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Soviet Journal of Quantum Electronics

Stimulated Raman scattering of light beams under saturation conditions

Alexander A. Betin, Guerman A. Pasmanik, L. V. Piskunova

Published Nov 30, 1975• 7 citations
Publisher

Abstract

A numerical solution is given of a system of coupled quasioptic equations describing the nonlinear interaction between exciting and stimulated-Raman-scattered waves. The boundary conditions are found by solving the problem in the approximation of fixed parameters of the exciting (pump) beam. It is shown that when the threshold for the parallel stimulated scattering is exceeded, the diffraction effects limit the rise of the intensity of the radiation transmitted by a nonlinear medium when the pump power is increased.

DOI
10.1070/qe1975v005n11abeh012117

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A numerical solution is given of a system of coupled quasioptic equations describing the nonlinear interaction between exciting and stimulated-Raman-scattered waves. The boundary conditions are found by solving the problem in the approximation of fixed parameters of the exciting (pump) beam. It is shown that when the threshold for the parallel stimulated scattering is exceeded, the diffraction effects limit the rise of the intensity of the radiation transmitted by a nonlinear medium when the pump power is increased.
An analysis is made of nonlinear nonstationary equations describing dynamics of the stimulated Raman scattering in optical resonators excited by external nonmonochromatic radiation. The threshold of the excitation of the stimulated scattering by nonmonochromatic radiation is found and its dependence on the dispersion of the active medium is deduced. Solutions are obtained for steady-state oscillations in a resonator and their characteristics are investigated as a function of the spectrum of the exciting radiation and of the dispersion of the active medium.
An investigation is made of the serious limitations on the growth of the amplitude of a Stokes wave associated with the optical Stark effect and with the dispersion of the group velocities of the interacting pulses. It is shown that when the distance traversed exceeds a certain length, the gain due to stimulated Raman scattering reaches saturation whereas the spectrum of the scattered light becomes broader and acquires a line structure. Saturation of the scattering is not manifested at pump intensities sufficient to bleach the scattering medium. The gain can be optimized by altering the offset from a resonance.
The depletion and saturation effect of stimulated Raman scattering in optical fibres has been investigated. Nonlinear energy coupled equations are solved analytically. Our study reveals that the Raman gain saturation effect caused by the generation of the second Stokes has to be taken into account in light amplification by stimulated Raman scattering although it can be ignored in spontaneous stimulated Raman scattering. We also show that it is advantageous to feed the fibre with small low Stokes signals in amplifying high-order Stokes signals, for easing the requirement of high pump power and long fibre length.
Parametric instability induced by the medium saturation in stimulated Raman scattering is investigated theoretically via a generalized detuning (1) where ω p,s,o are the frequency of the pump, Stokes, and phonon, ϕ ˙ p s is the phase modulation, and the last term is the nonlinear correction of the highly excited anharmonic molecule with an amplitude Q.The steady-state gain and hence the Stokes efficiency, in the presence of the anharmonic term, are governed by a cubic equation of |Q|2which is to be solved from the Bloch and Maxwell equations including the pump depletion. Numerical results are shown for the transition diagram of Stokes efficiency vs input pump intensity at various system conditions at the steady-state. For the transient regime, with pulse duration shorter than the dephasing time, we analyze the temporal profiles of the Stokes and the depleted pump based on a transformed equation which combines Bloch and Maxwell equation as follows: (2) where Tis a nonlinear time, G s is the steady-state gain, l0is the input pump intensity, and Uis the real part of the phonon amplitude Q.For an input pulse intensity given by sech2(t/t p ), Eq. (2) is solved numerically to study the transient pulse profiles in the presence of pump depletion and medium saturation.
Assuming the absence of parametric intermode interactions, a closed system of equations is derived for the pump wave and Stokes radiation intensities and for the reproduction factor in stimulated scattering in a waveguide under saturation conditions. Both parallel scattering and backscattering are analyzed. It is shown that as the backscattering reflection coefficient increases, the reproduction improves. In parallel scattering, the reproduction factor depends on the relationship between the initial correlation coefficient and the ratio of the input and pump signals.