Time-domain energetic properties of the TM-modes in a lossy waveguide

Abstract

The amplitudes and energetic properties of the TM-modal fields for a lossy waveguide are solved analytically in time-domain. Solving the boundary-eigenvalue for transverse Laplacian problem results a basis in the waveguide cross section. Elements of this basis depend on transverse coordinates, r, and the modal amplitudes depend on the longitudinal coordinate, z, and time, t. Exact solutions are derived and presented graphically.