Experimental reflectance spectra have been obtained for colloidal crystals whose widths ranged from one to several sphere monolayers, and their features in the higher order band energy range have been reproduced theoretically. In order to fit the measured data, optical extinction has been introduced in the theoretical model, which accounts for structure imperfections and disorder, the main sources of losses in an actual measurement. A complex spectrum in the high frequency region is observed even for one ordered monolayer, being this peak structure gradually modified as more layers are piled up. This allowed us to identify which peaks are reminiscent of the optical reflectance features of a single close-packed layer and which are the result of building up a three dimensional periodicity. A clear correlation between the amount of extinction introduced in the fitting and the slab width has been found, which demonstrates that wider real crystals produce less diffusely scattered light. At the same time, we find that the optical response of thinner crystals is more robust against the introduction of extinction than that of thicker ones, for which the effect is dramatic. DOI: 10.1103/PhysRevB.76.245103 PACS number͑s͒: 78.20.Bh, 78.40.Ϫq, 42.70.Qs, 41.20.Jb Improvements in the processes of fabrication of selfassembled three dimensional ͑3D͒ photonic crystals ͑PhCs͒, which are materials with a spatially periodic dielectric function in all three dimensions, have made possible the observation of high quality optical spectra in higher order band frequencies.1-3 Also, the appearance of localized modes inside band gaps in the photonic band structure due to the addition of local defects is a well-known effect, which is analogous to the doping of semiconductors.4 Point, line, or plane defects are created within the crystal by locally adding or removing material in a controlled manner, 5,6 so they are different from intrinsic defects, which are unintentional disruptions of the spatial periodicity of the dielectric function that arise during the fabrication process. Despite new fabrication techniques that have alleviated the effect of disorder in the so-called low-energy range, where the lattice constant is less than the wavelength of light, very recently, it has been demonstrated that extinction due to intrinsic defects in 3D PhCs strongly affects the shape of the experimental spectra in the high-energy range, where the lattice constant is greater than the wavelength.7 Also, calculations of the photonic band structure, performed considering extinction, have shown a clear correlation between the behavior of the imaginary part of the wave vector and the optical features observed in the spectra. This means that disorder, while having a small influence on the measured spectra in the low-energy range, amplifies its effects at higher energies and, consequently, further improvement of the fabrication techniques is required to achieve optical quality at those photon energies. 8 In order to perform a valid comparison between the opt...

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...

An analysis of the diffracted beams emerging from three-dimensional photonic crystals is herein presented. The wave vectors of nonspecular beams are calculated for a triangular two-dimensional lattice and the change in their directions as a function of the wavelength is confirmed experimentally for the case of face-centeredcubic colloidal crystals illuminated under normal incidence. A fluctuating behavior of beam intensity as a function of the wavelength of the incident light is predicted for perfectly ordered lattices. As it is the case for specularly reflected and ballistically transmitted beams, this modulation arises from multipole resonances of the sphere ensemble that are smoothed out via the diffuse light scattering produced by imperfections in the crystalline structure. When optical extinction is introduced in order to model the effect of imperfections, it is possible to accurately reproduce experimental observations. Three-dimensional ͑3D͒ photonic crystals, which are materials with a dielectric function having 3D spatial periodicity, have received much attention during the last decades mainly due to their potential applications in optical, infrared, and microwave devices. 1,2 This kind of material is the only one capable of avoiding light propagation in all directions when the dielectric contrast is high enough, so they can present a complete band gap in their photonic band structure. 3 This property has been used to mold the emission of optically active materials and proposed for several technological applications that are still under continuous research. 4 The advent of fabrication techniques, that take advantage of the self-assembling properties of spherical colloidal particles in the micrometer scale, has made it possible to observe stop bands 5 and even full gaps 6 in the visible and near infrared spectra. Improvements in these techniques have led to high quality colloidal crystals with a low density of defects. [7][8][9] This has enabled the observation of previously undetected optical effects in the so-called high energy range, where the lattice constant is equal or greater than the wavelength. For this range, interesting fundamental phenomena have been observed when light propagates through low dispersion modes, such as the superprism effect 10 or beam self-focusing. 11 The optical spectra features observed in this range, such as the appearance of reflectance peaks and transmittance dips in the absence of any band gap, have generated an intense debate on the physical mechanisms originating these features. [12][13][14][15] An interesting and almost unexplored phenomenon occurring in the high energy range is the opening of diffraction channels, 13 that is, a finite number of diffracted beams emerge from the crystal slab when the photon energy is greater than a threshold energy or diffraction cutoff. These diffracted beams are propagating waves that can be projected on a screen in order to measure their intensities. However, up to date, most of the experimental and theoretical analyses in the high...