Ray-Optical Evaluation of Scattering From Electrically Large Metasurfaces Characterized by Locally Periodic Surface Susceptibilities

This work continues the development of the ray-tracing method of de Jong (2021) for computing the scattered fields from metasurfaces characterized by locally periodic reflection and transmission coefficients. In this work, instead of describing the metasurface in terms of scattering coefficients that depend on the incidence direction, its scattering behavior is characterized by the surface susceptibility tensors that appear in the generalized sheet transition conditions (GSTCs). As the latter quantities are constitutive parameters, they do not depend on the incident field and, thus, enable a more compact and physically motivated description of the surface. The locally periodic susceptibility profile is expanded into a Fourier series subject to a spatially varying phase parameter, and the GSTCs are rewritten in a form that enables them to be numerically solved for the reflected and transmitted surface fields. The phase parameter can either be determined from a prescribed surface transformation or extracted from known surface susceptibilities. A method for the extraction of this phase parameter from a susceptibility profile using a spatial variant of the short-time Fourier transform (STFT) is proposed. The scattered field at arbitrary detector locations is constructed by evaluating critical-point contributions of the first and second kinds using a forward ray-tracing (FRT) scheme. The accuracy of the resulting framework has been verified with an integral equation-based boundary element method (BEM)-GSTC full-wave solver for a variety of examples, such as a periodically modulated metasurface, a metasurface diffuser, and a beam collimator.