The complex Bloch bands of a 2D plasmonic crystal displaying isotropic negative refraction

The propagation characteristics of a subwavelength plasmonic crystal are studied based on its complex Bloch band structure. Photonic crystal bands are generated with an alternative 2D Finite Element Method formulation in which the Bloch wave problem is reduced to a quadratic eigenvalue system for the Bloch wavevector amplitude k. This method constitutes an efficient and convenient alternative to nonlinear search methods normally employed in the calculation of photonic bands when dispersive materials are involved. The method yields complex wavevector Bloch modes that determine the wave-scattering characteristics of finite crystals. This is evidenced in a comparison between the band structure of the square-lattice plasmonic crystal and scattering transfer-functions from a corresponding finite crystal slab. We report on a wave interference effect that leads to transmission resonances similar to Fano resonances, as well as on the isotropy of the crystal's negative index band. Our results indicate that effective propagation constants obtained from scattering simulations may not always be directly related to individual crystal Bloch bands.