Luis A. Dorado

Physical origin of the high energy optical response of three dimensional photonic crystals

The physical origin of the optical response observed in three-dimensional photonic crystals when the photon wavelength is equal or lower than the lattice parameter still remains unsatisfactorily explained and is the subject of an intense and interesting debate. Herein we demonstrate for the first time that all optical spectra features in this high energy region of photonic crystals arise from electromagnetic resonances within the ordered array, modified by the interplay between these resonances with the opening of diffraction channels, the presence of imperfections and finite size effects. All these four phenomena are taken into account in our theoretical approach to the problem, which allows us to provide a full description of the observed optical response based on fundamental phenomena as well as to attain fair fittings of experimental results.

Optical analysis of the fine crystalline structure of artificial opal films.

Herein, we present a detailed analysis of the structure of artificial opal films. We demonstrate that, rather than the generally assumed face centered cubic lattice of spheres, opal films are better approximated by rhombohedral assemblies of distorted colloids. Detailed analysis of the optical response in a very wide spectral range (0.4 < or = a/lambda < or = 2, where a is the conventional lattice constant), as well as at perpendicular and off-normal directions, unambiguously shows that the interparticle distance coincides very approximately with the expected diameter only along directions contained in the same close-packed plane but differs significantly in directions oblique to the [111] one. A full description of the real and reciprocal lattices of actual opal films is provided, as well as of the photonic band structure of the proposed arrangement. The implications of this distortion in the optical response of the lattice are discussed.

Light generation at the anomalous dispersion high energy range of a nonlinear opal film

We study experimentally and theoretically light propagation and generation at the high energy range of a close-packed fcc photonic crystal of polystyrene spheres coated with a nonlinear material. We observe an enhancement of the second harmonic generation of light that may be explained on the basis of amplification effects arising from propagation at anomalous group velocities. Theoretical calculations are performed to support this assumption. The vector KKR method we use allows us to determine, from the linear response of the crystal, the behavior of the group velocity in our finite photonic structures when losses introduced by absorption or scattering by defects are taken into account assuming a nonzero imaginary part for the dielectric constant. In such structures, we predict large variations of the group velocity for wavelengths on the order or smaller than the lattice constant of the structure, where an anomalous group velocity behavior is associated with the flat bands of the photonic band structure. We find that a direct relation may be established between the group velocity reduction and the enhancement of a light generation processes such as the second harmonic generation we consider. However, frequencies for which the enhancement is found, in the finite photonic crystals we use, do not necessarily coincide with the frequencies of flat high energy bands.

Analysis of artificial opals by scanning near field optical microscopy

Herein we present a detailed analysis of the optical response of artificial opal films realized employing a near-field scanning optical microscope in collection and transmission modes. Near-field patterns measured at the rear surface when a plane wave impinges on the front face are presented with the finding that optical intensity maps present a clear correlation with the periodic arrangement of the outer surface. Calculations based on the vector Korringa–Kohn–Rostoker method reproduce the different profiles experimentally observed as well as the response to the polarization of the incident field. These observations constitute the first experimental confirmation of the collective lattice resonances that give rise to the optical response of these three dimensional periodic structures in the high-energy range.

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

We report on a study of electromagnetic waves propagation in thin periodically ordered photonic nanostructures in the spectral range where the light wavelength is on the order of the lattice parameter. The vector KKR method we use allows us to determine the group index from finite photonic structures including extinction providing confirmation of recently emerged results. We show that for certain frequencies the group velocity of opal slabs can either be superluminal or approach zero depending on the crystal thickness and the unavoidable presence of losses. In some cases, group velocity can be negative. Such behavior can be clearly attributed to the finite character of the three-dimensional structure and reproduces previously reported experimental observations. Calculations show that contrary to the predictions of extraordinary group velocity reductions for infinite periodic structures, the group velocity of real opals may exhibit strong fluctuations at the high energy range. Hence, a direct identification between the calculated anomalous group velocities, for an actual opal film, and the predicted propagating low dispersion modes for an ideal infinite ordered structure seems difficult to establish.

Angular dependence of the intensity of light beams diffracted by colloidal crystals

An experimental and theoretical analysis of the angular dependence of the diffracted light beams emerging from three-dimensional colloidal photonic crystals is herein presented. Diffracted beams are identified according to their associated reciprocal-lattice vectors, and their intensities are obtained as a function of the zenithal and azimuthal incidence angles. Significant changes in the beam intensities are observed for large zenithal incidence angles as the azimuthal angle is varied. This phenomenon is related to the excitation of new resonant modes inside the photonic crystal which cannot be observed under normal incidence conditions.

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

We perform a theoretical study on the group velocity for finite thin artificial opal slabs made of a reduced number of layers in the spectral range where the light wavelength is on the order of the lattice parameter. The vector KKR method including extinction allows us to evaluate the finite-size effects on light propagation in the ΓL and ΓX directions of fcc close-packed opal films made of dielectric spheres. The group is index determined from the phase delay introduced by the structure to the forwardly transmitted electric field. We show that for certain frequencies, light propagation can either be superluminal -positive or negative- or approach zero depending on the crystal size and absorption. Such anomalous behavior can be attributed to the finite character of the structure and provides confirmation of recently emerged experimental results.

Anomalous group velocity in a 3D photonic nanostructure

In recent years, a growing interest appeared in the systems that can provide a either a reduction of the speed of light, slow-light, or a superluminal light propagation. Experiments have confirmed the existence of both behaviors in three-dimensional ordered nanostructures, in the spectral range where the wavelength of light is on the order, or smaller, than the lattice constant [1]. Using periodic boundary conditions in a band structure calculation of a perfect 3D photonic crystal one finds that, in such frequency range, only propagating modes with a vanishing slope dispersion relation exist and, hence, a reduced group velocity is predicted [2].

Toward a full understanding of the growth dynamics, optical response, and crystalline structure of self-assembled photonic colloidal crystal films

Recent advances in the comprehension of the growth dynamics of colloidal crystal films opens the door to conscious design of experiments aiming at fabricating lattices in which the density of intrinsic defects is minimized. Since such imperfections have a dramatic effect on scattered light of wavelength smaller than the lattice constant, the evaluation of the experimental optical response at those energy ranges, based on the comparison to rigorous calculations, is identified as the most sensitive guide to accurately evaluate the progress towards the actual realization of defect free colloidal crystals. The importance of the existence of a certain distortion becomes particularly relevant at the above mentioned energy range. We have thoroughly analyzed the effect of fine structural features on the optical response to conclude that, rather than the generally assumed FCC lattice of spheres, opal films are better approximated by a rhombohedral assembly of distorted colloids. Interparticle distance of actual colloidal crystals coincides with the expected diameter for spheres belonging to the same close-packed (111) plane but differs significantly in directions oblique to the [111] one.

Nonlinear light generation at the high energy range of a 3D opal film

Most of the applications based on the special optical properties that photonic crystals (PC) offer to control the interaction between matter and electromagnetic radiation, are based on the periodic structure response at the low energy region of the spectra, where the first order Bragg diffraction takes place. Among those reported applications of PCs some are devoted to the nonlinear (NL) optical processes such as the second harmonic generation (SHG).