Abstract

In order to analyze various nonlinear phenomena in the optical microsphere one would need a reliable approximation of the field pattern inside the sphere that might be used as a tool for easy evaluation of the threshold situation. Indeed, apart from the difficulty with which the numerical solution of the spherical cavity is obtained, it is quite difficult then to employ the numerical solution for the prompt evaluation of the threshold condition in practice. In brief, one would need a simple analytic representation of the field mode which, though, retains the critical feature of the Lorenz-Mie resonances. We suggest a simple analytic theory that is based upon the Airy-function approximation to the spherical Bessel function. We show that all the boundary conditions that may happen in the spherical cavity can be readily classified in terms of just several spatial ranges so that the threshold situation falls into a set of the possibilities correspondingly.

© 1994 IEEE