Experimental and theoretical analysis of the intensity of beams diffracted by three-dimensional photonic crystals

Abstract

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...

Anomalous group velocity at the high energy range of a 3D photonic nanostructure

“…This approach is adequate to treat ordered assembles of spherical scatters and requires reduced computational effort. Besides, this method has also allowed finding an explanation of the physical origin of the optical response in terms of the electromagnetic resonances occurring in the finite sphere ensemble and even reproduces fine details such as the spectral and angular dependence of the intensity of the diffracted modes [16][17][18][19]8]. Furthermore, this same approach has already accounted for the experimental observation of a nonlinear light-matter interaction enhancement by slowing light at a particular high energy frequency range [5].…”

Analysis of artificial opals by scanning near field optical microscopy

“…6,7 Mainly the optical methods used for characterizing these kinds of structures imply the study of both far and near field ranges. Analysis of the far field is adequate for reflectivity studies or stop-gap determinations, 8,9 whereas near field based techniques allow extracting information on the photon local density of states of these sort of lattices. 3 The development of the scanning near field optical microscopy (SNOM) has recently opened new possibilities to examining the electric field pattern of one-and twodimensional metallic structures [10][11][12] as well as photonic crystals in the near field range.…”

Anomalous group velocity at the high energy range of real 3D photonic nanostructures

“…Recently, calculations based on the code reported by Stefanou et al [16,17] developed from the vector Korringa-KohnRostoker (KKR) method [18,19] have provided very accurate predictions of the spectral dependence of transmittance, reflectance and intensity of the diffracted modes of opal films [12,13,20]. This approach is indicated to treat ordered assembles of spherical scatters and requires reduced computational effort.…”