Electromagnetic Modeling of In-Plane Anisotropic Two-Dimensional Materials Embedded in Planar Layered Medium Using the Dyadic Green Function and Integral Equation Techniques

Abstract

This dissertation develops a general formulation and computational method to model the electromagnetic response of infinitely extended or arbitrarily shaped in-plane anisotropic conductive two-dimensional materials embedded in the planarly layered medium. They are used for computational analysis of surface plasmonic waves propagating on the metasurface and two-dimensional materials inspired by the recent development of photonics and Terahertz electromagnetic waves. The contributions of this dissertation can be concluded in three aspects. First, a modified transmission line analog formulation is introduced to compute the spectral-domain decomposition which can be used to compute the planar wave incident on multiple anisotropic conductive surfaces of infinite extent embedded in the layered medium. Secondly, spectral-domain dyadic Green function formulation is derived to model Hertzian dipole sources that incident on anisotropic conductive surfaces. Techniques to efficiently evaluate two-dimensional Fourier integral for computing the spatial-domain Green function are developed. A novel formulation of singularities extraction to resolve computational challenges arising from surface plasmonic waves is proposed. Finally, spectral-domain electric field integral equations are developed and implemented to model spatially dispersive two-dimensional materials of arbitrary shape that can have a surface conductivity tensor depending on wavevectors. A novel numerical method based on the Chebyshev polynomial approximation is proposed to compute the spectral-domain integral of the impedance matrix elements.