3-D NMM Method for Fully Anisotropic and Nonreciprocal Media

A new 3-D spectral numerical mode-matching (SNMM) method is developed to simulate electromagnetic waves in multilayered structures with fully anisotropic and nonreciprocal media. The SNMM method reduces the original 3-D layered structure into a series of 2-D waveguide eigenvalue problems plus a 1-D layered medium problem, which can be analytically solved by a recursion procedure. These waveguide eigenvalue problems with fully anisotropic and nonreciprocal media are solved numerically by the mixed spectral element method (MSEM) with exponential convergence. Based on the waveguide eigenmodes, the local reflection and transmission matrices and the global reflection matrices are expanded so that the new NMM method is suitable for fully anisotropic and nonreciprocal structures. The NMM method is applied to solve three models, including a three-layer symmetrical structure with inhomogeneous nonreciprocal media, the negative refraction of a YVO4 bicrystal, and a 3-D multilayer structure with nonreciprocal media. Numerical experiments indicate that this new NMM method is highly efficient and accurate for these models for fully anisotropic and nonreciprocal media.