Generalized antireflection coatings for complex bulk metamaterials

We present the optimized design of an antireflection coating to efficiently couple an incident plane wave into a metamaterial with a complex field profile. We show that such an antireflection coating must enable spatial engineering of the field profiles at the coating/metamaterial interface to achieve high transmission, and therefore it is required to be inhomogeneous. As a demonstration, we investigate theoretically a waveguide-based negative-index metamaterial, which under normal incidence cannot be excited due to the antisymmetric propagating eigenmode. Through careful engineering of the field profile, lateral position, and thickness of the coating layer, we enhance the transmission under normal incidence from 0% to 100%. This principle may generally be applied to overcome low coupling efficiency between incident plane waves and complex mode profiles in metamaterials.