Eigenmodes of Metafilm Waveguides With Nonlocal Two-Sided Boundary Conditions

Metafilm waveguides are used in broad areas of microwave, millimeter-wave, and terahertz applications. In electromagnetic simulations, equivalent boundary conditions represent metafilms for their easy modeling. Nonlocal two-sided boundary conditions of the second order provide adequate modeling accuracy for most metafilms. This article considers a planar metafilm waveguide described by the indicated boundary conditions. It is demonstrated that the classic approach for waveguide eigenmode determination does not provide correct results when applied to the metafilms with nonlocal boundary conditions. The reasons for the incorrectness are some unusual properties of metafilms with nonlocal boundary conditions and the requirement to satisfy a so-called boundary-contact condition for an irregular metafilm, which provides the uniqueness of a boundary-contact problem solution. A novel approach is introduced for correctly determining continuous and discrete eigenmode spectrums in open and shielded waveguides with nonlocal two-sided boundary conditions. An irregular metafilm in a parallel-plate waveguide is considered. It is demonstrated that using the corrected eigenmodes satisfies the boundary-contact condition at the point of irregularity. Some numerical results are presented, demonstrating the calculating accuracy of the proposed analytical approach.