Electromagnetic Modeling of a Magnetless Nonreciprocal Gyrotropic Metasurface

An analytical model of a recently invented magnetless nonreciprocal and gyrotropic traveling-wave ring metamaterial is developed. The metamaterial is, in fact, a metasurface, which consists of a 2D periodic array of pairs of broadside-parallel micro-rings loaded with a semiconductor-based unidirectional component. It emulates the operation of ferrites by inducing a rotating magnetic moment in the ring pairs. However, instead of requiring a magnetostatic bias, it operates with an electrostatic voltage bias, thus avoiding the classical issues related to permanent magnets in ferrites. The metamaterial has two modes of operation: a desired magnetic mode and a parasitic electric mode, which are related to the excitation of equal and opposite currents in the two rings of the pairs, respectively. The metamaterial exhibits these magnetic and electric responses when excited by a uniform magnetic and electric field, respectively. The magnetic response is analyzed through a transmission line model with a distributed voltage source that incorporates the voltage impressed in the rings by the external field. The magnetic moment and the subsequent magnetic polarizability are related to a traveling-wave resonance along the ring pair. For a perfectly matched unidirectional component, this resonance, and hence the magnetic polarizability, are lossless. However, in the presence of mismatch, the metamaterial becomes lossy, due to reflection and absorption of power at the ports of the component. Comparisons with full-wave simulations show the validity of the proposed model.