Theoretical study of nonreciprocal electromagnetic wave propagation by effective medium approach

Abstract

Breaking of reciprocity in an electromagnetic system allows exotic directional control of wave propagation. This nonreciprocal wave propagation (NRWP) for opposite propagating directions involving asymmetric power flow gains great attention because of its potential application in optical isolation which is inevitable for optical circuit. The realization of the NRWP usually requires breaking several spatial and temporal symmetries and leads to subwavelength array of complex scatterers. Effective medium theory is one of the common approaches to simplify the subwavelength array. In this thesis, we adopted the effective medium theory to design and study the NRWP (1) along surfaces of metamaterials and (2) through metasurfaces. In the first part of my thesis, we investigated the possibility to model the nonreciprocal edge mode on the boundary of the gyromagnetic cylinder lattice by local effective medium model. We start with the study of the band structures for different two-dimensional(2D) lattices of the gyromagnetic cylinder with same filling factor. The bandgap independent of the type of lattice with the same filling factor was identified near the gyromagnetic resonance of the cylinder. Consequently, a local effective medium model for the 2D gyromagnetic cylinder lattice described by anisotropic Maxwell Garnett equation was proposed. The effective medium confirms the bandgap is originated from the material resonance of the gyromagnetic cylinder and this bandgap is common for the biasing magnetic field in opposite direction. We then considered the boundary of two magnetic domains formed by oppositely magnetized square lattice of gyromagnetic cylinder and studied the edge modes in the common bandgap. Following the success in local effective medium modelling for each magnetic domain, we introduced the effective model for the boundary formed by oppositely magnetized truncated square lattice of the gyromagnetic cylinder by the boundary of the corresponding local effective medium of the truncated lattices. Two one-way edge modes can be found in both the lattice case and the effective model. The dispersion relation near the Brillouin zone centre could be reconstructed by the effective model. The difference in the dispersion relation of the edge modes between the effective medium case and the lattice case beyond the zone centre should be related to the non-local effect of the lattice. This example shows the non-local effect can be significant near the bandgap even the bulk band near the gap has negligible non-local effect. In the second part, we extend our study of NRWP to open system composed of metasurface that supports nonreciprocal transmittance defined as asymmetric transmittance under opposite normal incidence of plane wave. According to the effective surface current model for the bianisotropic metasurface, the metasurface supporting nonreciprocal transmittance needs to be lossy and possesses bianisotropic Tellegen artificial moving (TAM) property. We construct a lossy TAM metasurface by a chain of dimer composed of the dielectric cylinder and gyromagnetic cylinder. Based on the analytical coupled dipole model of the dimer chain, we derived the generalized Clausius Mossotti Equations which relates the macroscopic parameters in the effective surface current model to the microscopic parameters in the coupled dipole model. These equations verify the bianisotropic TAM property in this dimer system is introduced by the cross coupling of the dominated electric dipole response in dielectric cylinder and the magnetic dipole response in gyromagnetic cylinder. The effect of the cross coupling on the TAM property as well as the nonreciprocal transmittance was examined. Though the nonreciprocal transmittance is introduced by the cross coupling, the maximization of the nonreciprocal transmittance of the dimer system could be achieved not by maximizing the cross coupling but the balance between the direct coupling between the individual gyromagnetic or dielectric cylinder and cross coupling. Our finding could assist the future design and optimization for the nonreciprocal transmitting metasurface.