Analytical solution to electromagnetic wave transport in planar magneto-optical waveguide: modal dispersion, coupling, and nonreciprocal flow.

The magneto-optical (MO) materials are essential for designing nonreciprocal devices, like isolators and circulators. Even though the study of MO effect has a long history, the recent works of fabricating nonreciprocal nanostructures, novel MO metamaterials, and topological photonics have garnered significant attention in both theoretical and experimental research of MO materials. In this work, we consider the planar MO waveguide mode. By setting the general form of the fields and utilizing the boundary conditions, the analytical solution of MO modes is obtained. We have shown the potential of such effective solution in analyzing the dispersions and transport behaviors of MO modes in the waveguide. Crossings and avoided crossings of modes will happen, which may due to the strong coupling of TE and TM modes in the waveguide. Faraday rotation can be observed during the propagation of MO modes and the energy flow will precess in the waveguide. These results can be applied in predicting the evolution of the modes in MO waveguides, which has potential in designing MO nonreciprocal devices.