Mixed Spatial-Spectral Domain Integral Equation Solver for Higher-Order Boundary Conditions in Electromagnetics

Higher-order boundary conditions are a useful tool for simplification of complex electromagnetic problems. Recently, a systematic technique, known as the Extended GSTC method, has been developed for simulating spatially dispersive metasurfaces using higher-order boundary conditions. In general, if we want to perfectly capture the angular scattering response of a metasurface using higher-order boundary conditions, it would require the computation of derivatives of infinite order. Therefore, achieving a good approximation of the metasurface scattering response may require the calculation of numerical derivatives up to a prohibitively high order, leading to an ill-conditioned system of equations. Here we develop a mixed spatial-spectral Integral Equation (IE) solver in 2D that allows for the simulation of electromagnetic problems involving higher-order boundary conditions without the explicit computation of any numerical derivatives.