1. Backward and forward quasi- phase matched multiwave SRS in nonlinear periodical structures 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)

2. Outline Principle of quasi-phase matching System of multiwave SRS equations Numerical simulations results Conclusions References Backward and forward quasi-phase matched multiwave SRS in nonlinear periodical structures; Saint-Petersburg, 30 June – 2 July 2003 Makarov N.S., mak_nick@newmail.ruBespalov V.G., bespalov@admiral.ru

3. Principle of quasi-phase matching Raman active medium Nonlinearity  (2) Nonlinearity  (3) H2H2 H2H2 H2H2 H2H2  (3)  0  (3) =0 z I 2w LкLк d 31 c-axis LкLк Backward and forward quasi-phase matched multiwave SRS in nonlinear periodical structures; Saint-Petersburg, 30 June – 2 July 2003 Makarov N.S., mak_nick@newmail.ruBespalov V.G., bespalov@admiral.ru

4. Principle of quasi-phase matching at SRS Generalized phase on active layers input do not practically change, that in a final result provides a realization of quasi- phase matching conditions , rad  (3)  0  (3) =0 Backward and forward quasi-phase matched multiwave SRS in nonlinear periodical structures; Saint-Petersburg, 30 June – 2 July 2003 Makarov N.S., mak_nick@newmail.ruBespalov V.G., bespalov@admiral.ru

5. System of forward and backward multiwawe SRS equations  j i – wave mismatching, g j ± – steady-state Raman gain coefficient,  j – frequencies of interacting waves, E j ± – complex wave amplitudes Backward and forward quasi-phase matched multiwave SRS in nonlinear periodical structures; Saint-Petersburg, 30 June – 2 July 2003 Makarov N.S., mak_nick@newmail.ruBespalov V.G., bespalov@admiral.ru

6. Model verification: waves profiles at different input pump intensities (left – input pump and right – output pump) t, ns I, GW/cm 2 Backward and forward quasi-phase matched multiwave SRS in nonlinear periodical structures; Saint-Petersburg, 30 June – 2 July 2003 Makarov N.S., mak_nick@newmail.ruBespalov V.G., bespalov@admiral.ru

7. Model verification: waves profiles at different input pump intensities (left – output forward Stokes and right – output backward Stokes) t, ns I, GW/cm 2 Backward and forward quasi-phase matched multiwave SRS in nonlinear periodical structures; Saint-Petersburg, 30 June – 2 July 2003 Makarov N.S., mak_nick@newmail.ruBespalov V.G., bespalov@admiral.ru

8. Barium nitrate Hydrogen Raman gain dispersion Backward and forward quasi-phase matched multiwave SRS in nonlinear periodical structures; Saint-Petersburg, 30 June – 2 July 2003 Makarov N.S., mak_nick@newmail.ruBespalov V.G., bespalov@admiral.ru

9. Influence of high SRS components on calculations precision For best calculation accuracy it is necessary to take into account at least the generation of 3 Stokes and 3 anti-Stokes SRS components Backward and forward quasi-phase matched multiwave SRS in nonlinear periodical structures; Saint-Petersburg, 30 June – 2 July 2003 Makarov N.S., mak_nick@newmail.ruBespalov V.G., bespalov@admiral.ru

10. The influence of backward SRS on QPM realization (active layers length) Backward and forward quasi-phase matched multiwave SRS in nonlinear periodical structures; Saint-Petersburg, 30 June – 2 July 2003 Makarov N.S., mak_nick@newmail.ruBespalov V.G., bespalov@admiral.ru

11. The influence of backward SRS on QPM realization (passive layers length) Backward and forward quasi-phase matched multiwave SRS in nonlinear periodical structures; Saint-Petersburg, 30 June – 2 July 2003 Makarov N.S., mak_nick@newmail.ruBespalov V.G., bespalov@admiral.ru

12. Conclusions Our model of forward and backward multiwave SRS is quality and quantity compared with experimental results For best accuracy of QPM SRS simulations it is necessary to take into account the dispersion of Raman gain coefficient For studying of multiwave SRS influence on QPM structure realization it is necessary to take into account the generation at least of 3 Stokes and 3 anti-Stokes SRS components The influence of backward SRS on QPM structure realization results in the small difference between layers length of optimal QPM structure and small decreasing of resulting anti-Stokes conversion efficiency (~25% at backward and forward SRS, ~30% at forward SRS) The oscillations of optimal layers length are partially connected with backward SRS influence and with insufficient precision of layers length determination due to high computational complexity of this task Backward and forward quasi-phase matched multiwave SRS in nonlinear periodical structures; Saint-Petersburg, 30 June – 2 July 2003 Makarov N.S., mak_nick@newmail.ruBespalov V.G., bespalov@admiral.ru

13. References Armstrong J.A., Bloembergen N., Ducuing J., Pershan P.S. // Phys. Rev., 1962, 127, pp. 1918-1939. Bespalov V.G., Makarov N.S. Quasi-phase matching generation of blue coherent radiation at stimulated Raman scattering // Optics Communications 2002, 203 (3-6), pp. 413-420. Maier M., Kaiser W., Giordmaine J.A. Backward stimulated Raman scattering // Phys. Rev., 1969, V. 177, №2, pp. 580-599. Raijun Chu, Morton Kanefsky, Joel Falk Numerical study of transient stimulated Brillouin scattering // J. Appl. Phys., 1992, V. 71, №10, pp. 4653-4658. Zaporozhchenko R.G., Kilin S.Ya, Bespalov V.G., Stasel’ko D.I. Formation of the spectra of backward stimulated Raman scattering from the quantum noise of polarization of a scattering medium // Opt.&Spectr., 1999, V. 86, №4, pp. 632-639. 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, 1985, V. 3, pp. 677- 682. Backward and forward quasi-phase matched multiwave SRS in nonlinear periodical structures; Saint-Petersburg, 30 June – 2 July 2003 Makarov N.S., mak_nick@newmail.ruBespalov V.G., bespalov@admiral.ru