Abstract

A difficulty in applying the usual definition of gain or loss of a laser mode to the modes of a dielectric sphere is that there is a possible ambiguity in the normalization mode volume: the evanescent fields outside the sphere overlap with the radiating fields leaving the sphere. Here we show that an effective-average gain or loss for a resonant or near-resonant mode of a sphere can be computed by including the trapped external fields of a mode out to the first zero of the spherical Neuman function describing the field just outside the sphere. To verify the accuracy of the method, loss coefficients computed for layered spheres are used to estimate the Q of each mode. These estimated Q’s compare very well with exact Q’s of the modes computed analytically. Results computed by a time-independent perturbation method are also compared. Our method is used to compute a two-photon effective absorption coefficient for near-resonant excitation of a sphere. Results are shown as a function of input intensity and frequency. This method of calculating effective absorption or gain should be very useful in modeling lasing, stimulated Raman scattering (SRS), and other nonlinear processes in microspheres.

© 1992 Optical Society of America