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

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

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