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Soviet Journal of Quantum Electronics

Theory of amplification of the first Stokes component in a nonmonochromatic pump field under stimulated Raman scattering conditions

Igor' M Bel'dyugin, E M Zemskov, V I Chernen'kiĭ

Published Jun 30, 1978• 8 citations
Publisher

Abstract

A theoretical analysis is made of the problem of parallel amplification of the Stokes signal in a nonmonochromatic spatially inhomogeneous pump field in stimulated Raman scattering. Expressions are obtained for the spatial and temporal characteristics of the process of amplification of the Stokes signal. It is shown that in the course of amplification the slowly varying amplitude of the Stokes signal field becomes similar to the slowly varying amplitude of the pump field. The relationships obtained apply also, subject to certain restrictions, to other types of scattering.

DOI
10.1070/qe1978v008n06abeh010396

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A theoretical analysis is made of the problem of parallel amplification of the Stokes signal in a nonmonochromatic spatially inhomogeneous pump field in stimulated Raman scattering. Expressions are obtained for the spatial and temporal characteristics of the process of amplification of the Stokes signal. It is shown that in the course of amplification the slowly varying amplitude of the Stokes signal field becomes similar to the slowly varying amplitude of the pump field. The relationships obtained apply also, subject to certain restrictions, to other types of scattering.
A theoretical and experimental investigation was made of the amplification of a Stokes signal in a multimode pump field when the ratio of the spectral widths of the interacting fields was varied. In the pump intensity range I p < I cr ( I cr was a critical intensity) the gain increment was considerably less than the static value and it was governed entirely by the spectral distributions of the pump and Stokes signal. In the range I p > I cr the gain increment tended to the static value. An anomalous scatter of the Raman amplifier gain was observed experimentally for Δ ν s ≈Δ ν p ≫Δ ν l (Δ ν s ,Δ ν p , and Δ ν l were the line widths of the Stokes signal, pump, and spontaneous stimulated Raman scattering). A theory developed for the purpose indicated that the scatter was observed because the phase relationships between the interacting waves at the input into the medium varied from one measurement to another.
An analysis is made of the laws governing amplification of the Stokes wave in stimulated Raman scattering (STRS) in a dispersive medium for different models of wide-band pump radiation. An accurate solution of the STRS equations is obtained for pump radiation having a quadratically time-modulated phase. It is shown that for pump radiation for which the width of the instantaneous frequency spectrum is much less than the Raman scattering line width, the laws governing amplification of the Stokes wave differ substantially from those predicted by statistical STRS theory. Solutions of STRS equations in a dispersive medium are found for a model of temporally periodic pump radiation having a high intermode beat frequency.
Stimulated Raman scattering of a randomly modulated pump is investigated by the method of successive approximations. This involves expanding solutions in terms of small parameters, which are ratios of the correlation scales of random effects to other characteristic dynamic scales of the problem. Systems of closed equations are obtained for the moments of the amplitudes of the Stokes and pump waves and of the molecular vibrations. These describe the dynamics of the process allowing for changes in the pump intensity and statistics due to a three-wave interaction. By analyzing equations in higher-order approximations, it is possible to establish the conditions of validity of the first (Markov) and second approximations. In particular, it is found that these are valid for pump intensities JL both above and below the critical value Jcr near which the gain begins to increase rapidly and reproduction of the pump spectrum by the Stokes wave is initiated. Solutions are obtained for average intensities of the Stokes wave and molecular vibrations in the first approximation in a constant pump field. It is established that, for JLJcr, the Stokes wave undergoes rapid nonsteady-state amplification which is associated with an increase in the amplitude of the molecular vibrations. The results of the calculations show good agreement with known experimental data.
A theoretical analysis is made of the stimulated Raman scattering in gases in the presence of spatial degeneracy of the energy levels. Saturation of the population difference and influence of anti-Stokes radiation are allowed for. Various polarizations of the pump fields and of the Stokes and anti-Stokes radiation are considered. It is shown that the profile of the stimulated Raman line is generally a sum of three Lorentzian lines and the scattering includes scalar, symmetric, and antisymmetric components. The use of circularly polarized pump radiation suppresses the influence of anti-Stokes radiation on the gain of the Stokes wave.
A model is developed for the description of stimulated Raman scattering. This model allows for changes in the level populations due to radiative transitions and it can be used also for an arbitrary detuning of the pump radiation from the center of a line of an atom in the active medium. A study is made of the conversion of wide-band laser radiation into a Stokes signal. It is shown that this conversion is quite efficient and the Stokes signal gain corresponds to coherent scattering. This result is related to the matching of the phases of the pump and Stokes signals. Numerical investigations carried out using this model under the experimental conditions described elsewhere give results in agreement with the experimental data.