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Physical Review A

Rate equations in stimulated light scattering

Paul L. Kelley

Published Jul 1, 1979• 2 citations
Publisher

Abstract

A set of rate equations which gives results not previously obtained has been proposed for stimulated light scattering. These equations are shown to be invalid under the conditions where the novel results appear.
DOI
10.1103/physreva.20.372

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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.
Optical systems are scalable under low-intensity illumination since their governing equations are linearly dependent of the optical signal strength. Nonetheless, in high-intensity regimes, the induced polarization becomes nonlinear, rendering the simple scalability of the previous systems invalid. Despite this, canonical nonlinear phenomena such as filamentation and high-harmonic generation in free space have recently been demonstrated to be scalable. Here we will discuss the extension of the scale-invariance paradigm to stimulated Raman scattering and molecular modulation in hollow anti-resonant fibers filled with Raman-active gases. We have found that the complex in-fiber dynamics can be accurately reproduced under very different conditions by keeping the so-called gain reduction factor, that accounts for the coupling of the interacting fields, as well as the dephasing time unaltered. Such scaling strategy enables access to equivalent nonlinear propagation scenarios without sacrificing performance, laying the foundations for the design of nonlinear devices operating in exotic frequencies, like the ultraviolet, or quantum frequency convertors of non-classical light.
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).