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Canadian Journal of Physics

Numerical Solution of the Coupled Steady State Gain Equations for Stimulated Backward Scattering in Absorbing Fluids

Richard H. Enns, S. S. Rangnekar

Published Feb 1, 1975• 2 citations
Publisher

Abstract

A numerical solution to the problem of steady state stimulated backward scattering of light in absorbing fluids is presented. The solution is compared with Tang's solution to the corresponding problem in transparent media.
DOI
10.1139/p75-034

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Physical Review A•Aug 1, 1987•8 citations
The transient gain equations for stimulated backward scattering in absorbing fluids are solved numerically by the method of characteristics for an amplifier setup. In addition to the 'spiking' of the signal pulse previously noted by Maier, Kaiser, and Giordmaine, the existence of a characteristic dip in the amplification of the signal pulse in nonabsorbing fluids when the interaction region ceases to increase is reported. The effect of increasing absorption is to wipe out both the spike and the dip.
Characteristics of backward, stimulated light pulses are analyzed in the limit where rate equation approximation breaks down, and fluctuation dynamics (oscillator displacements for Raman and phonon amplitudes for Brillouin) must beconsidered. In this limit, the scattered photon flux N s is N s = a(dN l /dt), (d/dt + γ f )A f = bN l /Af,(d/dt + γ l ) = dN l /Af, where f,/referto fluctuations and pump, respectively; A f the fluctuation intensity, and constants a, b, and d depend on the medium characteristics. An analytical solution to this set of equations has been given by Maier et al.1 in the limit γ f →0 and γ l = 0. With these restrictions removed, analytical solution is difficult. Here, we are considering an analytical solution by reducing the set of equations to that of the cubic Schrodinger equation with real amplitude and by using Backlund transform. Preliminary calculations show that the solitary wave solutions are possible (a purely soliton solution is not admissible2 in the form of hyperbolic secant square).
A method is developed for studying transient stimulated Raman scattering in the quasi-steady-state regime when the input pump field consists of a repetitive periodic sequence of pulses. The method is most attractive for cases where the single-pulse duration is substantially shorter than the repetition time scale, making a straightforward numerical simulation very costly, time consuming, and potentially intractable. The method is applicable to any periodic electric field envelope including that generated by a finite number of longitudinal modes with arbitrary phase. A second numerically efficient method is developed for treating the buildup of the entire pulse train. In addition, an analytic solution is found in the undepleted-pump regime which illuminates the underlying physics of the process.