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Physical Review Letters

Polarization Dependence of Gain in Stimulated Raman Scattering

Allen M. Flusberg, Richard B. Holmes

Published May 18, 1987• 29 citations
Publisher

Abstract

We present a new, rotationally invariant formalism for the theory of stimulated Raman scattering. The formalism is applied to Raman transitions of well-defined rotational symmetry, e.g., rotational Raman (Stokes) transitions, yielding the explicit dependence of gain on light polarization, phase mismatch, and frequency offset.
DOI
10.1103/physrevlett.58.2039

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Journal of Physics B Atomic and Molecular Physics•Nov 1, 1970•5 citations
We present a detailed derivation of a new, rotationally invariant formalism for the theory of stimulated Raman scattering. The formalism is applied to Raman transitions of well-defined rotational symmetry, e.g., rotational Raman (S) transitions, yielding the explicit dependence of gain on light polarization, phase mismatch, and frequency offset. For a linearly polarized laser, the Stokes fields parallel and perpendicular to the laser field are decoupled. Far from Stokes--anti-Stokes phase matching, their gain coefficients are in the ratio of 4:3; at phase matching, both are suppressed and have zero exponential gain. For a circularly polarized laser, the circularly polarized Stokes fields circulating in the same and opposite senses as the laser field are decoupled. The gain of the opposite-sense field, which is decoupled from the anti-Stokes field, is independent of phase mismatch. Far from phase matching, the gain of the same-sense Stokes field is (1/6 that of the opposite-sense field; at phase matching, the same-sense field has zero exponential gain. An unpolarized laser is shown to have the lowest Raman gain; far from phase matching, its Stokes fields decouple into two incoherent, oppositely circularly polarized fields, but at phase matching all Stokes polarizations have zero exponential gain. The gradual transition away from phase matching is also treated explicitly, and it is shown that when the gain is suppressed the maximum Stokes growth occurs when the Stokes-laser beat is a fraction of a Raman linewidth off resonance.
A theory of nonstationary stimulated Raman scattering is developed, allowing for the coupling between the Stokes and anti-Stokes waves. The main equations are solved in the asymptotic approximation, which is valid for large values of the gain. The dependences of the gain on the phase mismatch Δ k , pulse duration τ p , and cell length l are discussed and the optimal angle for the observation of the anti-Stokes rings is calculated. Moreover, the spectral distributions of the Stokes and anti-Stokes waves are considered.
Stimulated Raman scattering (SRS) from a system that is both Raman active and infrared active has been investigated theoretically when a strong coherent resonant infrared light field, in addition to a pumping field, is applied. In the density matrix formulation, it is found that the gain function in steady state is redistributed as a result of the modulation on the populations and transition probabilities by the presence of the strong resonant field. The redistribution curve shows Rabi frequency splitting for the Stokes component and a new origin of anti-Stokes components of SRS that is anticipated in the present mechanism.
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.