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Soviet Journal of Quantum Electronics

Calculation of the threshold and of the efficiency of conversion by stimulated scattering in an amplifying medium

A. N. Pilipetskiǐ, Vladimir V. Shkunov

Published Feb 28, 1985• 3 citations
Publisher

Abstract

A calculation is made of the steady-state threshold of stimulated scattering in the forward and backward directions in a medium characterized by linear amplification. A numerical investigation is made of the steady-state stimulated scattering in the forward and backward directions under saturation conditions and a comparison of the two sets of results is made.

DOI
10.1070/qe1985v015n02abeh006248

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Soviet Physics Uspekhi•Oct 31, 1982•43 citations
A calculation is made of the steady-state threshold of stimulated scattering in the forward and backward directions in a medium characterized by linear amplification. A numerical investigation is made of the steady-state stimulated scattering in the forward and backward directions under saturation conditions and a comparison of the two sets of results is made.
A theoretical analysis is made of the problem of the time taken to establish steady-state lasing as a result of various types of stimulated scattering (Raman, Brillouin, and excited by heat evolution in a medium) and of the law governing amplification of Stokes waves after times much shorter than the relaxation time of vibrations of the medium for an arbitrary spectral line profile. It is shown that the characteristic times for the establishment of steady-state lasing in the case of stimulated scattering near the maximum of the gain profile are of the same type for different spectral lines profiles and have similar values.
Using well defined input pulses the amplification by stimulated thermal Rayleigh scattering was investigated experimentally as a function of time (within the pulse), of absorption coefficient, and of interaction length. The frequency difference between the two interacting light pulses was varied with an accuracy better than Δν/ν = 10-8. Amplification was measured in the backward direction and at several degrees from the forward direction. The various experimental observations are in good agreement with theory. The possibility of determining material parameters in this amplifier system is discussed
A theory is given of the stimulated scattering of light as a result of interaction of a strong electromagnetic wave with a dynamic grating (wave) of the population N of an excited state if N affects the refractive index of the medium. The medium is regarded as an assembly of two-level systems and the dependence of the permittivity ε on N is assumed to be linearized. If δε / δ N <0, the amplification due to the stimulated scattering is expected in the anti-Stokes region on illumination of an unexcited medium. Under lasing conditions the amplification should occur in the Stokes region of the strong electromagnetic field (wave). This mechanism may be the cause of the mutual coupling between laser modes.
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).
Various aspects of optical phase conjugation are discussed: the properties of the conjugate wave, its potential applications, the basic conjugation methods, and a brief history of the question. The theory for phase conjugation in stimulated scattering is set forth in detail. The basic experimental results on this conjugation method are also discussed in detail. Phase conjugation occurs because that configuration of the back-scattered field which has the conjugate wavefront is amplified to the greatest extent (at a doubled gain) in the intense speckle-inhomogeneous conjugate wave in a medium in which stimulated scattering occurs. Because of the large overall amplification in stimulated scattering, all the other, uncorrelated, configurations of the spontaneously scattered nucleating waves are amplified by a factor of 107 less and are discriminated against. The intervals of values of the various parameters in which the conjugate configuration (the specklon) exists are discussed theoretically, as is the effect of nonlinear selection and saturation on phase conjugation in stimulated scattering. There is a review of experimental results on the first observation of the effect, on the measurement of the angular structure of the uncorrelated waves and of the extent to which they are discriminated against, on the phase fluctuations of the conjugate wave, on the conjugation of subthreshold and depolarized radiation, and on phase conjugation in stimulated scattering in focused beams and for other scattered-wave amplification mechanisms.