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The present paper is devoted to the investigation of the guided wave problem. This problem is formulated as the eigenvalue problem with a compact self-adjoint operator pencil. Applying the minimax principle for the compact operators in the Hilbert space we obtain a necessary and sufficient condition for the existence of a preassigned number of linearly independent guided modes. As a consequence of this result we also derive simple sufficient conditions, which can be easily applied in practice. We give a statement of the problem in a bounded domain and propose an efficient method for solving the problem.

The present paper is devoted to the investigation of the guided wave problem. This problem is formulated as the eigenvalue problem with a compact self-adjoint operator pencil. Applying the minimax principle for the compact operators in the Hilbert space we obtain a necessary and sufficient condition for the existence of a preassigned number of linearly independent guided modes. As a consequence of this result we also derive simple sufficient conditions, which can be easily applied in practice. We give a statement of the problem in a bounded domain and propose an efficient method for solving the problem.

Cette thèse est dédiée à la résolution numérique tridimensionnelle des équations de Maxwell harmoniques, par des méthodes de décomposition de domaine couplant des résolutions par équations intégrales entre elles. Pour traiter les problèmes de diffraction d'ondes, la méthode des équations intégrales est un outil précieux. Elle consiste à paramétrer le champ électromagnétique solution par une source définie sur la surface de l'objet diffractant, solution d'une nouvelle équation linéaire (l'équation intégrale). Pour des applications à haute fréquence, le grand nombre d'inconnues (de l'ordre du million) nous oblige à utiliser un solveur itératif pour résoudre l'équation intégrale. Le problème du conditionnement des systèmes linéaires est alors crucial. De récents développements ont permis de construire une équation intégrale performante (la GCSIE) et de conditionnement stable avec la montée en fréquence. Cependant, la présence d'une cavité large et résonnante dans l'objet diffractant (telle que la cavité moteur d'un avion) dégrade le conditionnement de cette équation. Nous proposons deux méthodes de décomposition de domaine (DDM) afin de découpler le problème de la cavité du problème extérieur. La première (DDM en Y) s'exprime en fonction des opérateurs Dirichlet-to-Neumann Y, qui sont synthétisés via la résolution de problèmes métalliques par équations intégrales dans chaque sous-domaine. La seconde (DDM en S) s'exprime en fonction des opérateurs de scattering S, synthétisés par résolution de problèmes de type métal-impédant, donc bien posés à toute fréquence. La DDM en S permet ainsi de se débarrasser des phénomènes de résonance dans les cavités. Nous proposons dans un premier temps un préconditionneur analytique pour la DDM en Y, basé sur l'opérateur électromagnétique de simple couche. Nous calculons ensuite les modes guidés le long d'un cylindre infini tangent à la cavité près de l'interface, et nous diagonalisons les opérateurs Dirichlet-to-Neumann et scattering dans la base des traces de modes guidés sur l'interface. On extrait de cette étude deux préconditionneurs spectraux respectivement pour la DDM en Y et la DDM en S. Les résultats numériques confirment l'efficacité des préconditionneurs proposés / This work is dedicated to the numerical solution of the tridimensional harmonic Maxwell equations, using domain decomposition methods coupling integral equations between them. To deal with scattering problems, integral equations methods are a precious tool. They allow to look for the electromagnetic field by parameterizing it with a source only defined on the boundary of the scattering object, solution of a new linear equation (the integral equation). For applications at high frequency, the great number of unknowns forces the use of iterative methods. To accelerate the solution of integral equations, one moreover has to ensure the good condition number of the linear systems, or to propose well-suited preconditioners. An efficient method, the GCSIE, was developed in Onera. It is an intrinsically well-conditioned integral equation whose condition number remains stable whith the frequency increase. However, the existence of large and resonant cavities (such as air intakes) deteriorates the condition number. In order to circumvent this problem, we propose two domain decomposition methods (DDM) allowing to decouple the exterior problem from the problem of the cavities. The first one (Y-DDM) is based on Dirichlet-to-Neumann operators Y, which are built through the solution of metallic problems using integral equations in each subdomain. The second one (S-DDM) is based on scattering operators S, built through the solution of problems of metallic-impedant type, which are well-posed at any frequency. The S-DDM allows to avoid the resonance phenomena inside the cavities. First, we propose an analytic preconditioner for the Y-DDM, based on the electromagnetic single layer operator. We then calculate the modes guided along an artificial infinite cylinder, that is tangent to the cavity near the interface. We diagonalize the Dirichlet-to-Neumann and scattering operators in the basis of the traces of the guided modes on the interface. We deduce from this study two spectral preconditioners for the Y-DDM and the S-DDM. The numerical results confirm the efficiency of the employed preconditioners.

Bragg scattering of optical waves in thick gratings at extreme angles, where the scattered wave propagates parallel (extremely asymmetric scattering - EAS) or nearly parallel (grazing angle scattering - GAS) to the grating boundaries, is associated with many unique and practically important resonant phenomena. It has been demonstrated that one of the main physical mechanisms for these resonant phenomena is the diffractional divergence of the scattered wave inside and outside the grating region. This thesis fills the gaps in the theoretical and experimental understanding of Bragg scattering in gratings at extreme angles by investigating EAS and GAS in structures where diffractional divergence of waves is significantly affected by anisotropy and/or non-uniformities of the dielectric permittivity. Unusually high sensitivity of wave scattering in thick periodic gratings to small step-like variations of mean structural parameters at the grating boundaries is predicted and described for the case when the scattered wave (the +1 diffracted order) propagates almost parallel to the front grating boundary (the geometry of GAS). A unusual pattern of strong multiple resonances for bulk electromagnetic waves is predicted and analysed numerically in thick periodic holographic gratings in a guiding slab with mean permittivity that is greater than that of the surrounding media. It is demonstrated that these resonances are related to resonant generation of a new type of eigenmodes in a thick slab with a periodic grating. These eigenmodes are generically related to the grating -- they do exist not if the grating amplitude is zero. A new type of resonant coupling of bulk radiation into the conventional guided modes of a slab with a thick holographic grating is predicted and explained theoretically. It occurs in the presence of strong frequency detunings of the Bragg condition by means of interaction of the strongly non-eigen +1 diffracted order with the slab-grating boundaries. Therefore, it is only in the presence of step-like variations of the mean permittivity at the grating boundaries that this type of resonant coupling can occur. A new method for the analysis of EAS and GAS in anisotropic gratings is developed. This method is based on the consideration of the diffractional divergence of the scattered wave and the two-wave approximation in anisotropic gratings. Special efforts are focused on the analysis of EAS and GAS of extraordinary waves in uniaxial gratings. In particular, it is demonstrated that increasing curvature of the normal surface in the direction of propagation of the scattered wave results in increase of its diffraction divergence and the resonant amplitude. A theoretical model is developed for comparison of the theoretical predictions with data obtained from experimental observations of EAS in a holographic grating written in a photorefractive medium. The developed model is applied for the interpretation of experimental observations of EAS in BaTiO3 photorefractive crystals. Good agreement with the theoretical predictions is demonstrated.

The absorptance in vertical nanowire (nw) arrays is typically dominated by three optical phenomena: radial mode resonances, near-field evanescent wave coupling, and Fabry–Perot (F-P) mode resonances. The contribution of these optical phenomena to GaAs, InP and InAs nw absorptance was simulated using the finite element method. The study compared the absorptance between finite and semi-infinite nws with varying geometrical parameters, including the nw diameter (D), array period (P), and nw length (L). Simulation results showed that the resonance peak wavelength of the HE1n radial modes linearly red-shifted with increasing D. The absorptance and spectral width of the resonance peaks increased as L increased, with an absorptance plateau for very long nws that depended on D and P. Near-field coupling between neighbouring nanowires (nws) was observed to increase with increasing diameter to period ratio (D/P). The effect of F-P modes was more pronounced for shorter nws and weakly coupled light. Based on the collective observation of the correlation between nw geometry and optical phenomena in GaAs, InP, and InAs nw arrays, a periodic array of vertical InSb nws was designed for photodetectors in the low-atmospheric absorption window (λ = 3-5 μm) within the mid-wavelength infrared (MWIR) spectrum (λ = 3-8 μm). Simulations, using the finite element method, were implemented to optimize the nw array geometrical parameters (D, P, and L) for high optical absorptance (~0.8), which exceeded that of a thin film of equal thickness. The results further showed that the HE1n resonance wavelengths in InSb nw arrays can be tuned by adjusting D and P, thus enabling multispectral absorption throughout the near infrared (NIR) to MWIR region. Optical absorptance was investigated for a practical photodetector consisting of a vertical InSb nw array embedded in bisbenzocyclobutene (BCB) as a support layer for an ultrathin Ni contact layer. Polarization sensitivity of the photodetector was examined. Lastly, how light flux enters the nw top and sidewalls on HE11 resonance was investigated. / Dissertation / Doctor of Philosophy (PhD)

Dans un monde de plus en plus pollué par l'activité industrielle, la détection des espèces gazeuses nocives dans l'atmosphère est d'une importance essentielle. Le marché des capteurs de gaz est déjà bien développé, avec la présence de diverses technologies et principes de détection, chacune présentant des avantages et des inconvénients intrinsèques. Dans le cadre de cette thèse, un alliage entre deux ou plusieurs technologies de détection typiquement utilisées de façon autonome a été visée, afin d'améliorer les performances globales des systèmes capteurs ainsi formées. A ce fin, nous avons conçu et étudié des dispositifs capteurs basées sur la transduction optique, couplée à un matériau sensible au gaz cible à détecter. Plus précisément, nous avons intégré pour la première fois un matériau catalyseur pouvant accélérer le taux d'oxydation des espèces chimiques (tel le monoxyde de carbone ou l'hydrogène) avec une architecture optique capable d'absorber la chaleur cédée lors de cette oxydation. L'augmentation de température occasionnée est traduite en une variation d'intensité lumineuse constituante le signal de sortie du capteur. Les travaux effectués sur les mesures de la dispersion thermique et chromatique de l'indice de réfraction des matériaux constituant le transducteur optique par des techniques d'optique guidé, ellipsométrie et des techniques photométriques sont présentés. Le sondage par moyen optique des propriétés électriques des matériaux semiconducteurs a également été étudié, y compris les variations de ces propriétés en présence des gaz oxydants, réducteurs et combustibles. / In a world suffering from increasing air pollution due to spiraling industrial activity, the detection of toxic gasses in the atmosphere is of paramount importance. The gas detector market is already well developed, and features a wide variety of detection technologies and techniques, each presenting its own set of intrinsic advantages and drawbacks. In this thesis, a combination of two or more technologies typically used independently has been studied in order to improve the global performances of gas detection systems. To this length, we have conceived and studied detector architectures based upon optical transduction systems, coupled with a material presenting a specific sensitivity to the target gas. More precisely, we have for the first time integrated a catalyst designed to accelerate the oxidation rate of chemical species (such as carbon monoxide or hydrogen) with an optical component capable of absorbing the heat generated by the oxidation reaction. The associated increase in temperature is translated to a variation of the optical intensity comprising the exit signal of the detector. The work carried out measuring the chromatic and temperature dispersion of the refractive index of the materials comprising the optical transduction component by guided mode techniques, ellipsometry and photometric techniques is presented. The optical probing of the electrical properties of semiconductor materials has also been studied, including the variations of these properties following interactions with oxidizing, reducing, or combustible gasses.

This thesis fills in the gaps in the existing theory of wave phenomena in thick diffraction gratings at extreme angles of scattering, i.e. when the scattered wave propagates parallel or almost parallel to the grating boundaries. A consistent theory of a new type of Bragg scattering of bulk and guided optical modes in thick uniform and non-uniform, dissipative and non-dissipative, slanted periodic gratings has been developed. This type of scattering is called extremely asymmetrical scattering (EAS). One of the main distinctive features of EAS is the strong resonant increase of the scattered wave amplitude compared to the amplitude of the incident wave. Several unique combinations of strong resonances shaping a complex multi-resonant pattern of EAS in different types of gratings have been predicted and investigated theoretically and numerically. This includes the prediction of a new resonant wave effect in non-uniform gratings with varying phase – double-resonant EAS, the discovery of several sharp and strong resonances with respect to scattering angle in gratings with the scattered wave propagating almost parallel to the grating boundaries (grazing-angle scattering (GAS)) for the case of second-order scattering, and the prediction of a new type of eigenmode in gratings with second-order scattering (especially in gratings with large amplitude). In addition, several other important practical problems that may be crucial for the experimental observation and application of EAS and GAS have been solved. These are the determination of the tolerance of EAS to small grating imperfections, e.g., fluctuations of the grating amplitude, prediction of unusually high sensitivity of second-order EAS to small variations of mean structural parameters, determination of the effect of weak dissipation on EAS, etc. Physical reasons for the predicted resonances and effects are explained. In particular, the crucial role of the diffractional divergence for EAS and GAS has been revealed, especially for non-uniform gratings. Methods of analysis involve the approximate and rigorous approaches. The approximate method is based on understanding the role of the diffractional divergence in the geometry of EAS and the two-wave approximation (valid for any types of waves). The rigorous approach is based on the rigorous coupled-wave analysis (RCWA) and, in particular, the known enhanced T-matrix algorithm (by Moharam, et al.) that is numerically stable for narrow and wide gratings with arbitrary amplitude (valid only for bulk electromagnetic waves).