1. Multiwave quasi-phase matching stimulated Raman scattering with dispersion of Raman gain
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"

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

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

4. of quasi-phase matching at SRS
Principle
of quasi-phase matching at SRS
- Generalized phase
=2p-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 active layers input (1, 3) do not practically change, that in a final result provides a realization of quasi-phase matching conditions. 1 3 2 0
(3)0
(3)=0 4

5. System of steady-state multiwave SRS equations
j – wave mismatching, g – steady-state Raman gain coefficient, j – frequencies of interacting waves, Ej – complex wave amplitudes.
In this system the wave mismatching and Raman gain are the functions of coordinate for nonlinear ((3)0) and linear ((3)=0) layers.
Raman gain dispersion
Ba(NO3)2 H2 5

6. in hydrogen and barium nitrate
Multiwave SRS
in hydrogen and barium nitrate
Hydrogen
Barium 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. 6

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

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

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

10. Layers length errors for periodical QPM structure
Maximum allowed error is 15%
Maximum allowed error is 0.2%
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. 10

11. 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”. 12

13. 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, 2001.
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 13