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IEEE Journal of Quantum Electronics

Semiclassical theory and numerical modeling for stimulated rotational Raman scattering in homonuclear diatomic molecules

Claudio G. Parazzoli, C. Drutman, D. M. Capps

Published Apr 1, 1990• 2 citations
Publisher

Abstract

The semiclassical theory of nonresonant stimulated rotational Raman scattering (SRRS) in homonuclear diatomic molecules has been developed. Multiple rotational lines, the full degeneracy of the molecule, Stark shift, and four-wave mixing effects are considered. An arbitrary number of optical fields is allowed. The polarization state of the fields is dynamically computed during the propagation. A numerical code has been written in a user-friendly format based on the theoretical model with diffractive effects included. Numerical results which display the code capabilities are presented and comparisons to available experimental data are shown.>

DOI
10.1109/3.53393

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Physical Review A•May 1, 1986•4 citations
The semiclassical theory of nonresonant stimulated rotational Raman scattering (SRRS) in homonuclear diatomic molecules has been developed. Multiple rotational lines, the full degeneracy of the molecule, Stark shift, and four-wave mixing effects are considered. An arbitrary number of optical fields is allowed. The polarization state of the fields is dynamically computed during the propagation. A numerical code has been written in a user-friendly format based on the theoretical model with diffractive effects included. Numerical results which display the code capabilities are presented and comparisons to available experimental data are shown.>
The theory of stimulated Raman scattering has been treated at various levels of sophistication from plane-wave steady-state models through 3-D transient quantum-electrodynamic calculations.1 Many physical effects, such as pump depletion, dispersion, level degeneracy, ac Stark shift, and parametric coupling of Stokes and anti-Stokes light, can be important in experimental setups. We describe a recently developed computer code which treats these effects in detail. The code is based on integration of the coupled Maxwell-Bloch equations of quantum optics. We discuss numerical predictions of the code relating to these effects and present applications to experimental investigations such as Raman beam cleanup and transient amplification.2
Polarization effects in stimulated Raman and stimulated Rayleigh scattering and self focusing are investigated from the viewpoint of the scattering of polarized photons by molecules. Both stimulated vibrational Raman scattering in liquids and stimulated rotational Raman scattering in gases are considered, and it is demonstrated that the polarization changes and relative power thresholds for different laser polarizations should be somewhat different to those predicted in other theories. For example, the ellipticity eta 0 of the stimulated rotational Raman photons in the forward direction from Delta J=+or-2 transitions in gaseous symmetric top molecules is given in terms of the initial ellipticity eta 1 by sin 2 eta 0 = - 5 / 7 sin 2 eta 1 , whereas conventional theories predict that eta 0 and eta 1 are equal in magnitude and opposite in sign. Furthermore it is shown that deviations from this relation could provide a measure of the degree of optical orientation of the molecules.
Abstract The theory of multifrequency stimulated Raman scattering (SRS) of light on rotational transitions of molecules, which are simulated by a three-level quantum system, is developed. It is shown that the application of bichromatic pumping increases the scattered radiation spectrum width. The exact algebraic solution for the wave amplitudes is obtained in the simplest version of synchronous SRS on transitions with a negligibly low eigenfrequency. It is found that an increase in the ratio of the Raman transition frequency to the pump radiation frequency leads to predominance of the anti-Stokes scattering branch. The effect of wave asynchronism emerging due to linear and nonlinear dispersion of the medium as well as the phase difference of the pump waves on SRS is considered. All types of asynchronism narrow generated frequency spectrum and suppress the anti-Stokes scattering branch. Nonlinear dispersion ensures positive values of wave amplitudes due to phase jumps by π during the propagation of waves in a medium.
A general theory of transient stimulated Raman scattering and the phase-matching diagrams are developed based on an interaction Hamiltonian which includes all the possible competing interaction channels. In a Raman system pumped by multiple crossing beams with multiple Stokes and anti-Stokes components, these channels are defined by the interactions among fields at different frequencies and/or k vectors of the pump pairs and Stokes and anti-Stokes fields. An ensemble-averaged equation of motion for the active phonon mode is derived within the Markovian approximation in which the phonon-phonon coupling (pressure effect) is reduced to an energy relaxation and a phase fluctuation. A complete set of transient coupled equations including phase modulation, Stark shift, medium (anharmonic) saturation, and all the possible four-wave-mixing channels is presented. In the transient regime, it is found that the effects of the Stark shift on the Raman efficiency are mainly governed by the input pump energy in contrast to the steady-state theory where the pump intensity plays the main role. Both analytic and numerical methods are developed in describing the nonlinear effects due to the energy feedback mechanism in the strong pump-depletion regime. Twelve possible four-wave-mixing channels are analyzed for nonlinear phase diagrams characterized by the angles among pump pairs, and Stokes and anti-Stokes fields. Finally, numerical examples are shown for the effects of the coherence lengths of high-order Stokes fields and pump pairs on the generation of low-order Stokes fields.