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Soviet Journal of Quantum Electronics

Anti-Stokes emission in stimulated Raman scattering of ultrashort pulses

Joachım Herrmann

Published Feb 28, 1975• 5 citations
Publisher

Abstract

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.

DOI
10.1070/qe1975v005n02abeh010900

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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.
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 semiclassical model of nonstationary stimulated Raman scattering with account of forward and backward waves of different frequencies is proposed. Equations for the elements of a collective density matrix and electric-field amplitudes are obtained applying the averaging method. It is shown that forward waves are generated by a united polarization component, whereas each of the backward waves is formed by its own component. The description is based on the approximation of small scattering angles and assumes that the quantities considered do not depend on transverse coordinates. The emission dynamics of forward-backward Stokes pulses is investigated both for the linear case and under the strong depletion of pumping and level populations. The domain of applicability of the model of nonstationary forward stimulated Raman scattering is determined.
Analytic and numerical solutions are obtained for the equations describing the propagation of several pulses of different frequencies through a Raman medium. The transient case is treated, and the analysis includes Stokes, pump, and anti-Stokes frequency components. The effect of phase mismatch \ensuremath{\Delta}k between these waves is investigated. An analytic solution is found that describes the phenomenon of transient Stokes--anti-Stokes gain suppression in the limit \ensuremath{\Delta}k=0. For nonzero values of \ensuremath{\Delta}k, the behavior of the transient gain coefficient is found to follow a scaling rule that is the analog of a similar result known from the steady-state limit. Calculations are performed to identify conditions that enhance conversion to anti-Stokes radiation. It is found that there is an optimum strength of the Stokes seed, and that proper phase matching of the initial waves is essential.
It is shown that transient anti-Stokes stimulated Raman scattering (SRS) acts as a vacuum field fluctuations amplifier at Stokes frequency, the fluctuations being amplified up to macroscopic values. This makes their investigation possible by studying macroscopic energy fluctuations of transient SRS anti-Stokes pulses. The proposed theory also gives a quantitative description of angular distribution of self-generated anti-Stokes emission around the exact phase-matching angle recently observed by Duncan et al. ( Opt. Lett. , 11 (1986) 803) in the transient regime.
We have studied the diffractive coupling of Stokes, anti-Stokes, and pump fields in stimulated Raman scattering. We find that, depending on the strength of the anti-Stokes field relative to that of the Stokes, both soliton dynamics and beam-pointing fluctuations are affected for finite Fresnel numbers. The generation of the anti-Stokes waves can inhibit a gain-focusing mechanism that we predicted for the Stokes field, when a soliton propagates in the medium. Although no qualitative differences arise in the beam-pointing fluctuations of the Stokes field, we predict that the anti-Stokes beam may be much more stable than the Stokes counterpart. Our analysis shows that for a Fresnel number of 5, the difference can be as large as 70%, while for Fresnel numbers of order unity, it is nearly 10%.