Investigation of Nonreciprocal Dispersion Phenomena in Anisotropic Periodic Structures Based on a Curvilinear FDFD Method

The aim of this paper is the investigation of nonreciprocal phenomena in anisotropically loaded 2-D periodic structures. For this purpose, our well-established 2-D curvilinear finite difference frequency domain method is combined with periodic boundary conditions and extended toward the eigenanalysis of periodic structures loaded with both isotropic and general anisotropic materials. The periodic structures are simulated in a 2-D domain, while uniformity is considered along the third axis. The propagation constant along the third axis can either be zero (in-plane-propagation) or nonzero (out-of-plane propagation). Particular effort was devoted to the identification of the appropriate irreducible Brillouin zone to be scanned during the eigenanalysis. It was herein realized that similar to geometrically artificial crystal anisotropy, the wave propagation directional asymmetries modify the irreducible Brillouin zone in the microwave regime as well. Both gyrotropic and particularly magnetized ferrite as well as full tensor anisotropic (arbitrarily biased ferrite) material loadings are investigated through the eigenanalysis of different periodic structures, including strip grating. Interesting nonreciprocal backward wave and unidirectional phenomena are justified as expected.