Surface polaritons in magnetic metamaterials from perspective of effective-medium and circuit models

Surface waves are responsible for many phenomena occurring in metamaterials and have been studied extensively. At the same time, the effects of inter-element coupling on surface electromagnetic waves (polaritons) remain poorly understood. Using two models, one relying on the effective-medium approximation and the other on equivalent circuits, we studied theoretically surface polaritons propagating along an interface between air and a magnetic metamaterial. The metamaterial comprised split rings that could be uncoupled or coupled to each other in the longitudinal or transverse directions (along or perpendicular to the propagation direction). A metamaterial without inter-element coupling supported a single polariton. When a moderate longitudinal coupling was included, it changed the wave dispersion only quantitatively, and the results of the effective-medium and the circuit models were shown to agree at low wavenumbers. However, the presence of a transverse coupling changed the polariton dispersion dramatic...