Quality factors and effective-average modal gain or loss in inhomogeneous spherical resonators: application to two-photon absorption

A method is presented for calculating the quality factors (Q's) and the effective-average gain and loss coefficients for the modes of a dielectric sphere which has a spatial perturbation of the imaginary part of the refractive index. The method is applicable to gain calculations in spherical lasers, to spatial hole burning and to stimulated Raman scattering in spheres. A time-independent perturbation method is also used to compute the Q's of the resonances. Results computed using both methods are compared with analytical results for layered spheres. The methods are used to compute the near-resonance backscattering by a sphere having an intensity-dependent (two-photon absorption) loss. >