Quasi-phase matching transient SRS generation Victor G. Bespalov Russian Research Center "S. I. Vavilov State Optical Institute" Nikolai S. Makarov Saint-Petersburg State Institute of Fine Mechanics and Optics (Technical University)

Principle of quasi-phase matching Nonlinearity  (2) Nonlinearity  (3) 2 Raman active medium

System of transient SRS equations  – wave mismatching, g – steady-state Raman gain coefficient,  i – frequencies of interacting waves, T 2 – dephasing time, q – phonon wave, A j – complex wave amplitudes, z=z’+t’/c, t=t’. 3

Principle of quasi-phase matching at SRS - Generalized phase  =2  p -  a -  s -(k a +k s -2k p )r, where k i – is the wave vector of interacting wave, that describes the direction of energy conversion “pump – Stokes – anti-Stokes”, on passive layers input (  0,  2 ) and active layers input (  1,  3 ) do not practically change, that in a final result provides a realization of quasi- phase matching conditions.  (3)  0  (3) =0 4

- It is possible to create conditions, at which anti-Stokes conversion coefficient reaches ~25% and the anti-Stokes wave intensity is practically compared to Stokes wave intensity Quasi steady-state SRS  pulse  25Т 2 (Т 2 =0.203 ns,  pulse =10 ns). 5

Highly transient SRS  pulse <<25Т 2 (Т 2 =0.203 ns,  pulse =25 ps). 6 - The efficiency of anti-Stokes SRS conversion much depends on a ratio of dephasing time T 2 to pulse duration

Optimum ratio of input Stokes/pump intensities 7 - There is an optimum value of input Stokes/pump waves intensities ratio. - This dependence can be approximated as I s /I p,opt =0,1359g -2,6146

Critical pump wave intensity 8 - There is a critical value of pump intensity. - This dependence can be approximated as I cr.p =0.4Δ/g

Conclusions The conversion efficiency can reached more than 25% The efficiency of anti-Stokes SRS conversion much decreased with increasing of a ratio of dephasing time T 2 to pulse duration For each medium there is an optimal ratio I s /I p, at which conversion efficiency is maximal For each medium there is a critical value of pump intensity 9

References J. A. Armstrong, N. Blombergen, J. Ducuing, P. S. Pershan, “Interaction between light waves in a nonlinear dielectric” Phys. Rev., 127, pp , R. B. Andreev, V. A. Gorbunov, S. S. Gulidov, S. B. Paperni, V. A. Serebryakov, “About parametrical effects at SRS generation of higher components in gases”, Quantum Electronics, 9(1), pp , A. P. Hickman, W. K. Bischel, “Theory of Stokes and anti-Stokes generation by Raman frequency conversion in the transient limit”, Physical review A, 37(7), pp , J. J. Ottusch, M. S. Mangir, D. A. Rockwell, “Efficient anti-Stokes Raman conversion by four-wave mixing in gases” J. Opt. Soc. Am., B 8, pp , Makarov N. S. (Scientist supervisor – Bespalov V. G.) “Generation of anti-Stokes SRS radiation in conditions of quasi-phase matching”, in book “Problems of coherent and nonlinear optics”, pp , Bespalov V. G., Makarov N. S., “Quasi-phase matching anti-Stokes SRS generation”, Opt. & Spectr., vol. 90, No. 6, pp ,