Effective dielectric constant of periodic composite structures

Abstract

Using a plane-wave-expansion method, we obtained expressions for the effective dielectric constants of composite periodic dielectric materials as the long-wavelength limit of the photonic-band-structure problem. The effective dielectric constants of several classes of photonic-band-gap structures are computed and we found that in the long-wavelength limit, they can be isotropic, uniaxial, or biaxial, depending on the symmetry of the structure under consideration. We also found that the scalar wave approximation gives poor results for effective dielectric constants while the Maxwell-Garnett theory offers very good approximations in the low-filling-ratio regimes.