Mode Expansion in Time Domain technique for short pulse propagation in a regular waveguide with inhomogeneous smooth varying filling

Mode Expansion in Time Domain method is based on expansion of transient fields in a waveguide onto a basis of frequency independent coupled mode configurations with mode amplitudes being functions of longitudinal coordinate and time. In this paper the method is applied to a regular waveguide with smoothly varying transverse inhomogeneous dielectric filling (for example, slanted boundary). Approaches to constructing the bases and the corresponding waveguide evolutionary equations are discussed and compared against purely numerical solution based on full wave FDTD modeling.