Effective parameters for photonic crystals with large dielectric contrast

We investigate the effective permittivity epsilon(e) and permeability mu(e) for photonic crystals with large dielectric contrast by use of the effective-medium model. In the quasistatic regime, the effective parameters are characterized by the anomalous dispersion near the resonances. For TM polarization, the region of negative epsilon(e) spreads over a wide range of frequency and there exists a frequency interval where epsilon(e) and mu(e) are simultaneously negative. For TE polarization, the resonance widths are much smaller and the region of doubly negative parameters is not present. The underlying mechanisms are illustrated with the field patterns associated with the leading and high-order resonances. The effective parameters are also examined by the band structures of the photonic crystal with regard to photonic band gaps and special propagating branches. In the static regime, epsilon(e) and mu(e) are simplified to the Maxwell-Garnett mixing rule and the resonance feature becomes insignificant.