The Proper EM Field Spectra of an Open Integrated Microstrip Waveguide

Abstract

Continuous EM field spectrum of an integrated open waveguide structure is identified as the branch cut contribution to singularity expansion of those fields in the complex axial transform plane. Those singularities in that plane include poles associated with the guiding structure and branch points contributed by layered background environments. The manner in which singularities in background environments manifest themselves as branch points in the complex axial transform plane is reviewed.Using a spectral microstrip current profile [1], the EM fields in the background layer environments of the integrated open waveguide are recovered from the spectral domain by integration contour deformation on the different Riemann sheets of the complex ζ-plane. During the integration both around branch cuts and along real axis, singularities in the complex transverse transform plane migrate in a complicated manner. EM fields are computed through those two methodologies are numerically validated.Extensive numerical results show the nature of EM fields physically in the open waveguide structure, which can be decomposed into discrete and continuous spectra in the layered background environments.