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

2. Outline Principals of quasi-phase matching Systems of SRS equations Numerical simulations results Conclusions References 2

3. Principals of quasi-phase matching  (2)  (3) 3 Raman active medium

4. System of transient SRS equations  – waves mismatching, g – steady-state Raman gain coefficient,  i – frequencies of interacting waves, T 2 – dephasing time, q – phonon wave, A j – complex wave amplitudes. 4

5. System of steady-state SRS equations In this system the waves mismatching and Raman gain are the functions of coordinate for nonlinear (  (3)  0) and linear (  (3) =0) layers.  – waves mismatching, g – steady-state Raman gain coefficient,  i – frequencies of interacting waves, A j – complex wave amplitudes. 5

6. Efficiency of anti-Stokes SRS generation in Raman-active media Hydrogen  = 3.84 rad/cm g = 3.0 cm/GW. - There is an optimal ratio I s /I p, for maximal conversion efficiency. - The ratio depended from waves mismatching and steady- state Raman gain coefficient. 6

7. Energy conversion at quasi-phase matching Hydrogen  = 3.84 rad/cm g = 3.0 cm/GW I s (0) = 0.0023 GW/cm 2 efficiency  30% - At optimum ratio I s /I p, conversion efficiency reached more than 30%, but Stokes intensity is higher then anti-Stokes intensity. 7

8. Comparison of quasi-phase and phase matching Hydrogen  = 3.84 rad/cm g = 3.0 cm/GW 1 - quasi-phase matching 2 - without (quasi-) phase matching 3 - phase matching - Conversion efficiency at quasi-phase matching is lower than at phase matching and higher than at simple focusing in Raman media. 8

9. Lengths of active and passive zones H2H2 - Structure of layers is not periodical. - Similar plot can be achieved for barium nitrate. - It is essentially different from quasi-phase matching in  (2) media. - Lengths of active/passive layers are monotonously decreased/ increased. 9

10. Characteristic zone lengths - It is possible to approximate this dependence as La = 2.6/  and Lp = 3.9/ . - With increasing of waves mismatching structure become more periodical. 10

11. Critical pump wave intensity - There is a critical value of pump intensity. - This dependence can be approximated as I cr.p =0.4Δ/g 11

12. Conclusions - For each medium there is an optimal ratio I s /I p, at which conversion efficiency is maximal. - The Conversion efficiency can reached more than 30% - Structure of layers is not periodical. Lengths of active layers are monotonously decreased and lengths of passive layers are monotonously increased. - With increasing of waves mismatching structure become more periodical. - For each medium there is a critical value of pump intensity. 12

13. Acknowledgment I would like to thank: SPIE - The International Society for Optical Engineering for registration fee. CRDF - US Civilian Research & Development Foundation for support of my participation. 13

14. References 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. 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. 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. 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. 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. Bespalov V. G., Makarov N. S., “Quasi-phase matching anti-Stokes SRS generation”, Opt. & Spectr., vol., No. 5, 2001 (accepted for publication) 14