Effective medium theory of two-dimensional photonic crystal for transverse electric mode beyond the long-wavelength limit

Abstract

An effective medium theory of two-dimensional photonic crystal for TE mode beyond the long-wavelength limit has been established based on the Mie scattering theory. Först, the proposed theory has been used to study the negative-refractive-index photonic crystals for TE mode. This theory can be used to calculate the effective indices and the effective impedance, and to predict the position of the band gap. Results agree well with the band structures, especially when the equifrequency surface contours are almost circular. Then the proposed theory is used to study the zero-refractive-index photonic crystals for TE mode. It can be seen a triply-degenerate point at Γ point, forming a Dirac cone in the band structures. It has been called an “accidental-degeneracy-induced Dirac point”, where the effective index is zero and the effective impedance is 1. Results calculated using the proposed theory agree well with the band structures. This means that the theory can be used well beyond the long-wavelength limit. Furthermore, the additional impedance information, which cannot be obtained by band structures, can be derived from the proposed theory.