THEORY OF NONLINEAR OPTICS IN DIELECTRIC SPHERES .3. PARTIAL-WAVE-INDEX DEPENDENCE OF THE GAIN FOR STIMULATED BRILLOUIN-SCATTERING

I give analytical formulas for the gain of TE and TM electrostrictive stimulated Brillouin scattering (SBS) in a spherical microdroplet when both the laser and Brillouin frequencies coincide with single partial waves that correspond to Debye-Mie resonances. Numerical evaluations of the analytical formula for the gain of a resonant TM mode in a water droplet show that the SBS gain peaks at the ratio-eta of the bulk-medium laser wavelength to the acoustic wavelength that depends on the values of the partial-wave index m for the laser and the SBS fields. This dependence can be explained by a simple geometrical picture based on vector addition. In the cases studied, maximum SBS gain occurs when m(B) = -m(L) = +/- \l(L)\ (where l(L) is the laser partial-wave order), corresponding to laser and SBS waves that counterpropagate in a tightly guided mode around a great circle of a spherical droplet.