Magneto-optical double zero-index media and their electromagnetic properties in the bulk

Abstract

Double-zero-index media (DZIM) with zero permittivity and permeability are one important class in zero-refractive index photonics. Here, we extended the concept of DZIM and proposed a more general type, i.e., the magneto-optical DZIM (MODZIM), of which the permittivity and the determinant of the Hermitian permeability tensor are simultaneously zero. By formulating the Maxwell’s equations in the basis of complex-valued axes and using some mathematical principles, we studied the electromagnetic (EM) properties in the bulk of the MODZIM with different boundaries and impurities. Inside the MODZIM which is infinite along in the out-of-plane direction, it is shown that the scalar (out-of-plane) field is not uniform in general, in contrast to traditional DZIM where the scalar field is always uniform in the bulk. Nevertheless, for a normal incidence, the uniform scalar field inside the MODZIM can be achieved by optimizing the boundary conditions and doping some types of impurities, such as resonant round cylinders and arbitrary shaped media with a zero permeability. As long as the scalar field is uniform, the propagation of the EM wave inside the MODZIM can be analyzed with closed-form expressions. Our work will extend the study of zero-refractive-index photonics and provide deeper understanding of wave dynamics in the bulk of MODZIM.