A Time-Domain Thin-Sheet Volume Integral Equation for Non-Dispersive Bi-Isotropic Media

Bi-isotropic and bi-anisotropic materials are expected to revolutionize wireless communications through the extended use of metasurfaces. This paper proposes a time-domain integral equation solver to simulate non-dispersive biisotropic materials under the thin-sheet approximation. Thin-sheet approximation is used to convert the time-domain volume integral equation for non-dispersive bi-isotropic media into a surface integral equation. This surface equation is discretized in space using Rao-Wilton-Glisson (RWG) basis functions for the tangential components of the electric and magnetic fluxes and pulse basis functions for their normal components (relative to the surface of the thin sheet). In time, shifted Lagrange polynomials are used for discretization. Applying Galerkin testing in space and point matching in time yields a matrix system. This matrix system is solved for the unknown basis expansion coefficients at each time step via time-marching. Numerical results demonstrate the accuracy of the proposed method. Future work includes extending this solver to dispersive bi-anisotropic media and use it in the simulation of metasurface represented by generalized sheet transition conditions (GSTCs).