Theory of temporal pump stochasticity in stimulated Raman scattering in dispersionless media

Abstract

A diagrammatic formalism is presented which gives exact results for the forward Stokes wave in dispersionless media in the field of a temporally stochastic pump. Both pump and Stokes waves are assumed to be plane waves, but transient effects are treated exactly. Results are derived in the Bourret approximation for the n-point functions (n≳2) but are exact to all orders in the mean pump field and its two-point function. The generalization to treat general n-point functions within this formalism is possible and the method of doing so is indicated. The partial summation of diagrams corresponding to previous treatments is identified and the next order terms are evaluated. It is found that for high gain systems, approximations made in previous work may be quite poor.