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Journal of Physics A Mathematical and General

The Thirring model as an approximation to the theory of two-photon propagation

A. M. Kamchatnov, Heinz Steudel, Alexander A. Zabolotskii

Published Nov 7, 1997• 3 citations
Publisher

Abstract

We consider the two-photon propagation process under the two-fold approximation that (i) the excitation of the upper level of medium molecules remains small during the process, (ii) the intensity of one of the two participating electromagnetic waves is always small compared to that of the other wave. It is then shown that in the limit of the strong dynamical Stark effect the equations describing this process can be reduced to the classical Thirring model equations. This reduction permits one to develop a much simpler theory of wave interaction than was possible in the case of the original equations. As an example, the periodic solutions of two-photon propagation are considered and the Whitham modulational equations are obtained. The different forms of U - V pairs for the Thirring model are discussed in the appendix. Analogous theory can be developed for the stimulated Raman scattering process.

DOI
10.1088/0305-4470/30/21/020

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We consider the two-photon propagation process under the two-fold approximation that (i) the excitation of the upper level of medium molecules remains small during the process, (ii) the intensity of one of the two participating electromagnetic waves is always small compared to that of the other wave. It is then shown that in the limit of the strong dynamical Stark effect the equations describing this process can be reduced to the classical Thirring model equations. This reduction permits one to develop a much simpler theory of wave interaction than was possible in the case of the original equations. As an example, the periodic solutions of two-photon propagation are considered and the Whitham modulational equations are obtained. The different forms of U - V pairs for the Thirring model are discussed in the appendix. Analogous theory can be developed for the stimulated Raman scattering process.
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A photon theory of the stimulated Raman effect is developed. A system of coupled equations for the amplitudes of scattered photons and molecular vibrations are derived. The molecular vibration coordinates are then eliminated using the random phase approximation. The equations which result assume the form of coupled equations for the first Stokes and anti-Stokes lights. The secular equation which characterizes the solution of these coupled equations is shown to be equivalent to that of Shen and Bloembergen. Using this secular equation, the condition for temporal growth of the scattered lights is obtained and is compared with that for the spatial growth, which was obtained previously by Shen and Bloembergen. It is shown that both types of growth (temporal and spatial) proceed with comparable rates if the damping of the molecular vibration is large. If its damping is small, however, the temporal growth prevails over the spatial growth. Typical line-shape of the anti-Stokes line is obtained in the case of small damping. The result shows a strong directionality, as is the case of large damping.
The evolution equations of two-frequency stimulated Raman scattering in a molecular quasithree- level medium with static dipole moments have been derived in the approximations of the nondepletion of the pump field and the unidirectional propagation of the Stokes field. Completely integrable particular cases of the resulting system of equations have been found. New mechanisms of controlling the parameters of microwave pulses generated in such a system have been studied within this model. The numerical analysis and particular exact solutions demonstrate the possibility of switch between the regimes of generation of narrow Stokes field pulses and nearly rectangular pulses.
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