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Soviet Journal of Quantum Electronics

Theory of wavefront reversal of radiation having a spatially inhomogeneous average intensity distribution

Igor' M Bel'dyugin, Iosif G. Zubarev

Published Mar 31, 1982• 0 citations
Publisher

Abstract

A spectral method is used in an attempt to find a unified approach to describe several variants of wavefront reversal in stimulated scattering: in a waveguide and when spatially inhomogeneous and single-mode radiation is focused by a lens. It is found that this involves allowing for a specific correlation between the spatial spectral components in the expansion of the pump field. Approximate solutions are found for the scattered field in these cases.

DOI
10.1070/qe1982v012n03abeh012178

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A spectral method is used in an attempt to find a unified approach to describe several variants of wavefront reversal in stimulated scattering: in a waveguide and when spatially inhomogeneous and single-mode radiation is focused by a lens. It is found that this involves allowing for a specific correlation between the spatial spectral components in the expansion of the pump field. Approximate solutions are found for the scattered field in these cases.
A theoretical analysis is made of stimulated light scattering in a pump beam possessing both fine-structure inhomogeneity (and thus, "gray" divergence) and a continuously varying amplitude and phase envelope due to focusing of the beam with a lens into an unbounded medium. An equation is derived to describe the gain of the pump-reproducing field component, and a solution of this equation, excitable by spontaneous radiation noise, is found in the constant pump field approximation. In this case, the scattered wave is localized in a narrow (compared with the pump wave) near-axial zone and, unlike scattering in a waveguide, the reproduction of the pump wave is partial and dependent on the correlation between the "gray" and diffraction-limited divergence. The disagreement between this theoretical conclusion and the complete reproduction observed earlier experimentally indicates the importance of saturation effects in the scattering of focused beams.
A theoretical analysis is made of wavefront reversal with a spatially inhomogeneous state of polarization of the pump radiation in symmetric trace-free stimulated scattering (backscattering). Mode theory is used to find solutions of the equation for the self-interaction of the pump radiation and also to find four linear indendent solutions for the scattered field having a structure correlated with that of the pump field. The increments for these solutions are determined. It is shown that, in contrast to scalar scattering, in the case of symmetric tracefree scattering (stimulated scattering of the Rayleigh line wing) of completely depolarized pump radiation the solution corresponding to complete spatial-polarization wavefront reversal has the largest increment. Reproduction of the wavefront of the depolarized pump radiation in stimulated forward scattering is discussed.
A theoretical investigation is made of stimulated scattering of spatially inhomogeneous radiation under saturation conditions. A system of kinetic equations describing the interaction between the pump radiation and Stokes waves, correlated and uncorrelated with the exciting field, is derived and solved. A quantitative criterion is derived for the quality of wavefront reversal in the case of generation of Stokes radiation from the spontaneous noise and also in the case of a "Brillouin" amplifier.
An analysis is made of stimulated backscattering in the case when the pump (laser) radiation has a continuous frequency spectrum and a time-dependent (nonfactorizable) speckle structure. The gain increments μ ( p ) and the corresponding specklon solution for a Stokes wave are found in the case of an arbitrary ratio of the widths of the pump line Δω l , and of the stimulated scattering line Γ. These solutions correspond to partial wavefront reversal, i.e., to reversal of the spectral band of the pump radiation within an interval of width of the order of Γ/2 around a certain frequency p . A comparison of the specklon gain increments with the increments for uncorrelated waves makes it possible to determine the conditions for wavefront reversal.