José María Rico-García

Optical antennas for nano-photonic applications

Antenna-coupled optical detectors, also named optical antennas, are being developed and proposed as alternative detection devices for the millimetre, infrared, and visible spectra. Optical and infrared antennas represent a class of optical components that couple electromagnetic radiation in the visible and infrared wavelengths in the same way as radioelectric antennas do at the corresponding wavelengths. The size of optical antennas is in the range of the detected wavelength and they involve fabrication techniques with nanoscale spatial resolution. Optical antennas have already proved and potential advantages in the detection of light showing polarization dependence, tuneability, and rapid time response. They also can be considered as point detectors and directionally sensitive elements. So far, these detectors have been thoroughly tested in the mid-infrared with some positive results in the visible. The measurement and characterization of optical antennas requires the use of an experimental set-up with nanometric resolution. On the other hand, a computation simulation of the interaction between the material structures and the incoming electromagnetic radiation is needed to explore alternative designs of practical devices.

Photonic crystal characterization by FDTD and principal component analysis

We demonstrate the capabilities of principal component analysis (PCA) for studying the results of finite-difference time-domain (FDTD) algorithms in simulating photonic crystal microcavities. The spatial-temporal structures provided by PCA are related to the actual electric field vibrating inside the photonic microcavity. A detailed analysis of the results has made it possible to compute the phase maps for each mode of the arrangement at their respective resonant frequencies. The existence of standing wave behavior is revealed by this analysis. In spite of this, some numerical artifacts induced by FDTD algorithms have been clearly detailed through PCA analysis. The data we have analyzed are a given set of maps of the electric field recorded during the simulation.

Toy model to describe the effect of positional blocklike disorder in metamaterials composites

We study theoretically the effect of a new type of blocklike positional disorder on the effective electromagnetic properties of one-dimensional chains of resonant, high-permittivity dielectric particles, where particles are arranged into perfectly well-ordered blocks whose relative position is a random variable. This creates a finite order correlation length that mimics the situation encountered in metamaterials fabricated through self-assembled techniques, whose structures often display short-range order between near neighbors but long-range disorder, due to stacking defects. Using a spectral theory approach combined with a principal component statistical analysis, we study, in the long-wavelength regime, the evolution of the electromagnetic response when the composite filling fraction and the block size are changed. Modifications in key features of the resonant response (amplitude, width, etc.) are investigated, showing a regime transition for a filling fraction around 50%.

Characterization of photonic crystal microcavities with manufacture imperfections.

The manufacture of a photonic crystal always produce deviations from the ideal case. In this paper we present a detailed analysis of the influence of the manufacture errors in the resulting electric field distribution of a photonic crystal microcavity. The electromagnetic field has been obtained from a FDTD algorithm. The results are studied by using the Principal Component Analysis method. This approach quantifies the influence of the error in the preservation of the spatial-temporal structure of electromagnetic modes of the ideal microcavity. The results show that the spatial structure of the excited mode is well preserved within the range of imperfection analyzed in the paper. The deviation from the ideal case has been described and quantitatively estimated.

Angular shifts of paraxial beams by refraction in a plane dielectric/dielectric interface

The longitudinal and transverse angular shifts in the refraction of a paraxial beam are calculated by using the planewave decomposition of the amplitude of the electric field distribution of the incident beam. The transmission coefficients are expanded into powers of the spatial frequencies. In this paper these spatial frequencies need to be within the paraxial approach around the main direction of propagation of the beam. The beam is characterized by the moments of the square of the modulus of the angular spectrum of the electric field. To compute them, it is necessary to calculate how the spatial frequencies of the beam change along the refraction. The state of polarization of the beam is also included in the analysis. Numerical results are obtained to show the dependence of the angular shifts on the polarizations state and the symmetry of the beam. 2002 Elsevier Science B.V. All rights reserved.

Measurement limitations in knife-edge tomographic phase retrieval of focused IR laser beams

An experimental setup to measure the three-dimensional phase-intensity distribution of an infrared laser beam in the focal region has been presented. It is based on the knife-edge method to perform a tomographic reconstruction and on a transport of intensity equation-based numerical method to obtain the propagating wavefront. This experimental approach allows us to characterize a focalized laser beam when the use of image or interferometer arrangements is not possible. Thus, we have recovered intensity and phase of an aberrated beam dominated by astigmatism. The phase evolution is fully consistent with that of the beam intensity along the optical axis. Moreover, this method is based on an expansion on both the irradiance and the phase information in a series of Zernike polynomials. We have described guidelines to choose a proper set of these polynomials depending on the experimental conditions and showed that, by abiding these criteria, numerical errors can be reduced.

Application of tomographic techniques to the spatial-response mapping of antenna-coupled detectors in the visible

A tomographiclike method based on the inverse radon transform is used to retrieve the irradiance map of a focused laser beam. The results obtained from multiple knife-edge measurements have been processed through a kriging technique. This technique allows us to map both the beam irradiance and the uncertainty associated with the measurement method. The results are compared with those achieved in the standard fitting of two orthogonal knife-edge profiles to a modeled beam. The application of the tomographiclike technique does not require any beam model and produces a higher signal-to-noise ratio than the conventional method. As a consequence, the quality of the estimation of the spatial response map of an antenna-coupled detector in the visible is improved.

Multivariate analysis of photonic crystal microcavities with fabrication defects

Photonic crystal microcavities are defined by the spatial arrangement of materials. In the analysis of their spatial-temporal mode distributions Finite-Difference Time-Domain (FDTD) methods have proved its validity. The output of the FDTD can be seen as the realizations of a multidimensional statistic variable. At the same time, fabrication tolerances induce an added and unavoidable variability in the performance of the microcavity. In this contribution we have analyzed the modes of a defective photonic crystal microcavity. The location, size, and shape of the cylinders configuring the microcavity are modelled as having a normal distribution of their parametric descriptors. A principal component analysis is applied to the output of the FDTD for a population of defective microcavities. The relative importance of the defects is evaluated, along with the changes induced in the spatial temporal distribution of electromagnetic field obtained from the calculation.

Numerical artifacts in finite-difference time- domain algorithms analyzed by means of principal components

Finite-difference time-domain (FDTD) algorithms are affected by numerical artifacts and noise. In order to obtain better results we propose the use of the principal component analysis based on multivariate statistical techniques. It allows a straightforward discrimination between the numerical noise and the actual electromagnetic field distributions, and the quantitative estimation of their respective contributions. Besides, the FDTD results can be filtered to clean the effect of the noise. The method has been applied successfully to two dimensional simulations: propagation of a pulse in vacuum using total field-scattered field techniques, and mode computation in a two-dimensional photonic crystal. In this last case, PCA has revealed hidden electromagnetic structures related to actual modes of the photonic crystal.

Spatial characterization of light detectors with nanometric resolution

The miniaturization of light detectors in the visible and infrared has produced devices with micrometric and sub-micrometric spatial features. Some of these spatial features are closely linked with the physical mechanism of detection. An example of these devices is an optical antennas. To spatially characterize optical antennas it is necessary to scan a probe beam on the plane of the optical antenna. The mapping of this response is then treated and analyzed. When the response of the antenna is monitorized at visible or near-infrared frequencies, a sub-micron scanning step is necessary. In this paper we show the experimental set-up of a measurement station having a spatial resolution of 50 nanometers. This station is devoted to spatially characterize micrometric detectors, and specially optical antennas. The origin of the uncertainties of the measurement protocol is shown and practically analyzed. This station is also applied for characterizing the temporal, spectral, and polarization sensitivity specifications of light detectors with the previously mentioned resolution.