R-900 Ti-Pure particles from E. I. duPont de Nemours & Co.,Inc.). The dye and scatterers were dispersed in amixture of monomethyl methacrylate (75%) and hy-droxyethyl methacrylate (25%). The typical scattererconcentration was ,1011 scatterersy cm3 and resultedin a transport mean free path of .70 mm at the probewavelength. The sample sheets had square shapes,with dimensions ,10 cm on a side and ,1 mm thick.

We used a frequency-doubled and Q-switchedNd:YAG laser with a pulse duration of 7 ns and arepetition rate of 20 Hz (Fig. 1). The emitted 532-nmradiation was divided by a beam splitter (70–30), withthe transmitted beam (70%) used to pump a dye laser(Rhodamine 610) tuned to 591 nm with a 5-ns pulseduration. The pump and the probe beams overlappedspatially and temporally on the sample surface andhad diameters of 6 and 4 mm, respectively. The probebeam was collimated by a pair of lenses (L1 and L2)through a distance of 8 m and was linearly polarizedby polarizer P1. The normal to the front surface of the

Fig. 1. Experimental setup: BS1, BS2, beam splitters;L1–L3, lenses. F, longpass optical filter; P1, P2, polar-izers; PMT, photomultiplier tube.

1996 Optical Society of America

1686 OPTICS LETTERS / Vol. 21, No. 20 / October 15, 1996

sample was placed at an angle with the incident probelaser beam so that the directly reflected light wasrejected from the detector. To avoid local saturationin the sample and to average all speckle formation,we placed the sheet on a rotating stage. This did notcause a reduction in the backscattering signal becausethe rotation velocity was sufficiently small that thesample could be considered at rest during the timeduring which the light propagates inside the sample.The scattered light from the medium was collectedby a 50-cm focal-length lens, L3. A 100-mm pinholewas attached to the window of a photomultipliertube (PMT) placed at the focal plane of the collectinglens. We mounted the PMT upon a movable stagedriven by a stepper motor to scan the PMT in thedirection normal to the backscattered light. We usedpolarizer P2 as an analyzer to measure selectively thepolarization-conserving or reversing channel.

Most of the pump energy was converted into anemission with wavelength centered at 570 nm. Thewidth of the emission depended on the pumping energyand exhibited a spectral width that ranged from 5 nmfor high pumping energies to 30 nm for low pumpingenergies. To separate the backscattered signal fromthis emission we used a longpass f ilter (F) and lock-in detection of the probe beam, which was choppedmechanically at 5.6 Hz. To improve the signal-to-noise ratio it was necessary for the lock-in integrationtime to be set to 10 s and the duration of each PMTscan to be 15 min.

Figure 2 shows the spectrum of the light emitted inthe backscattering direction as measured by an opticalmultichannel analyzer. When the sample is opticallypumped with an energy of 4.5 mJ the intensity of thebackscattering signal is amplified by a factor of 2.8.The spectrum also shows the scattering gain mediumemission peak, centered at 570 nm, which appearslower than it actually is because it has been attenuatedby filter F.

By scanning the position of the PMT over the focalplane of the collecting lens we observed that in thepolarization-conserving channel there is a cone of am-plified light in the backscattering direction of the probebeam. The pump beam energy was varied by opticaldensity filters, and scans were taken with pump ener-gies ranging from no pump to 4.5 mJ. We observedthat the light intensity of these cones increases withthe pump energy, whereas the widths decrease. Forthe polarization-reversing channel we also observedamplification, but we did not observe any enhance-ment of light in the backscattering direction. The ef-fect of the narrowing of the light cones with increasingpump energies is easily seen in Fig. 3, where the coneshave been scaled to the same height and backgroundlevel. In all the measured signals the enhancementfactor sIpeakyIbackgroundd is almost constant and assumesa value close to 1.6. These results are summarized inFig. 4, where we show the dependence of the width ofthe cone (FWHM) and the enhancement factor on theamplification.

In conclusion, we have studied coherent backscatter-ing from amplifying random media for which the am-plifier and the random scattering medium are distinct

and the available gain is very large s200 cm21d, andsignificant amplif ication takes place over one trans-port length. We observed that when the gain wasincreased the peak of the backscattering cone sharp-ened and consequently the width of the cone was re-duced. We also observed that the enhancement factorremained constant.

Although the available gain coefficient is ,2 ordersof magnitude higher than in the previous experimentwith powders, the observed cone narrowing is not sig-nificantly larger. This might be understood in termsof the typical gain–length product available for diffu-sive paths in both of these otherwise different systems.In the case of the experiments with amplifying pow-ders5 the pump absorption length is of the order of0.4 cm and the available gain is ,1.5 cm21.13 A typi-cal injected photon from the probe laser is expectedto traverse a path whose length is of the order of thepump absorption length in the material. This leads

Fig. 2. Spectrum of the light emitted in the backscatter-ing direction obtained with an optical multichannel an-alyzer. The peak at the probe wavelength, 591 nm, isamplif ied by 2.8 when the sample is pumped with 4.5 mJof 532-nm radiation. The inset shows more clearly the re-gion around the 591-nm peak for the two cases of no pump-ing and 4.5-mJ pumping.

Fig. 3. Comparison between the line shapes of thebackscattering cones with and without pumping. Thesignals were scaled and plotted to have equal backgroundlevels. The narrower line shape is the signal for a pump-ing energy of 4.5 mJ, corresponding to an amplif icationof 2.8, and the wider line shape is the signal withoutpumping. The dashed curves are Lorentzian f its to theexperimental signals.

October 15, 1996 / Vol. 21, No. 20 / OPTICS LETTERS 1687

Fig. 4. Width of the cone (FWHM), represented bysquares, and enhancement factor sIpeakyIbackgroundd, repre-sented by f illed circles, as functions of the amplif ication.The solid curve is a f it by the model of Zyuzin.4

to a gain–length product of the order of 0.6 in thepowder experiments. In our separated dye and scat-terers experiments the available gain is of the orderof 200 cm21, but the pump absorption coeff icient andhence the typical available photon amplification pathlength is 100 mm. This leads to a gain–length productof the order of 2. Thus it appears from the two experi-mental results that the gain–length product availablefor coherent backscattering is comparable in these twosystems with large differences in gain. These resultsindicate that theories need to be developed to treatthe problem of a finite gain layer in contact with apassive or weakly absorbing scattering medium to ex-plain quantitatively the proper scaling in an amplifyingscattering system. In addition, theories that are non-perturbative may also be developed to treat media forwhich significant amplif ication occurs on the scale ofone transport length.

The authors thank Spectra Science Corporation forfunding this research and R. M. Balachandran for help-ful discussions. A. E. Perkins thanks the NationalPhysical Science Consortium and the Lawrence Liver-more National Laboratory for fellowship stipend sup-port. P. C. de Oliveira thanks the Conselho Nacionalde Pesquisas (Brazil) for financial support.

*Permanent address, Departamento de Fısica, Uni-versidade Federal da Paraıba, Joao Pessoa, ParaibaBrazil.

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