Resonant spectra of dielectric spheres

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Abstract
The natural resonant frequencies and poles associated with the electromagnetic modes of a dielectric sphere with a relative index of refraction of 1.4 have been calculated for size parameters ranging from 1 to 50. Determining pole locations in the complex plane entailed the computation of spherical Bessel functions for large complex arguments. The symbolic programming language reduce was used to provide independent verifications of the convergence and accuracy of the numerical Bessel function routines required in these computations. To determine pole locations, we used a standard zero-finding routine to find the zeros of the scattering coefficient denominators. In addition, we used a separate zero-counting routine in conjunction with the search routine to ensure that all poles within a given region of the complex plane were found. The real parts of the calculated poles agree with the location of peaks in the resonance spectrum (calculated for real frequency excitation), whereas the imaginary parts are related to the widths of these peaks. The intensity inside the sphere, averaged over all spherical angles, was computed as a function of radius. When the particle is excited at resonance, the internal intensity exhibits a sharp peak near, but not on, the surface. The intensity was found to be the strongest when the particle is driven at resonant frequencies whose poles have small imaginary components in the complex plane.