Analytical solutions for electromagnetic surface states at the interface between metal and gyromagnetic media

Abstract

We systematically study the surface states at the interface between semi-infinite metal and gyromagnetic media, considering three orthogonal magnetization directions. By solving a full vectorial polarization-complete evanescent wave equation derived from Maxwell’s equations and all four boundary conditions, we obtain rigorous analytical solutions for the surface states. All analytical dispersion equations and field equations under the three configurations are solved. Simultaneously, the solutions also reveal the intriguing features of surface plasmon polaritons (SPPs) under the gyromagnetic effect. In the polar configuration (where the magnetization is perpendicular to the interface), the gyromagnetic effect uniquely results in candlelight-like field patterns in SPP. In the transversal configuration (where the magnetization is parallel to the interface and perpendicular to propagation), the unidirectional magnetic surface state is found. In the longitudinal configuration (where the magnetization is parallel to propagation), the SPP also exhibits candlelight-like field patterns but manifests a different polarization from the polar configuration. Our results reveal peculiar behaviors of SPPs under the gyromagnetic effect and would deepen the understanding of the magneto-optical effect on interfaces.