1 July 1998

Ž .Optics Communications 152 1998 351–354

Parametric suppression of Raman gainin coherent Raman probe scattering

S. Sogomonian ), G. Grigorian, K. GrigorianInstitute for Physical Research of Armenian Academy of Sciences, 378410 Ashtarak-2, Armenia

Received 2 February 1998; accepted 25 March 1998

Abstract

We report on the observation of Raman gain suppression by parametric four-wave mixing in coherent Raman probescattering with a noncollinear pump and probe arrangement. The effect has been observed in coherent Stokes scattering ofpicosecond pulses from polaritons in a LiIO crystal. The angular intensity pattern of Stokes probe scattering shows a3

distinct dip in phase-matching directions of a noncollinear parametric four-photon interaction K qK X sK qK , whereL L S A

two photons at the laser frequency, one from the pump beam and another one from the probe beam scatter into Stokes andanti-Stokes photons. The interference between this process and Raman scattering results in an additional dark ring in theangular intensity pattern of Stokes scattering of the pump pulse. q 1998 Elsevier Science B.V. All rights reserved.

PACS: 42.65Keywords: Stimulated Raman scattering; Raman gain suppression; Parametric four-photon interaction

1. Introduction

It has been known for many years that interferenceŽ .between stimulated Raman scattering SRS and paramet-

Ž .ric four-wave mixing FWM process leads to suppressionw xof normal exponential Raman gain 1,2 . This Raman-

Ž .gain-suppression RGS effect predicted long ago byw xBloembergen and Shen 1,2 results in dark rings in the

angular intensity pattern of Stokes and anti-Stokes emis-sion. The dark ring corresponds to the cone of phase-matching directions of the FWM process where two pho-tons at the pump frequency scatter into two photons atStokes and anti-Stokes frequency. More recently, the phys-ical mechanism of RGS and the energy transfer betweenthe light and the Raman medium was discussed by Bobbs

w xand Warner 3 . Experimental evidence of the RGS effectw xhas been obtained by several authors, both in Stokes 4–8

) Corresponding author. E-mail: root@ipr. arminco.com

w xand anti-Stokes emission 5,6 . Raman gain reduction by afactor of 107 in phase-matching direction has been ob-

w xserved in a Raman generator-amplifier arrangement 5 .In this Communication we report on an experimental

observation of parametric suppression of Raman gain incoherent Stokes probe scattering of picosecond pulses witha noncollinear pump and probe wave-vector geometry.

2. Experimental

Experiments were performed with frequency doubledsingle picosecond pulses at 527 nm from a passivelymode-locked Nd:phosphate glass laser. A single pulseswitched out from the pulse train passed through a two-stage optical amplifier and was subsequently frequency-doubled in a KDP crystal. The fundamental pulse durationmeasured by the single-shot second-harmonic-beam-auto-

w x Ž .correlator 9 not shown in the figure was about 6–8 ps.The energy of the second harmonic pulse was roughly 1mJ, and the spectral bandwidth was equal to 15 cmy1. The

0030-4018r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved.Ž .PII S0030-4018 98 00175-8

( )S. Sogomonian et al.rOptics Communications 152 1998 351–354352

Ž . Ž .Fig. 1. a Experimental setup. b Wave-vector diagram forcoherent Stokes scattering.

second harmonic beam passed through a Galilean tele-scope which reduced the beam diameter to approximately2 mm. Our experiment employs the well-known pump-probe arrangement for coherent Raman probe scattering ofdelayed probing pulses in a noncollinear wave vector

w xgeometry 10 . The experimental setup is shown schemati-Ž .cally in Fig. 1 a . A beam splitter BS in the path of the

input pulse provides a probing pulse of smaller intensity,approximately 8% of the pump pulse. A variable delay linein the path of the probe beam brings the pulses into timecoincidence on the sample. The angle between pump andprobe beams amounts to a few degrees. As the Ramanmedium we used a y-cut 2 cm-long LiIO crystal. Both3

spontaneous and stimulated Raman scattering in this crys-w xtal have been studied extensively 11–14 . The strongest

Raman-active mode that can be observed in SRS withpump propagating along the X or Y crystallographic axis

Ž .is the polariton mode associated with phonons of A zsymmetry at 795 cmy1. Both pump and probe pulses ofidentical frequencies and polarizations propagated throughthe specimen as ordinary waves, symmetrically with re-spect to the Y-axis. With an ordinary polarized pump waveat 532 nm the Raman Stokes shift for the forward scatter-ing is equal to 760 cmy1. A color filter F, of about 80%transmission at Stokes wavelength was placed after thecrystal to block the pump light. The angular intensity

distribution of Stokes light in both pump and probe chan-Ž .nels was recorded photographically by a camera. Fig. 1 b

shows the wave vector diagram for coherent Stokes scat-tering. The diagram is symmetric with respect to the Y-axiswhich is the bisecting direction of the crossing anglebetween the two beams. The weak probing pulse is coher-ently scattered by the polariton mode which is excited viastimulated Raman scattering of the intense pump pulse.

3. Results and discussion

Fig. 2 shows the spatial distribution of the Stokesintensity for zero delay between pump and probe pulsesŽ . Ž .a , and for the probe pulse delayed by 10 ps b . The

Ž .picture in Fig. 2 a has several interesting features. Itconsists of a diffuse region of Stokes emission producedby the pump beam, two non-concentric dark rings ofdifferent radius and contrast, and two bright straight linesof different intensity. Schematic illustration of two darkrings and two emission lines is presented in Fig. 3. The

Ž .Fig. 2. Spatial intensity distribution of Stokes emission. a ZeroŽ .delay between pump and probe. b Probe pulse is delayed by 10

ps.

( )S. Sogomonian et al.rOptics Communications 152 1998 351–354 353

Fig. 3. Schematic illustration of observed dark rings and emissionŽ .lines shown in Fig. 2 a . The angular parameters are: r s tan u ,1

Ž . Ž 2 2 2 .Rs tan u , Ss tan wr2 , d s tan a , d s R y r yS r2S.2

small dark ring which is more pronounced is centered inthe direction of the pump beam k-vector and represents theusual RGS in a single beam geometry. Its angular radiuscorresponds to phase-matching directions for parametricStokes–anti-Stokes coupling,

2v sv qv , 2 K sK qK , 1Ž .L S A L S A

Žwhere two photons at pump frequency both from the.pump beam scatter into a photon at Stokes frequency and

one at the anti-Stokes frequency. This small ring could beŽ Ž ..observed without probe beam as well Fig. 2 b and the

pattern is similar to those reported previously by severalw xauthors 4–8 . An additional dark ring of larger radius has

lower contrast but is still clearly visible. It is centered inthe bisecting direction of the crossing angle between thepump and probe beams. The location and angular radius ofthe additional ring were found to depend upon the crossingangle: the larger the crossing angle, the larger the angularradius and the distance between the centers of the tworings. We attribute the suppression of Raman gain in theseadditional directions to another parametric Stokes–anti-Stokes coupling process where two photons at pump fre-quency, one from the pump beam and another from theprobe beam are transformed into Stokes and anti-Stokesphotons with conservation of energy and momentum,

v sv qv , K qK X sK qK , 2Ž .L S A L L S A

where K and K X are the wave vectors of the pump andL L

probe beams, respectively. The wave vector diagrams forŽ . Ž .parametric four-photon processes 1 and 2 are depicted

Ž . Ž .in Fig. 4. The angular radii of small u and large u1 2

rings can be found from phase-matching conditions ofŽ . Ž .parametric processes 1 and 2 , respectively,

K 2 yK 2 q4K 2S A L

cos u s , 3Ž .1 4K KS L

K 2 yK 2 q2 K 2 1qcos wŽ .S A Lcos u s . 4Ž .2 '2 K K 2 1qcos wŽ .S L

Fig. 4. Wave-vector diagram for two four-photon parametricŽ .processes which suppress the Raman gain: i 2 K s K q K ,L S A

Ž . Xii K q K s K q K . Stokes emission is suppressed at theL L S A

surface of two cones with half-apex angles u and u .1 2

Under the conditions of our experiment and for cross-ing angle ws35 mrad the observed angular radii wereu obs s19.2"0.5 mrad and u obs s26.0"0.5 mrad which1 2

are in good agreement with the calculated values u cal s1cal Ž . Ž .19.6 mrad, u s26.4 mrad. The straight lines I and II2

Ž .shown in Fig. 1 b and Fig. 3 represent coherent StokesŽ . Ž .scattering of probe I and pump II pulses. The essen-

tially different divergence of coherent Stokes scattering intwo orthogonal planes resulting in a line-shaped pattern isdue to the volume phase-matching conditions and can beunderstood as follows. A collimated pump beam generatesstimulated Stokes emission within a cone of small anglesaFa with respect to the pump k-vector. a repre-max max

sents the divergence of the Stokes beam, and is determinedby the geometry of the pumped region a fdr2 L,max

where d is the beam diameter and L is the interactionŽ .length a was about 2.58 in our experiment . Corre-max

sponding to the cone of Stokes k-vectors, a cone ofmaterial excitation is generated in the Raman medium. Thevolume phase-matching is illustrated by the k-vector dia-gram in Fig. 5. It can be readily seen that the diagram issymmetric with respect to the XY plane which is orthogo-nal to the ZY plane and contains the bisecting direction of

Žthe crossing angle between pump and probe beams ZY is.the plane made up by k-vectors of the two beams . Due to

Fig. 5. Volume phase-matching diagram for Stokes probe scatter-ing illustrating the origin of two bright lines in the angulardistribution of the Stokes emission.

( )S. Sogomonian et al.rOptics Communications 152 1998 351–354354

this symmetry, only material excitations whose k-vector liein the XY plane may satisfy phase-matching conditionsand thereby, contribute to coherent Stokes scattering. As aresult, coherent Stokes scattering of both pump and probe

Žpulses has a large divergence in the XY plane comparable.to divergence of Stokes beam produced by the pump , but

is highly collimated in the ZY plane. The presence ofŽ .coherent Stokes scattering of the pump pulse line II is

attributed to the fact that the probe pulse was not weakŽenough in our experiment 8% of the pump pulse, as

.already mentioned . Though the intensity of the probepulse is below the threshold of SRS, its interaction withthe excited Raman medium increases the number of coher-ently driven material excitations whose wave vectors Q liein the XY plane. This leads to enhancement of Stokesscattering of the pump pulse in the corresponding direc-tions where phase-matching conditions are fulfilled. Actu-ally, the observed Stokes emission in the pump channel isa superposition of Stokes light generated via single-beam-SRS and coherent Stokes scattering of the pump pulse. Thetime resolution of our experiment was insufficient to studythe temporal evolution of Raman gain suppression. Whenthe probing pulse was delayed by a time of 6–10 ps thecoherent Stokes scattering disappeared. The observed an-

Ž Ž ..gular distribution of the Stokes light Fig. 2 a was identi-cal to the that observed with blocked probe beam, that is,to the usual single beam SRS pattern. This behavior is notsurprising because the dephasing time of the materialexcitation is short compared to the pump pulse duration.According to spontaneous Raman spectroscopy and in-

w xfrared reflection data 12 the damping constant of thepolariton associated with a phonon at 795 cmy1 is Gf16cmy1. With this value of G the dephasing time is esti-

Ž .y1mated to be 2p cG f0.33 ps which is much less thanthe pump pulse duration of 6 ps.

4. Conclusion

In conclusion, we have observed parametric suppres-sion of Raman gain in coherent Raman probe scattering.We believe that it would be interesting and informative toperform a time-resolved study of the Raman gain suppres-sion effect using other Raman medium with a longerdephasing time. The temporal evolution of dark bands maygive a better understanding of energy transfer betweenlight and the Raman medium in the Raman-resonant FWM

w xprocess 3 .

References

w x1 N. Bloembergen, Nonlinear Optics, Benjamin, New York,1965.

w x Ž .2 N. Bloembergen, Y.R. Shen, Phys. Rev. Lett. 12 1964 504.w x Ž .3 B. Bobbs, Ch. Warner, J. Opt. Soc. Am. B 7 1990 234.w x Ž .4 Chiao, B.P. Stoicheff, Phys. Rev. Lett. 12 1964 290.w x5 M.D. Duncan, R. Mahon, J. Reintjes, L.L. Tankersley, Op-

Ž .tics Lett. 11 1986 803.w x6 G.G. Grigorian, S.B. Sogomonian, V.L. Strizhevsky, Optica

Ž .Spektrosk. 61 1986 998.w x7 K. Leung, M. Oron, D. Klimek, R. Holmes, A. Flusber,

Ž .Optics Lett. 13 1988 33.w x8 K. Hakuta, M. Suzuki, M. Katsuragawa, J.Z. Li, Phys. Rev.

Ž .Lett. 79 1997 209.w x9 R.N. Gyuzalian, S.B. Sogomonian, Z.Gy. Horvath, Optics

Ž .Comm. 29 1979 239.w x Ž .10 A. Laubereau, W. Kaiser, Rev. Mod. Phys. 50 1978 607.w x Ž .11 Y.N. Polivanov, Sov. Phys. Usp. 21 1978 805.w x12 W. Otaguro, E. Wiener-Avnear, A. Arguello, S.P.S. Porto,

Ž .Phys. Rev. B 4 1971 4542.w x Ž .13 R. Claus, Z. Naturforsch. 25a 1970 301.w x Ž .14 H.W. Schroetter, Z. Naturforsch. 26a 1971 165.