Calculation of TM0n Dispersion Relations in a Corrugated Cylindrical Waveguide

The TM_0n-mode Maxwell equations in a cylindrical geometry are converted to a state-vector system of coupled linear differential equations, in which the boundary conditions for a waveguide of varying diameter are included in the coefficient matrix of the state-vector system. The particular problem of periodic boundary conditions is solved for a waveguide with a sinusoidally undulating wall.