Angular redistribution of near-infrared emission from quantum dots in 3D photonic crystals

We study the angle-resolved spontaneous emission of near-infrared light sources in 3D photonic crystals over a wavelength range from 1200 to 1550 nm. To this end PbSe quantum dots are used as light sources inside titania inverse opal photonic crystals. Strong deviations from the Lambertian emission profile are observed. An attenuation of 60 % is observed in the angle dependent radiant flux emitted from the samples due to photonic stop bands. At angles that correspond to the edges of the stop band the emitted flux is increased by up to 34 %. This increase is explained by the redistribution of Bragg-diffracted light over the available escape angles. The results are quantitatively explained by an expanded escape-function model. This model is based on diffusion theory and adapted to photonic crystals using band structure calculations. Our results are the first angular redistributions and escape functions measured at near-infrared, including telecom, wavelengths. In addition, this is the first time for this model to be applied to describe emission from samples that are optically thick for the excitation light and relatively thin for the photoluminesence light.Comment: 24 pages, 8 figures (current format = single column, double spaced

Spherical harmonic decomposition applied to spatial-temporal analysis of human high-density EEG

We demonstrate an application of spherical harmonic decomposition to analysis of the human electroencephalogram (EEG). We implement two methods and discuss issues specific to analysis of hemispherical, irregularly sampled data. Performance of the methods and spatial sampling requirements are quantified using simulated data. The analysis is applied to experimental EEG data, confirming earlier reports of an approximate frequency-wavenumber relationship in some bands.Comment: 12 pages, 8 figures, submitted to Phys. Rev. E, uses APS RevTeX style

Anomalous Coherent Backscattering of Light from Opal Photonic Crystals

We studied coherent backscattering (CBS) of light from opal photonic crystals in air at different incident inclination angles, wavelengths and along various [hkl] directions inside the opals. Similar to previously obtained CBS cones from various random media, we found that when Bragg condition with the incident light beam is not met then the CBS cones from opals show a triangular line shape in excellent agreement with light diffusion theory. At Bragg condition, however, we observed a dramatic broadening of the opal CBS cones that depends on the incident angle and [hkl] direction. This broadening is explained as due to the light intensity decay in course of propagation along the Bragg direction {\em before the first} and {\em after the last} scattering events. We modified the CBS theory to incorporate the attenuation that results from the photonic band structure of the medium. Using the modified theory we extract from our CBS data the light mean free path and Bragg attenuation length at different [hkl]. Our study shows that CBS measurements are a unique experimental technique to explore photonic crystals with disorder, when other spectroscopical methods become ambiguous due to disorder-induced broadening.Comment: 10 pages, 5 figure

Hyperbolic planforms in relation to visual edges and textures perception

We propose to use bifurcation theory and pattern formation as theoretical probes for various hypotheses about the neural organization of the brain. This allows us to make predictions about the kinds of patterns that should be observed in the activity of real brains through, e.g. optical imaging, and opens the door to the design of experiments to test these hypotheses. We study the specific problem of visual edges and textures perception and suggest that these features may be represented at the population level in the visual cortex as a specific second-order tensor, the structure tensor, perhaps within a hypercolumn. We then extend the classical ring model to this case and show that its natural framework is the non-Euclidean hyperbolic geometry. This brings in the beautiful structure of its group of isometries and certain of its subgroups which have a direct interpretation in terms of the organization of the neural populations that are assumed to encode the structure tensor. By studying the bifurcations of the solutions of the structure tensor equations, the analog of the classical Wilson and Cowan equations, under the assumption of invariance with respect to the action of these subgroups, we predict the appearance of characteristic patterns. These patterns can be described by what we call hyperbolic or H-planforms that are reminiscent of Euclidean planar waves and of the planforms that were used in [1, 2] to account for some visual hallucinations. If these patterns could be observed through brain imaging techniques they would reveal the built-in or acquired invariance of the neural organization to the action of the corresponding subgroups.Comment: 34 pages, 11 figures, 2 table

3D optical Yagi–Uda nanoantenna array

Future photonic circuits with the capability of high-speed data processing at optical frequencies will rely on the implementation of efficient emitters and detectors on the nanoscale. Towards this goal, bridging the size mismatch between optical radiation and subwavelength emitters or detectors by optical nanoantennas is a subject of current research in the field of plasmonics. Here we introduce an array of three-dimensional optical Yagi–Uda antennas, fabricated using top-down fabrication techniques combined with layer-by-layer processing. We show that the concepts of radiofrequency antenna arrays can be applied to the optical regime proving superior directional properties compared with a single planar optical antenna, particularly for emission and reception into the third dimension. Measuring the optical properties of the structure reveals that impinging light on the array is efficiently absorbed on the subwavelength scale because of the high directivity. Moreover, we show in simulations that combining the array with suitable feeding circuits gives rise to the prospect of beam steering at optical wavelengths