Numerical dispersion analysis for spherical FDTD

Analyses of spherical functions-based numerical dispersion relation are performed for the finite-difference time-domain method in spherical coordinates. Errors in the numerically rendered wavenumber due to finite mesh densities are analyzed as a function of absolute position within the spherical mesh, solutions mode orders and mesh density. Solution singularities near the origin and the z-axis are properly tracked and fully quantified for the different spherical solution modes.