Compact FDTD Formulation for Structures With Spherical Invariance

A compact, fully vectorial finite-difference time-domain algorithm is formulated for the efficient analysis of structures with spherically invariant material properties. Using this method, the full three dimensional vector solution to Maxwell´s equations can be computed using only a one dimensional computational grid. This is accomplished by expanding the electric and magnetic fields in sinusoids and associated Legendre functions to handle the azimuthal and longitudinal field variation, respectively. The method is illustrated by obtaining the electric field, resonance frequency and quality factor for different modes of a dielectric microsphere.