Graphical exegesis of the TE and TM surface waves on a stratified microstrip

This paper describes the graphical significance of the complex variable functions that represent the transverse electric (TE) and transverse magnetic (TM) surface waves propagating on a multilayered microstrip. The functions are derived from a solution of the wave equations satisfying the boundary conditions. The functions are presented in terms of the wavenumbers and are proved to be analytical. A transformation between functional related complex planes is effectuated in order to visualize some characteristics of the surface wave functions. Finally, the transformed functions are simultaneously solved to corroborate the graphical features.