Mode Expansion in Time Domain for Conical Lines with Angular Medium Inhomogeneity

A new modification of the method of Mode Expansion in Time Domain is proposed for studying transient signals propagation in conical lines (including multi-connected ones) with inhomogeneous and time-dependent medium. The method is based on expanding the fields in spherical coordinate system into series of angular dependent modes with mode amplitudes being governed by a system of coupled evolutionary equations. The medium parameters (permittivity and permeability) are taken in a factorized form as a product of angular dependent factor and a factor that depends on time and radial coordinate. The introduced method can be applied to analysis of propagation and radiation in conical-like antennas with dielectric filling.