Multiwave stimulated Raman scattering with quasi-phase matching 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)

Outline Principle of quasi-phase matching System of multiwave SRS equations Multiwave SRS with/without Raman gain dispersion QPM Multiwave SRS Conclusions References 2

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

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 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 00 11 22 33

System of steady-state multiwave SRS equations In this system the wave mismatching and Raman gain are the functions of coordinate for nonlinear (  (3)  0) and linear (  (3) =0) layers.  j – wave mismatching, g – steady-state Raman gain coefficient,  j – frequencies of interacting waves, E j – complex wave amplitudes. 5 Raman gain dispersion Ba(NO 3 ) 2 H2H2

Multiwave SRS in hydrogen and barium nitrate 6 HydrogenBarium nitrate Without dispersion of g: P – pump, S1 – first Stokes, S2 – second Stokes, S3 – third Stokes; With dispersion of g: P’ – pump, S1’ – first Stokes, S2’ – second Stokes, S3’ – third Stokes.

7 Multiwave QPM SRS in hydrogen and barium nitrate HydrogenBarium nitrate 1 – pump, 2 – first Stokes, 3 – first Anti-Stokes, 4 – second Stokes.

Influence of high SRS components on calculations precision 8 For best calculation accuracy it is necessary to take into account at least the generation of 4 Stokes and 4 anti-Stokes SRS components.

Multiwave QPM SRS: periodical structure 9 HydrogenBarium nitrate 1 – pump, 2 – first Stokes, 3 – first Anti-Stokes, 4 – second Stokes, 5 – second Anti-Stokes, 6 – third Stokes, 7 – third Anti-Stokes.

Layers length errors for periodical QPM structure 10 For periodical QPM structure it is necessary to choose the passive layers length with high accuracy, because even the small error in layer length causes the essential decreasing of anti-Stokes SRS generation efficiency, whereas for aperiodical QPM structure the error may reached more than 5% of layer length. Maximum allowed error is 15%Maximum allowed error is 0.2%

Conclusion Our numerical calculations have shown that for best accuracy of QPM SRS simulations it is necessary to take into account the dispersion of Raman gain coefficient and for studying of multiwave SRS influence on QPM structure realization it is necessary to take into account the generation at least of 4 Stokes and 4 anti-Stokes SRS components. We received the model of periodical QPM Raman media in which the efficiency of multiwave anti-Stokes generation reached ~40%. We determined that high precision of passive layers length of periodical QPM structure in hydrogen is required due to strongly influence of layers length error on anti-Stokes SRS generation efficiency. In barium nitrate it is possible to realize periodical structure for efficient generation of 3 Stokes and 3 Anti-Stokes SRS components. 11

12 Acknowledgments I would like to thank the organizing committee of Conference for partial supporting of my participation. This work was partly supported by Grant RP of U.S. Civilian Research and Development Foundation and Program of Ministry of Education “Femtosecond optics and technologies”.

References V. G. Bespalov, N. S. Makarov, “Quasi-phase matching anti-Stokes SRS generation”, Proc. SPIE, vol. 4268, 2001, pp V. G. Bespalov, and N. S. Makarov, “Quasi-phase matching generation of blue coherent radiation at stimulated Raman scattering”, Optics Comm., 203 (3-6) (2002) pp V. G. Bespalov, N. S. Makarov, “SRS generation of anti-Stokes radiation under phase quasi-matching conditions”, Opt. & Spectr., vol. 90, No. 6, 2001, pp V. G. Bespalov, N. S. Makarov, “Transient quasi-phase matching SRS generation”, Proc. SPIE, (ICONO-2001), 2001 (accepted for publication). N. S. Makarov, “Analytical solution of quasi-phase matching anti-Stokes SRS amplification in silica fiber”, in book Modern technologies, pp , SPb, V. G. Bespalov, N. S. Makarov, “Simultaneously Stokes and anti-Stokes Raman amplification in silica fiber”, Proc. SPIE, vol. 4638, 2002 (accepted for publication). Bischel W. K., Dyer M. J. “Wavelength dependence of the absolute Raman gain coefficient for the Q(1) transmission in H2”, J. Opt. Soc. Am. B, vol. 3, 1985, pp