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Soviet Journal of Quantum Electronics

Quasiequilibrium intensity distribution of the components of stimulated Raman scattering

S. A. Reshetnyak, Leonid A. Shelepin

Published Oct 31, 1975• 2 citations
Publisher

Abstract

A quasiequilibrium distribution of the intensities of the Stokes and anti-Stokes components of the stimulated Raman scattering is obtained. Allowance is made for two-photon and four-photon processes. The distribution is obtained in an analytic form and it is in satisfactory agreement with the experimental results.
DOI
10.1070/qe1975v005n10abeh012032

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A calculation is made of the intensity of the Stokes radiation in the stimulated Raman scattering of ultrashort light pulses in a dispersive medium employing the asymptotic approximation for arbitrary modulation of the amplitude and phase of the pump pulse. Particular attention was paid to the effect of phase modulation on the stimulated Raman scattering. Calculations were also made of the intensity of the anti-Stokes component in the scattering of an ultrashort pulse in a dispersive medium and of the optimal angle for the observation of the anti-Stokes rings.
A theory of nonstationary stimulated Raman scattering is developed, allowing for the coupling between the Stokes and anti-Stokes waves. The main equations are solved in the asymptotic approximation, which is valid for large values of the gain. The dependences of the gain on the phase mismatch Δ k , pulse duration τ p , and cell length l are discussed and the optimal angle for the observation of the anti-Stokes rings is calculated. Moreover, the spectral distributions of the Stokes and anti-Stokes waves are considered.
The process of stimulated Raman scattering is described by the model of 2D oscillator. The photons of Stokes mode are described by one mode of the oscillator and phonons of the medium are described by the other mode of oscillator. The interaction of photons and phonons is taken to be quadratic in the creation and annihilation operators of the photons and phonons. New time-dependent integrals of motion are found for stimulated Raman scattering within the framework of this model. The photon-phonon probability-distribution function is found in terms of Hermite polynomials of four variables. It is shown that the squeezing phenomenon can be transferred from one mode to the other due to interaction. The statistical dependence appears due to interaction as well. An explicit formula of the photon-number probability distribution as a function of the laser-field intensity and the medium parameters is obtained both in terms of Hermite polynomials of two variables and in terms of Legendre polynomials after the averaging of the photon-phonon probability-distribution function over the phonon mode. The mean photon number and its dispersion in the Stokes mode are expressed as functions of the medium parameters and a parameter of the interaction. It is shown that if the medium is initially prepared, then after the interaction with laser field the photons are created in squeezed state. The classical propagator for stimulated Raman scattering is found within the framework of the symplectic tomography scheme.
An experimental investigation was made of the distribution of the energies of pulses of forward (concurrent) and backward first Stokes components of stimulated Raman scattering (STRS), and of pump (exciting) radiation pulses, transmitted by a scattering medium. The study was carried out under linear, intermediate, and nonlinear scattering conditions. The dependences of the coefficients of variation and of the asymmetry of the distributions on the energy of the pump pulses were determined. The statistical properties of the energy of the backward STRS pulses differed in a number of respects from the forward STRS pulses, including a relatively high coefficient of variation in the former case. An interpretation of these differences was developed. It was found that STRS gave rise to fluctuations of the energy of the transmitted pump pulses and the statistical characteristics of these pulses were determined. The results obtained for forward STRS were in satisfactory agreement with the conclusions reached on the basis of a quantum theory.
The results of the investigation of Stokes energy statistics in the linear regime of stimulated Raman scattering with a broad-band pump are presented. The pulse-energy distributions and their standard deviations were measured. The comparison of the experimental data with known ones for coherent pump shows the strong difference in the distribution shape and the standard deviation value. This difference is explained as a manifestation of the non-Gaussian (super-Gaussian) statistics in stimulated scattering with a broad-band pump. The results of numerical calculations for statistics of Stokes intensity are in a qualitative agreement with the experimental findings.