Nonreciprocal propagation of surface electromagnetic waves in structures comprising magneto-optical materials

Abstract

This paper investigates theoretically the effect of nonreciprocity on surface electromagnetic waves (SEWs) propagating in magneto-optical structures in mutually opposite directions, i.e., on waves with tangential wave numbers $k$ of opposite sign. Namely, of our interest is a correlation between the numbers of forward ($k>0$) and backward ($k<0$) propagating SEWs, which manifests itself as a limit on the total number of SEWs. The peculiarity of this limit is that the maximum total number of forward- and backward-propagating SEWs is less than the sum of the maximum numbers of SEWs for each of the opposite directions taken individually. We derive a relation between the electromagnetic surface impedances relevant to forward- and backward-propagating waves. Afterward, by using general properties of these impedances valid regardless of the crystallographic symmetry, we analyze the roots of dispersion equations without solving them explicitly. Various types of magneto-optical structures are considered. In particular, it is shown that, in the bicrystal formed of two half-infinite magneto-optical media, the maximum total number of forward- and backward-propagating SEWs is two at a given value of $|k|$, whereas in each of the mutually opposite directions two SEWs can exist. For example, if two forward-propagating SEWs are known to exist, then no backward-propagating SEW exists. In the case where a metal film is inserted between two different half-infinite magneto-optical media, the maximum number of SEWs in one direction is four but the maximum of the total number of forward- and backward-propagating SEWs is six rather than eight.