Spectral analysis considerations relevant to leaky modes of open-boundary waveguides

The behavior of significant features in the transverse spectral plane for the Sommerfeld-type integrals associated with the open-boundary waveguiding systems is investigated, particularly for the microstrip transmission line in a planar layered background environment. The locations of the integration contour and branch points are chosen to be consistent with continuous physical transitions between operating regimes. The rationale for choosing branch cuts in the transverse spectral plane is given. Pole singularities arising from the layered background surround are then obtained in a manner consistent with the cutting of the transverse spectral plane. Trajectories of the poles and branch points are presented for typical leaky modes.<>