Rotationally invariant theory of stimulated Raman scattering

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Abstract
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.