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Abstract
This paper describes the steepest-descent evaluation of the radiation field for both TE and TM modes of an asymmetric planar open waveguide. The cover, film and substrate field will be formulated in the spectral domain. The steepest-descent path in the complex axial transform plane (ζ-plane) is identified as a direct method and that in the complex -plane ( = σ + jη: complex polar coordinate) is also identified as an indirect method in order to validate the steepest-descent path in the complex axial transform plane (ζ-plane). The branch cut integration will be rigorously analyzed through complex-phasor diagrams. An alternative integration path will be also identified since it is an effective method to validate the steepest-descent and branch cut integrations. Then, the steepest-descent evaluation of cover and substrate fields and numerical results for TE modes will be presented and numerical implementation for TM modes will be accommodated in the future research.