Backward and forward multiwave stimulated Raman scattering

1. Backward and forward multiwave stimulated Raman scattering 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. Abstract Backward and forward multiwave stimulated Raman scattering; Saint-Petersburg, 20 June – 4July 2003 Makarov N.S., mak_nick@newmail.ru Bespalov V.G., bespalov@admiral.ru Stimulated Raman scattering (SRS) is widely used for frequency conversion and multiple wavelengths generation. Due to difficult SRS experiments it is interest the numerical simulation of multiwave SRS for optimizing the conditions for simultaneously generation of Stokes and anti-Stokes SRS components. First, the model of SRS described the energy exchange between pump and Stokes waves was presented, then this model was enlarged for the case of multiwave interaction taking into account the generation of high-order Stokes and anti-Stokes SRS components. However, this model describes only the interaction between forward SRS components and does not take into account the generation of backward Stokes wave, while at the experiments in compressed gases the researchers observes the simultaneously generation of forward and backward SRS components. So for numerical simulations of backward SRS one used the system of connected differential equations, described the interaction of forward pump and backward Stokes wave. In this work we present a new system of connected differential equations for complex amplitudes of forward and backward interacting waves described multiwave backward and forward stimulated Raman scattering, where Ej are complex amplitudes of interacting waves ((+) corresponds forward components and (-) corresponds backward components), gj are Raman gain coefficients, q are complex amplitudes of phonon wave, j=0+j, 0 is the frequency of pump wave,  is the Raman shift frequency, ji are the wave mismatchings and T2 are the dephasing times. This system is the extension of multiwave SRS model and it may be reduced to well-known systems of forward multiwave SRS and backward SRS. Preliminary simulations with 2 Stokes (forward and backward) and 1 anti-Stokes SRS components were compared with experimental results with nanosecond-pumped SRS in compressed hydrogen. The results of numerical simulations are quantity and quality agreed with experimental results.

3. System of forward and backward multiwawe SRS equations Backward and forward multiwave stimulated Raman scattering; Saint-Petersburg, 20 June – 4July 2003 Makarov N.S., mak_nick@newmail.ru Bespalov V.G., bespalov@admiral.ru

4. Used notifications Backward and forward multiwave stimulated Raman scattering; Saint-Petersburg, 20 June – 4July 2003 Makarov N.S., mak_nick@newmail.ru Bespalov V.G., bespalov@admiral.ru ji – wave mismatching, gj± – steady-state Raman gain coefficient, j – frequencies of interacting waves, Ej±– complex wave amplitudes

5. Raman gain dispersion Backward and forward multiwave stimulated Raman scattering; Saint-Petersburg, 20 June – 4July 2003 Makarov N.S., mak_nick@newmail.ru Bespalov V.G., bespalov@admiral.ru Barium nitrate Hydrogen

6. Model verification: waves profiles at different input pump intensities (left – input pump and right – output pump) I, GW/cm2 I, GW/cm2 t, ns t, ns Backward and forward multiwave stimulated Raman scattering; Saint-Petersburg, 20 June – 4July 2003 Makarov N.S., mak_nick@newmail.ru Bespalov V.G., bespalov@admiral.ru

7. Model verification: waves profiles at different input pump intensities (left – output forward Stokes and right – output backward Stokes) I, GW/cm2 I, GW/cm2 t, ns t, ns Backward and forward multiwave stimulated Raman scattering; Saint-Petersburg, 20 June – 4July 2003 Makarov N.S., mak_nick@newmail.ru Bespalov V.G., bespalov@admiral.ru

8. The power profiles of interacting waves at forward and backward SRS in hydrogen Backward and forward multiwave stimulated Raman scattering; Saint-Petersburg, 20 June – 4July 2003 Makarov N.S., mak_nick@newmail.ru Bespalov V.G., bespalov@admiral.ru

9. Conclusions Backward and forward multiwave stimulated Raman scattering; Saint-Petersburg, 20 June – 4July 2003 Makarov N.S., mak_nick@newmail.ru Bespalov V.G., bespalov@admiral.ru • Our model of forward and backward multiwave SRS is the extension of multiwave SRS model and it may be reduced to well-known systems of forward multiwave SRS and backward SRS. • 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 • Then the input pump intensity is near threshold, than the radial profile of waves can be neglected due to smooth changes of output waves on input intensity changes • Then the input pump intensity is much more than threshold, than the radial profile of waves must be taken into account due to jump changes of output waves on input intensity changes

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