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Quasi-phase matching t ransient SRS generation. Nikolai S. Makarov Saint-Petersburg State Institute of Fine Mechanics and Optics (Technical University). Victor G. Bespalov Russian Research Center "S. I. Vavilov State Optical Institute". Principle of quasi-phase matching.
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Quasi-phase matching transient SRS generation Nikolai S. Makarov Saint-Petersburg State Institute of Fine Mechanics and Optics (Technical University) Victor G. Bespalov Russian Research Center "S. I. Vavilov State Optical Institute"
Principle of quasi-phase matching Nonlinearity (2) Nonlinearity (3) Raman active medium 2
System of transient SRS equations – wave mismatching, g – steady-state Raman gain coefficient, i – frequencies of interacting waves, T2– dephasing time, q – phonon wave, Aj– complex wave amplitudes, z=z’+t’/c, t=t’. 3
Principle of quasi-phase matching at SRS -Generalized phase =2p-a-s-(ka+ks-2kp)r, where ki – 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
Quasi steady-state SRS pulse25Т2 (Т2=0.203 ns,pulse=10 ns). - 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 5
Highly transient SRS pulse<<25Т2 (Т2=0.203 ns,pulse=25 ps). - The efficiency of anti-Stokes SRS conversion much depends on a ratio of dephasing time T2 to pulse duration 6
Optimum ratio of input Stokes/pump intensities - There is an optimum value of input Stokes/pump waves intensities ratio. -This dependence can be approximated asIs/Ip,opt=0,1359g-2,6146 7
Critical pump wave intensity - There is a critical value of pump intensity. -This dependence can be approximated as Icr.p=0.4Δ/g 8
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 T2 to pulse duration • For each medium there is an optimal ratio Is/Ip, at which conversion efficiency is maximal • For each medium there is a critical value of pump intensity Conclusions 9
J. A. Armstrong, N. Blombergen, J. Ducuing, P. S. Pershan, “Interaction between light waves in a nonlinear dielectric” Phys. Rev., 127, pp. 1918-1939, 1962. • 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. 56-60, 1982. • 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 2516-2523, 1988. • 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. 68-77, 1991. • 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. 180-190, 2000. • Bespalov V. G., Makarov N. S., “Quasi-phase matching anti-Stokes SRS generation”, Opt. & Spectr., vol. 90, No. 6, pp. 1034-1037, 2001. References 10