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Soviet Journal of Quantum Electronics

Theory of generation and amplification of Stokes and anti-Stokes waves in gaseous media

Nikolai E. Kornienko, A. M. Steba, V. L. Strizhevskiǐ

Published Nov 30, 1982• 2 citations
Publisher

Abstract

A theoretical analysis is made of generation and amplification of Stokes and anti-Stokes waves in gaseous media allowing for Raman and parametric processes and saturation effects. Allowance is also made for any difference between the Raman polarizabilities of the Stokes and anti-Stokes waves which may be caused in particular by the occurrence of one-photon quasiresonances of the interacting waves. Assuming that pump and Stokes (or anti-Stokes) waves are applied at the entrance to a medium (inverted or uninverted), a general solution is found for the amplitudes of the interacting waves under exact resonance and phase-matching conditions. This is used as the basis to investigate their spatial evolution (in particular, for inverse Raman light scattering) and expressions are found for the maximum efficiencies for conversion of the pump to Stokes and/or anti-Stokes waves. It is shown that depending on the relationship between the Raman polarizabilities and also on the input parameters of the waves, conditions of parametric bleaching of the medium with nonzero amplitudes of all the waves or conditions of complete conversion of the pump to the Stokes and anti-Stokes waves or to one of these are established asymptotically. An investigation is made of the stability of these solutions.

DOI
10.1070/qe1982v012n11abeh006152

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A theoretical analysis is made of generation and amplification of Stokes and anti-Stokes waves in gaseous media allowing for Raman and parametric processes and saturation effects. Allowance is also made for any difference between the Raman polarizabilities of the Stokes and anti-Stokes waves which may be caused in particular by the occurrence of one-photon quasiresonances of the interacting waves. Assuming that pump and Stokes (or anti-Stokes) waves are applied at the entrance to a medium (inverted or uninverted), a general solution is found for the amplitudes of the interacting waves under exact resonance and phase-matching conditions. This is used as the basis to investigate their spatial evolution (in particular, for inverse Raman light scattering) and expressions are found for the maximum efficiencies for conversion of the pump to Stokes and/or anti-Stokes waves. It is shown that depending on the relationship between the Raman polarizabilities and also on the input parameters of the waves, conditions of parametric bleaching of the medium with nonzero amplitudes of all the waves or conditions of complete conversion of the pump to the Stokes and anti-Stokes waves or to one of these are established asymptotically. An investigation is made of the stability of these solutions.
A theoretical analysis is made of the simultaneous generation of Stokes and anti-Stokes waves initiated by two-photon additional illumination. This is done allowing for Raman and parametric processes, saturation effects, and also for a possible difference between the Raman polarizabilities for the Stokes and anti-Stokes waves. The conditions for the establishment of various asymptotic regimes are determined and general expressions are derived for the ultimate conversion efficiencies, assuming that pump and additional illumination are fed into a medium (inverted or uninverted) under exact resonance and phase-matching conditions. The spatial evolution of the amplitudes of the interacting waves is investigated by an accurate analytic solution of the problem in an important particular case and using solutions in the approximation of a constant pump wave or constant additional illumination.
Analytic and numerical solutions are obtained for the equations describing the propagation of several pulses of different frequencies through a Raman medium. The transient case is treated, and the analysis includes Stokes, pump, and anti-Stokes frequency components. The effect of phase mismatch \ensuremath{\Delta}k between these waves is investigated. An analytic solution is found that describes the phenomenon of transient Stokes--anti-Stokes gain suppression in the limit \ensuremath{\Delta}k=0. For nonzero values of \ensuremath{\Delta}k, the behavior of the transient gain coefficient is found to follow a scaling rule that is the analog of a similar result known from the steady-state limit. Calculations are performed to identify conditions that enhance conversion to anti-Stokes radiation. It is found that there is an optimum strength of the Stokes seed, and that proper phase matching of the initial waves is essential.
We present a statistical theory of forward and backward Raman amplification and spontaneous generation in dispersive media pumped by a phase-diffusion field of arbitrary bandwidth. It is shown that, unless the Stokes input is correlated with the pump, the Stokes output and the pump are statistically orthogonal, even if the Stokes field builds up spontaneously. The growth of the average Stokes field amplitude is not affected by dispersion. A general expression is given for the average Stokes intensity which is valid both above and below the critical pump intensity for overcoming the decorrelating effects of group-velocity dispersion. If the length of the medium is much greater than the coherence length associated with the dephasing of the two waves, then the average intensity of stimulated Raman scattering (SRS) depends on the pump bandwidth. For relatively short medium lengths the average intensity of spontaneously initiated SRS is essentially independent of the bandwidth of a phase-diffusion pump field.
A theoretical analysis is made of the stimulated Raman scattering in gases in the presence of spatial degeneracy of the energy levels. Saturation of the population difference and influence of anti-Stokes radiation are allowed for. Various polarizations of the pump fields and of the Stokes and anti-Stokes radiation are considered. It is shown that the profile of the stimulated Raman line is generally a sum of three Lorentzian lines and the scattering includes scalar, symmetric, and antisymmetric components. The use of circularly polarized pump radiation suppresses the influence of anti-Stokes radiation on the gain of the Stokes wave.
An analysis is made of parametric excitation of anti-Stokes components of stimulated Raman scattering in an optical resonator filled with a medium whose refractive index is dispersion-free. The case of steady generation of the first Stokes component is considered. Expressions are obtained for the amplitudes of steady-state fluctuations of the anti-Stokes components in the case of a weak reaction of these components on the pump radiation and on the first Stokes component. Various cases of frequency dependences of the intrinsic resonator losses are considered. Conditions are found under which a large number of anti-Stokes components with similar intensities is excited so that the anti-Stokes radiation leaving the resonator is a periodic sequence of ultrashort (femtosecond) pulses with one pulse per period.
A calculation is made of the intensity of the Stokes radiation in the stimulated Raman scattering of ultrashort light pulses in a dispersive medium employing the asymptotic approximation for arbitrary modulation of the amplitude and phase of the pump pulse. Particular attention was paid to the effect of phase modulation on the stimulated Raman scattering. Calculations were also made of the intensity of the anti-Stokes component in the scattering of an ultrashort pulse in a dispersive medium and of the optimal angle for the observation of the anti-Stokes rings.