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Soviet Journal of Quantum Electronics

Stimulated scattering of light by waves representing excited-state populations

Alexandr P Bogatov, P G Eliseev

Published Apr 30, 1983• 1 citation
Publisher

Abstract

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.

DOI
10.1070/qe1983v013n04abeh004215

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Soviet Journal of Quantum Electronics•Jan 31, 1985•1 citation
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.
Summary form only given. There are a number of the well-known kinds of stimulated scattering in Nd:YAG laser crystals, including Raman scattering, Brillouin scattering, and thermal scattering. In this report we present for the first time the study of another type of stimulated scattering of the light beam with resonance frequency in the inverted media. The mechanism of this stimulated scattering is connected with the diffraction of the original beam on the moving refractive index grating caused by the wave of the metastable level population induced by the interference field of the incident wave and the scattered wave.
The influence of a strong field resonant to the Raman transition on the behavior of the Stokes harmonic in saturated two-wave stimulated Raman scattering is theoretically considered based on the description of a gas of three-level atoms by medium density matrix equations. The vibrational mode of energy redistribution between laser and scattered radiation, threshold with respect to the resonant field intensity, is predicted. The action of optical fields on the absorption and amplification of the resonant field in a Raman medium is described.
The spectral perturbation is considered in a semiconductor active medium in the vicinity of the frequency of a strong electromagnetic wave. The nonlinear interaction of waves via the dynamic interference grating, or nonlinear scattering by population waves leads to the shift of resonance frequencies, which is manifested, in particular, in a change of the mode-beating spectrum of the laser. The spectral profile of this perturbation depends on the amplitude—phase coupling factor α. For large α, the profile becomes symmetrical in detuning from the strong-mode frequency. A change in the group refractive index corresponding to the 'slowing' of light is also calculated.
The stimulated Raman scattering (SRS), arising from the interaction between molecules of a medium and two strong light fields - a resonant field and a pumping field - is studied theoretically. The transitions of molecules between a given pair of levels is assumed to be both Raman active and infrared active. A semiclassical approach, in which the density matrix method is used for the quantum mechanical description for the medium, is employed. We expand the density matrix in various orders within which the zeroth-order is referred to as the solution of the equation of motion of the density matrix when only the resonant field is applied. -- We obtain a set of equations in second order of the density matrix element p₁₀⑵ (ω) from which the gain function can be derived. This set of equations in the special case of steady state is accidentally similar to those obtained by Mollow in his study of the power spectrum of a strong driven two-level system. We have shown that the SRS in the steady state under the resonant field interaction, is drastically reduced in general. When the flopping frequency is larger than the relaxation constants (Ω > r), we find there appears both weak positive and weak negative gains on both sides of the ordinary SRS components. Since we retain our second-order equations in a general form rather than the form for steady state, we are able to take account of the dependence on the transient zeroth solution. By employing the Laplace transform technique with the help of convolution products, we are able to solve for ρ₁₀⑵(ω) in the stationary flopping state. When the intensity of the resonant field is high, we have found theoretically that both the Stokes and anti-Stokes component become doublets and equally displaced by the amount of the flopping frequency, Ω, on the opposite sides of ordinary Stokes and anti-Stokes components, respectively. The gain maxima are approximately the order of Ω/4r times the ordinary gain of the Stokes component, where Ω/r >> 1 if the flopping exists. The gains are therefore large in comparison with the ordinary gain for SRS in the steady state.
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.