Differential Method for Periodic Structures

www.fresnel.fr/numerical-grating-bookInternational audienceThe chapter represents a revised version of the previously published chapter in the first edition of the book. It contains a detailed presentation of the differential theory of gratings, having one- ore two-dimensional periodicity and made of isotropic or anisotropic materials. Special attention is given to the numerical factorization of the products of discontinuous functions using the normal-vector method aiming to faster convergence in the Fourier space. Periodic structures with different forms and made of different materials are considered. The chapter presents also a numerical analysis of different integration schemes used to solve the diffraction problem

Introduction to Diffraction Gratings: Summary of Applications

International audienceThe most important properties of diffraction gratings are revisited in view of different applications: classical (spectroscopic, filtering, waveguiding) and modern (plasmonics, photonic crystals). This chapters serves as an entering chapter for the whole monograph dedicated to the theories of diffraction by periodic structures

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

Notes de Maths : Vecteurs, Dérivées et Opérateurs différentiels

1. Vecteurs 2. Dérivées 3. Opérateurs différentielsLicenceL'introduction sur les vecteurs et les opérateurs différentiels pour les étudiants en L2 et L3 de physique et chimi

Differential Theory of Periodic Structures

www.fresnel.fr/numerical-grating-bookInternational audienceThe chapter contains a detailed presentation of the differential theory of gratings, having one- ore two-dimensional periodicity and made of isotropic or anisotropic materials. Special attention is given to the numerical factorization of the products of discontinuous functions using the normal-vector method aiming to faster convergence in the Fourier space. Periodic structures with different forms and made of different materials are considered. The chapter presents also a numerical analysis of different integration schemes used to solve the diffraction problem

Electrostatique et Magnetostatique : Notes du cours

Electrostatique Charge électrique, types de charges. Loi de Coulomb. Champ électrique, lignes de champ Dipôle électrostatique Flux du champ électrostatique, théorème de Gauss Energie et potentiel du champ électrostatique Théorème d'Ostrogradski, théorème de Gauss - présentation différentielle Equations de Laplace et de Poisson Discontinuité de champ électrique Type de matériels : conducteurs, isolateur et semi-conducteurs Conducteurs dans champ électrostatique. Cage électrostatique. Corona décharge Courant électrique et la loi d'Ohm Condensateurs Diélectriques dans champ électrostatique, constante diélectrique, permittivité relative, polarisabilité de milieu Magnétostatique Force magnétique, champ magnétique. Loi de Biot et Savart. Force sur charge en mouvement dans un champ magnétique, la force de Lorentz Mouvement cyclotron et aurore boréale Loi de Laplace, effet Hall Champ créé par une charge en mouvement et un courant électrique Flux de champ magnétique Dipôle magnétique Interactions magnétiques Théorème d'Ampère, théorème de Stokes LES équations principales d'électrostatique et magnétostatique Discontinuité de champ magnétique Force magnétohydrodynamique Potentiel vecteur Electromagnétisme (dynamique) L'induction électromagnétique et la première des équations de Maxwell Inductance mutuelle Courant de déplacement et la deuxième des équations de Maxwell LES équations de Maxwell et les ondes électromagnétiques Propriétés magnétiques des matériaux (diamagnétisme, paramagnétisme et ferromagnétisme) Champ H, susceptibilité et perméabilité magnétiqueLicenceLes notes du cours en électrostatique et magnétostatique sont destinées aux étudiants en deuxième année (L2) de la licence généralistes des universités en physique ou physique-chimie. Le cours commence avec la force Coulombienne et l'étude des charges électriques, contient la présentation du théorème de Gauss, introduit la loi d'induction de Faraday et finit avec la contribution de Maxwell

Thermal annealing and transformation of dimer F centers in neutron-irradiated Al2O3 single crystals

This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014-2018 and 2019-2020 under grant agreement No 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission. In addition, the research leading to these results has received funding from the Estonian Research Council grant (PUT PRG619).The precise study of the thermal annealing of the F2-type dimer defects, being under discussion in the literature for a long time and responsible for the number of absorption bands below 4.5 eV, has been performed in corundum single crystals irradiated by fast neutrons with a fluence of 6.9 × 1018 n/cm2. The Gaussian components of the radiation-induced optical absorption with the maxima at 4.08, 3.45 and 2.75 eV have been considered as a measure of the F2, F2+and F22+centers, respectively. In contrast to the Fand F+ centers, the concentration of which continuously decreases at the sample heating up to 1100 K, the concentration of dimer defects with different charge states passes the increasing stages above 500 K starting from the F22+centers. The tentative mechanisms of such rise of the F22+centers as well as of the subsequent transformation/rise of dimer centers, F22+→F2+→F2at 650-800 K are considered. The possible sources of carriers needed for the recharging of dimer centers are also analysed on the basis of thermally stimulated luminescence measurements up to ~850 K.EUROfusion Consortium, Euratom research and training programme 2014-2018 and 2019-2020, grant agreement No 633053; Estonian Research Council grant (PUT PRG619); Institute of Solid State Physics, University of Latvia as the Center of Excellence has received funding from the European Union’s Horizon 2020 Framework Programme H2020-WIDESPREAD-01-2016-2017-TeamingPhase2 under grant agreement No. 739508, project CAMART

Grating theory: new equations in fourier space leading to fast converging results for tm polarization

Using theorems of Fourier factorization, a recent paper [J. Opt. Soc. Am. A 13, 1870 (1996)] has shown that the truncated Fourier series of products of discontinuous functions that were used in the differential theory of gratings during the past 30 years are not converging everywhere in TM polarization. They turn out to be converging everywhere only at the limit of infinitely low modulated gratings. We derive new truncated equations and implement them numerically. The computed efficiencies turn out to converge about as fast as in the TE-polarization case with respect to the number of Fourier harmonics used to represent the field. The fast convergence is observed on both metallic and dielectric gratings with sinusoidal, triangular, and lamellar profiles as well as with cylindrical and rectangular rods, and examples are shown on gratings with 100% modulation. The new formulation opens a new wide range of applications of the method, concerning not only gratings used in TM polarization but also conical diffraction, crossed gratings, three-dimensional problems, nonperiodic objects, rough surfaces, photonic band gaps, nonlinear optics, etc. The formulation also concerns the TE polarization case for a grating ruled on a magnetic material as well as gratings ruled on anisotropic materials. The method developed is applicable to any theory that requires the Fourier analysis of continuous products of discontinuous periodic functions; we propose to call it the fast Fourier factorization method

Atomic, electronic and magnetic structure of an oxygen interstitial in neutron-irradiated Al2O3 single crystals

This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014-2018 and 2019-2020 under Grant Agreement No. 633053 and Enabling Research project: ENR-MFE19.ISSP-UL-02 “Advanced experimental and theoretical analysis of defect evolution and structural disordering in optical and dielectric materials for fusion application”. The views and opinions expressed herein do not necessarily reflect those of the European Commission. In addition, the research leading to these results has received funding from the Estonian Research Council grant (PUT PRG619).A single radiation-induced superoxide ion O2- has been observed for the first time in metal oxides. This structural defect has been revealed in fast-neutron-irradiated (6.9×1018n/cm2) corundum (α-Al2O3) single crystals using the EPR method. Based on the angular dependence of the EPR lines at the magnetic field rotation in different planes and the determined g tensor components, it is shown that this hole-type O2- center (i) incorporates one regular and one interstitial oxygen atoms being stabilized by a trapped hole (S = 1/2), (ii) occupies one oxygen site in the (0001) plane being oriented along the a axis, and (iii) does not contain any other imperfection/defect in its immediate vicinity. The thermal stepwise annealing (observed via the EPR signal and corresponding optical absorption bands) of the O2- centers, caused by their destruction with release of a mobile ion (tentatively the oxygen ion with the formal charge −1), occurs at 500–750 K, simultaneously with the partial decay of single F-type centers (mostly with the EPR-active F+ centers). The obtained experimental results are in line with the superoxide defect configurations obtained via density functional theory (DFT) calculations employing the hybrid B3PW exchange-correlation functional. In particular, the DFT calculations confirm the O2- center spin S = 1/2, its orientation along the a axis. The O2- center is characterized by a short O–O bond length of 1.34 Å and different atomic charges and magnetic moments of the two oxygens. We emphasize the important role of atomic charges and magnetic moments analysis in order to identify the ground state configuration.Eesti Teadusagentuur PUT PRG619; H2020 Euratom ENR-MFE19,633053; Institute of Solid State Physics, University of Latvia as the Center of Excellence has received funding from the European Union’s Horizon 2020 Framework Programme H2020-WIDESPREAD-01-2016-2017-TeamingPhase2 under grant agreement No. 739508, project CAMART

Distinctive features of diffusion-controlled radiation defect recombination in stoichiometric magnesium aluminate spinel single crystals and transparent polycrystalline ceramics

This work has been performed within the framework of the EUROfusion Enabling Research project: ENR-MFE19.ISSP-UL-02 “Advanced experimental and theoretical analysis of defect evolution and structural disordering in optical and dielectric materials for fusion application”. The views and opinions expressed herein do not necessarily reflect those of the European Commission. Research of A.L, E.F.,, V.S and E.S has been partly supported by the Estonian Research Council grant (PUT PRG619); has been also carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014–2018 and 2019–2020 under grant agreement No 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission.MgAl2O4 spinel is important optical material for harsh radiation environment and other important applications. The kinetics of thermal annealing of the basic electron (F, F+) and hole (V) centers in stoichiometric MgAl2O4 spinel irradiated by fast neutrons and protons is analyzed in terms of diffusion-controlled bimolecular reactions. Properties of MgAl2O4 single crystals and optical polycrystalline ceramics are compared. It is demonstrated that both transparent ceramics and single crystals, as well as different types of irradiation show qualitatively similar kinetics, but the effective migration energy Ea and pre-exponent D0 are strongly correlated. Such correlation is discussed in terms of the so-called Meyer-Neldel rule known in chemical kinetics of condensed matter. The results for the irradiated spinel are compared with those for sapphire, MgO and other radiation-resistant materials.Institute of Solid State Physics, University of Latvia as the Center of Excellence has received funding from the European Union’s Horizon 2020 Framework Programme H2020-WIDESPREAD-01-2016-2017-TeamingPhase2 under grant agreement No. 739508, project CAMART