Effect of extinction on the high-energy optical response of photonic crystals

Abstract

An analysis of the optical response of photonic crystals in the high-order band energy range is herein presented. High and abruptly fluctuating specular reflectance is predicted for perfect lattices at those energies even in the absence of any photonic gap or pseudogap. As optical extinction is gradually introduced, it is possible to reproduce experimental results found in the literature and which have recently been the subject of an intense debate. Band structure calculations demonstrate that extinction is extraordinarily amplified in the high-energy range and is responsible for the features so far observed in that range in real crystals. DOI: 10.1103/PhysRevB.75.241101 PACS number͑s͒: 42.70.Qs, 41.20.Jb, 78.20.Bh, 78.40.Ϫq The large spatial anisotropy of the dielectric constant in two-and three-dimensional photonic crystals ͑PCs͒ results in very complex band structures.1 In the higher-order bands, the interaction of multiple wave vectors propagating along different crystalline directions gives rise to very low dispersion modes, and although full gaps may open if the dielectric contrast is high enough, most practically feasible lattices present a wide passband in which the photon density of states fluctuates abruptly.2 Interesting fundamental phenomena with great potential applications have been observed when light propagates through higher band modes, such as the superprism effect 3 or beam self-focusing. 4 Different experimental and theoretical works have deepened our knowledge of this energy range.5-7 However, the optical features observed in the reflectance and transmittance spectra of real crystals are not yet fully understood.Here we present a complete description of the optical response of real PCs in the high-energy range, in which the spatial variation of the dielectric constant is on the order of the wavelength. We chose a face-centered cubic ͑fcc͒ lattice of low-refractive-index spheres to analyze the effect of extinction on the optical properties in this range. We start by describing the band structure and predicting the optical response of a fcc crystal with almost no losses and then gradually introduce extinction in its components. At those energies for which very low-dispersion propagation modes are attained, we predict that perfect lattices should present a strongly fluctuating optical response that rapidly smooths out as extinction is gradually increased. A similar behavior has been reported by Modinos et al. 8 although it seems to have been overlooked in the literature so far. Furthermore, we observe that a residual imaginary part of the dielectric constant introduced in the spheres gives rise to extraordinarily high values of the extinction for the high-energy region. We found that this extinction amplification effect is responsible for the shape of all actual reflectance and transmittance spectra so far reported, all experimental data available being explained by our model.Transmittance and reflectance spectra, as well as the band structure, were calculated using the code reported by S...

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