Classification and Analysis of IE-Based Zero-Thickness Metasurface Forward Solvers

The use of integral equation (IE)-based zero-thickness metasurface forward solvers has become prominent in recent years due to providing a computationally efficient means to analyze and design metasurface structures. This has led to the development of several independent methods that can be found in the literature. However, these works have largely been treated in isolation, which makes it difficult to recognize the similarities and differences between the methods. Herein, we aim to bridge these works by presenting a classification and analysis of the available IE-based zero-thickness metasurface forward solvers. This is enabled by the development of a unified mathematical framework that is used to analyze and compare the formulation of these methods. This procedure allows us to show that, under appropriate transformations, each method is in fact analytically equivalent. Despite this analytical equivalence, we highlight the numerical differences that exist and should be taken into account when using any of these solvers.