Theory of nonlinear optics in dielectric spheres II Coupled-partial-wave theory of resonant, resonantly pumped stimulated Brillouin scattering

Abstract

I derive a self-consistent-field, coupled-mode theory of the generation of stimulated Brillouin scattering (SBS) in transparent dielectric spheres by using full vector-partial-wave theory. The results are expressed in an analytical form that is suitable for efficient numerical evaluation. The theoretical method introduced in this paper uses the Racah–Wigner angular-momentum calculus to derive selection rules for the allowed nonlinear couplings of partial waves and uses Fourier–Bessel and Fourier–Dini expansions for the radial eigenfunctions of the electromagnetic and acoustic normal modes. The derivation shows that the SBS field must be resonant in order to satisfy the electromagnetic boundary conditions.