Analytic Properties of Diffraction Gratings

International audienceThe chapter presents a review of most important general properties of gratings, which a user should not ignore and that are derived directly from the boundary value problem without any use of computer. These analytic properties are valuable at least for two reasons. First, they strongly contribute to a better understanding of an instrument which puzzled and fascinated many specialists of Optics since the beginning of the 20th century. Secondly, they allow a theoretician to check the validity of a new theory or its numerical implementation, although one must be very cautious: a theory can fail while its results satisfy some analytic rules. Specially, this surprising remark apply to properties like energy balance or reciprocity theorem. The first part of this chapter is devoted to the use of the elementary laws of Electromagnetics for stating the boundary value problems of gratings in various cases of materials and polarizations. Then, we deduce from the boundary value problems the most important analytic properties of gratings

Integral Method for Gratings

International audienceThe chapter containes a detailed presentation of the surface integral theory for modelling light diffraction by surface-relief diffraction gratings having a one-dimensional periodicity. Several different approaches are presented, leading either to a single integral equation, or to a system of coupled integral equations. Special attention is paid to the singularities of the kernels, and to different techniques to accelerate the convergence of the numerical computations. The theory is applied to gratings having different profiles with or without edges, to real metal and dielectrics, and to perfectly conducting substrates

Total absorption of light by lamellar metallic gratings

International audienceLamellar gratings illuminated in conical (off-plane) mounting can achieve with suitable optogeometrical parameters (grating profile, angle of incidence and wavelength) a total absorption of light for any polarization provided there is only the zeroth propagating order. A detailed analysis shows that electromagnetic resonances are involved and their nature strongly depends on the polarization. When the incident electric field is parallel to the cross-section of the grating, the resonance is provoked by the excitation of surface plasmons. For the orthogonal polarization, total absorption occurs for deep gratings only, when the grooves behave like resonant optical cavities. It is possible to reduce the optimal grating height by filling the grooves with a high refractive index material

Impatient Bandits: Optimizing Recommendations for the Long-Term Without Delay

Recommender systems are a ubiquitous feature of online platforms. Increasingly, they are explicitly tasked with increasing users' long-term satisfaction. In this context, we study a content exploration task, which we formalize as a multi-armed bandit problem with delayed rewards. We observe that there is an apparent trade-off in choosing the learning signal: Waiting for the full reward to become available might take several weeks, hurting the rate at which learning happens, whereas measuring short-term proxy rewards reflects the actual long-term goal only imperfectly. We address this challenge in two steps. First, we develop a predictive model of delayed rewards that incorporates all information obtained to date. Full observations as well as partial (short or medium-term) outcomes are combined through a Bayesian filter to obtain a probabilistic belief. Second, we devise a bandit algorithm that takes advantage of this new predictive model. The algorithm quickly learns to identify content aligned with long-term success by carefully balancing exploration and exploitation. We apply our approach to a podcast recommendation problem, where we seek to identify shows that users engage with repeatedly over two months. We empirically validate that our approach results in substantially better performance compared to approaches that either optimize for short-term proxies, or wait for the long-term outcome to be fully realized.Comment: Presented at the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD '23

Gratings: Theory and Numeric Applications

International audienceThe book containes 11 chapters written by an international team of specialist in electromagnetic theory, numerical methods for modelling of light diffraction by periodic structures having one-, two-, or three-dimensional periodicity, and aiming numerous applications in many classical domains like optical engineering, spectroscopy, and optical telecommunications, together with newly born fields such as photonics, plasmonics, photovoltaics, metamaterials studies, cloaking, negative refraction, and super-lensing. Each chapter presents in detail a specific theoretical method aiming to a direct numerical application by university and industrial researchers and engineers

Gratings: Theory and Numeric Applications, Second Revisited Edition

International audienceThe second Edition of the Book contains 13 chapters, written by an international team of specialist in electromagnetic theory, numerical methods for modelling of light diffraction by periodic structures having one-, two-, or three-dimensional periodicity, and aiming numerous applications in many classical domains like optical engineering, spectroscopy, and optical telecommunications, together with newly born fields such as photonics, plasmonics, photovoltaics, metamaterials studies, cloaking, negative refraction, and super-lensing. Each chapter presents in detail a specific theoretical method aiming to a direct numerical application by university and industrial researchers and engineers.In comparison with the First Edition, we have added two more chapters (ch.12 and ch.13), and revised four other chapters (ch.6, ch.7, ch.10, and ch.11

Diffraction gratings: An amazing phenomenon

International audienceThe paper describes and explains the most surprising Wood's anomaly: the total absorption of a plane wave by a shallow metallic grating. After a numerical and experimental evidence of the total absorption, we develop a quantitative phenomenological theory. Assuming that the anomalies are caused by the excitation of surface plasmon polaritons on the grating surface, we use theorems on analytic functions of the complex variable for representing the amplitudes of the scattered waves accurately through a phenomenological formula. The original rigorous grating theory used for numerical computations is outlined and some practical applications of strong absorptions are presented

Electromagnetic scattering by a set of objects: an integral method based on scattering operator

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Maxwell: A new vision of the world

International audienceThe paper outlines the crucial contributions of James Clerk Maxwell to Physics and more generally to our vision of the world. He achieved 150 years ago a synthesis of the pioneering works in magnetostatics, electrostatics, induction and, by introducing the notion of displacement current, gave birth to Electromagnetics. Then, he deduced the existence of electromagnetic waves and identified light as one of them.Maxwell equations deeply changed a Newtonian conception of the world based on particle interactions by pointing out the vital role of waves in physics. This new conception had a strong influence on the development of quantum physics. Finally, the invariance of light velocity in Galilean frames led to Lorentz transformations, a key step toward the theory of relativity