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Soviet Journal of Quantum Electronics

Generation of Stokes and anti-Stokes waves initiated by two-photon additional illumination

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

Published Feb 28, 1983• 0 citations
Publisher

Abstract

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.

DOI
10.1070/qe1983v013n02abeh004040

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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.
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.
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.
Raman scattering as a candidate for photon-pair generation is explored recently both theoretically and experimentally. Here, we systematically analyze the Stokes–anti-Stokes photon-pair generation in Raman scattering, akin signal–idler photon-pair emission in the spontaneous parametric down conversion, to obtain suitable conditions for photon-pair generation. Non-zero mean phonon number and losses in the phonon mode are observed to be relevant parameters in this context in addition to the Raman active material properties and pump power. Specifically, the Raman active materials with stronger anti-Stokes coupling compared to the Stokes coupling constant are suitable for photon-pair generation. Ideal Stokes–anti-Stokes photon-pair generation is possible even for non-zero thermal phonons provided that the phonon losses are negligible. Here, we characterized the performance of photon-pair generation using noise-reduction parameter in detail. We also discuss the effect of phonon losses on the observed non-classical features.
A three-dimensional analysis of stimulated Raman emission is presented for a medium through which a cylindrical laser beam passes. The buildup of the Stokes radiation from the spontaneous fluctuations in the Raman medium is considered. A generalization of the fluctuation-dissipation theorem is derived relating the current-current fluctuations at the Stokes frequency to the laser-induced (negative) conductance at this frequency. The anti-Stokes radiation is treated as arising from the interaction of the laser field and the molecular vibrations accompanying the Stokes radiation. The anti-Stokes radiation emerges in a narrow cone around the familiar phase-matching direction given by ${\mathbf{\ensuremath{\beta}}}_{\ensuremath{-}}=2{\mathbf{k}}_{L}\ensuremath{-}{\mathbf{\ensuremath{\beta}}}_{+}$, where ${\mathbf{\ensuremath{\beta}}}_{\ensuremath{-}}$ and ${\mathbf{\ensuremath{\beta}}}_{+}$ are the (real parts of the) propagation constants of Stokes and anti-Stokes waves in the medium, and kL{\mathbf{k}}_{L}kL​ is the laser propagation vector. The angular width of the anti-Stokes radiation cone is evaluated.
Coupled differential equations are formulated to model the generation of coherent anti-Stokes Raman radiation in molecular gases. They include the basic coherent interaction of incident pump and idler (Stokes) waves to generate the anti-Stokes radiation plus other radiation and absorption processes which influence saturation due to population depletion of the lowest energy level. Other factors considered are simultaneous excitation of more than one vibration frequency, a quasi-monochromatic idler beam slightly off the true Stokes frequency, and the temporal laser pulse shape. Some effects of these various physical factors on saturation are presented graphically.