Calculation of effective permittivity, permeability, and surface impedance of negative-refraction photonic crystals.

We consider the eigen-fields of a two-dimensional negative-refraction photonic crystal and obtain negative effective permittivity and negative effective permeability. Effective permittivity, permeability, and surface impedance are calculated by averaging the eigen-fields. The value of the surface impedance is shown to be location-dependent and is validated by finite-difference time-domain simulations. The unique power propagation mechanism in the photonic crystal is demonstrated through time-evolution of eigen-fields.