Numerical solution of time-dependent Maxwell's equations in spherical coordinates

We consider the discretization of Maxwell's time dependent equation in spherical coordinates. We are interested in scattering problems and so we shall not consider the singularity at r = 0. We describe a new technique to deal with the singularity at the poles. Furthermore, even when the poles do not cause any explicit divisions by zero nevertheless the closer spacing of the grid near the poles decreases the allowable time step. We implement a Fourier filtering method to reduce the higher modes near the poles and so allow a larger time step. Finally we analyze the use of a PML to prevent reflections in the radial direction. Previous descriptions of a spherical PML required the use of 6 extra variables. We show how it can be solved using only two additional variables in the artificial layer.