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Publication# Accurate, Stable and Efficient Modal Calculations of Photoelectrically Useful Absorption in Lamellar Metallic and Semiconductor Diffraction Gratings

Résumé

Solar energy has seen tremendous advances in the past years. For thin film photovoltaics, which use less of the expensive semiconductor materials, insufficient light absorption can be a limiting factor. It is hoped that by using diffractive optics to improve the light absorption, the cost per Watt could sink. Correspondingly, the optics of such structures need to compensate for the low absorption by high (structural) resonance, which is challenging to calculate. To estimate optimal structures, a numerical method should be able to assess feasible structures with widely varying geometries quickly. Modal methods allow for an efficient analysis of structures with varying height through the separation of eigenvalue and boundary value problem. First, the thesis aspires to further develop the modal methods for the calculation of optical properties of layered structures containing weakly absorbing metals and semiconductors. Second, the thesis aims to calculate absorption enhancements in idealized, prototypical structures by applying the newly developed methods. The calculations should only depend on material parameters and not contain additional assumptions. These absorption enhancements are not tied to a priori assumptions such as mode couplings, but they solely follow the physics of the structure investigated. The first part of the thesis is concerned with the methodical improvements. A first emphasis is put on studying peculiar properties of the eigenvalue problem, and on new developments of methods to solve it within a layer. Furthermore, it shows several variants for the numerical implementation of the eigenvalue problem. This part includes a new method to calculate the eigenvalues that can be adapted to two dimensional grating problems of arbitrary shape. The new method integrates the eigenvalue problem by making use of a two point trapezoidal formula, and satisfies the boundary condition between different materials exactly. It is energy conserving and the rate of convergence depends on the approximation order. The eigenvalues show a monotonic convergence that allows for extrapolation. The second methodical emphasis is placed on variants of the implementation of the boundary value problem that connects the grating to the incoming and outgoing plane waves. This algorithm describes the propagation of the incident energy to the semiconductor layer and the substrate by solving a non-recursive and numerically stable system of linear equations. A novel variant reduces the bandwidth of the corresponding matrix by a third. The third part of the thesis concerns calculations using the improved methods. First, the improved calculations are verified by showing that the energy conservation of the modal method, as well as the well-behavedness of the condition number of the calculation. Next, numerical results for the new methods are compared to results from the literature for analytic modal methods, and a comparison with existing software is made. Thereafter, the interface plasmons occuring for H polarization are investigated. In the last part of the thesis, calculations are made for the material specific absorption of light in metallic gratings covered by semiconductors, with a special interest in the absorption in the semiconductor. Here, the spectra for rectangular, sinusoidal gratings, and asymmetric gratings are calculated, and the absorption improvement is investigated through an analysis of the involved modes.

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Publications associées (7)

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Photonic crystals are periodic dielectric structures, where the periodicity varies in one, two or three dimensions. Analogous to the periodic potential of electrons in semiconductors, the periodic variation of the dielectric constant influences the electromagnetic properties. The energy of the light is separated in bandgaps, energy ranges in which the propagation of the light is forbidden for certain directions and energies. These properties suggest that photonic crystals may be suitable for fabrication of the components needed for integrated optics. Since the fabrication of three dimensional photonic crystals is still limited by complex fabrication problems we have studied two dimensional photonic crystals. These photonic crystals can be fabricated by standard microelectronic technology. The photonic crystals studied in this thesis consist of GaAs and InP based low index vertical waveguides with a matrix of holes etched into it. The fabrication of photonic crystals with good optical properties is an important factor for photonic crystal devices in integrated optics. In the first part we studied the optical properties of photonic crystal slabs and of Fabry-Pérot cavities. These structures were measured by the internal light source technique, which allows quantitative normalized transmission measurements. The photonic crystals were etched by three different dry etching technologies. Out-of plane scattering is described by a 2D-FDTD fit of the transmission spectra and by a semi-analytical model. The finite hole depth and the conical shape of the holes are important structural parameters. The detailed study of their effects yields an important feedback for the critical parameters of the fabrication process. Photonic crystal waveguides are another group of components in integrated optics. We measured two types of straight photonic crystal waveguides by the endfire technique. Here the light is coupled by optical fibers and ridge waveguides in the photonic crystal waveguides. The transmission spectra reveal fringes which are due to multiple interference of the light in the sample. This interference contains information about propagation losses of the waveguides and an analysis based on the Fourier transform of the transmission spectra enabled us to deduce the propagation losses of the photonic crystal waveguides. The necessity of tuning or trimming the optical properties of photonic crystals is an important issue either compensating fabrication imperfections (trimming) or controlling the optical properties on demand (tuning) for devices like filters. We have shown that it is possible to tune the optical properties of planar photonic crystal cavities by temperature. The experimental results were validated by theoretical calculations. Also we have shown that is possible to tune the optical properties of photonic crystals by infiltrating liquid crystals in the holes. Liquid crystals are a birefringent material whose optical axis can be tuned by external fields (electric, temperature, photonic source, etc.). Phase transitions exhibiting abrupt changes in the refractive index are important characteristics of liquid crystals. The holes of the photonic crystal are infiltrated by a reversible and reliable infiltration process. The infiltration efficiency and the orientation of the molecules in the holes were determined by polarization resolved internal light source measurements. We have shown that the frequency of the Fabry-Pérot resonance changes at the phase transitions of the liquid crystal.

The behavior of nematic liquid crystals in spatially varying electrical fields is investigated. Director profiles of nematic-liquid-crystal phase gratings are simulated for different orientations of the liquid-crystal director field with respect to the electrode grating. With increasing spatial frequency of the grating the fringing electric field becomes important and the diffraction pattern changes. The optical properties are analyzed and measurements are performed.

2000The different parts of the electromagnetic spectrum result in diverse effects upon interaction with matter: according to the wavelength, the radiation has energy appropriate for the excitation of a specific physical process. X-rays can be used as a tool to analyze the structure of matter since their wavelength is comparable with the interatomic distances. Infrared light is in the spectral region that excites molecular vibrations and is employed to investigate the chemical composition of a material. Visible radiation can study the optical properties of a sample, such as the fluorescence and the absorbance, and provide a chemical fingerprint when the inelastically scattered light is detected. In this thesis work these light sources are used in diverse experimental approaches to study structured biological specimens, resulting in a detailed chemical and physical characterization at the atomic and molecular scale. Conventional spectroscopy is often not enough sensitive and spatially resolved to detect specific elements or domains in a sample. The need of imaging objects on increasingly finer scales and spatially localize specific molecules, brought to combine infrared, visible and Raman spectroscopy with scanning near-field microscopy giving rise to a powerful nanospectroscopic tool used to perform simultaneous topographical measurements and optical/chemical characterizations with subwavelength resolution, overcoming the diffraction limit of light. Our study combines X-ray diffraction and reflectivity with optical nanospectroscopy to investigate the order and clustering of lipid bilayers, the interaction between solid-supported membranes and embedded alamethicin peptides, the optical and chemical properties of hippocampal neuron cells and the trafficking mechanism of specific neuron receptors.

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