Mixed Spatial-Spectral Domain Analysis of Spatially Dispersive Metasurfaces Using Higher-Order Boundary Conditions

Higher-order boundary conditions are a useful tool for simplification of complex electromagnetic problems, such as spatially dispersive metasurfaces. A technique known as the extended generalized sheet transition conditions (GSTCs) method has recently been proposed that allows for the systematic simulation of spatially dispersive metasurfaces using higher-order boundary conditions. A general metasurface, in general, requires a boundary condition of infinite-order spatial derivatives to accurately model the surface, making them unsuitable for conventional full-wave modeling techniques where higher-order derivatives are computed numerically. Here, we propose a mixed spatial-spectral-domain representation of the boundary conditions that avoid the explicit computation of higher-order derivatives while still being in a form suitable for integration into standard numerical methods. We integrate these boundary conditions into an integral equation solver which is then successfully validated through several numerical examples.