The homogeneous problem for a corrugated metamaterial of arbitrary permittivity and permeability: Choosing the proper Riemann surface

To obtain the eigenmodes of the electromagnetic field at a periodically corrugated metamaterial we consider the analytic extension to the complex plane of the solution to the boundary-value problem for a metamaterial grating. We build a proper Riemann sheet for these eigenmodes and we present numerical examples illustrating their propagation characteristics. Particularly, we pay special attention to regimes corresponding to ideally transparent metamaterials with a negative index of refraction, where the eigenmodes can radiate into the metamaterial medium.