Rapid Surface-Wave Dispersion and Plane-Wave Reflection Analyses of Planar Corrugated Surfaces by Asymptotic Corrugations Boundary Conditions Even for Oblique Azimuth Planes

The asymptotic corrugations boundary condition (ACBC) is used together with classical theory of vector potentials to analyze planar corrugations. A transcendental characteristic equation is derived, from which the dispersion diagram can be obtained, thereby conveying surface wave passband and stopband properties, even for propagation within oblique azimuth planes as well as both principal TE and TM polarizations. From the formulation, field distributions for the regions within the grooves and above the corrugations can also be generated. When compared with the dispersion graphs obtained from characteristic equations derived by the classical transverse resonance technique (TRT), the newly presented ACBC method provides superior accuracy. Explicit formulas for the complex reflection coefficient (amplitude and phase) for both TE and TM polarized plane-wave incidences are also derived as closed-form analytic functions of all parameters (especially the azimuth phi angle of incidence) using a novel concept of unusual transversely phased plane-waves. These proposed approaches are massively more efficient than full-wave solvers, providing unparalleled speedup of computation by thousands of times. The surface-wave and reflection properties of planar corrugations are thus herein analyzed in a unified, complete, and elegant manner that is also highly efficient but yet accurate. This thorough work is thus a great boost to the continued use of corrugated surfaces as artificial magnetic conductors (AMC), electromagnetic bandgap (EBG) structures, and soft/hard surfaces in all walks of antenna design, especially in terms of speed and accuracy.