Handling of Singularity in Finite-Difference Time-Domain Procedure for Solving Maxwell's Equations in Cylindrical Coordinate System

A consistent approach to determine the components of electric and magnetic fields at $r=0$ for a cylindrical coordinate system in a finite-difference time-domain calculation procedure is proposed. It is based on the superposition of cylindrical and Cartesian coordinate systems and transformation between them. Simple formulas have been derived for calculating the electromagnetic field components at a coordinate center; they can be used for solving two-dimensional and three-dimensional problems in a cylindrical coordinate system. The proposed method is used for calculating the outflow of an electromagnetic wave from a circular waveguide into free space.