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

Design of metallic nanoparticles gratings for filtering properties in the visible spectrum

Plasmonic resonances in metallic nanoparticles are exploited to create efficient optical filtering functions. A Finite Element Method is used to model metallic nanoparticles gratings. The accuracy of this method is shown by comparing numerical results with measurements on a two-dimensional grating of gold nanocylinders with elliptic cross section. Then a parametric analysis is performed in order to design efficient filters with polarization dependent properties together with high transparency over the visible range. The behavior of nanoparticle gratings is also modelled using the Maxwell-Garnett homogenization theory and analyzed by comparison with the diffraction by a single nanoparticle. The proposed structures are intended to be included in optical systems which could find innovative applications.Comment: submitted to Applied Optic

Waveguide mode in the box with an extraordinary flat dispersion curve

The extraordinary flattening of the dispersion curve of the so-called cavity resonator integrated guided-mode resonance filters (CRIGFs) is analyzed and explained as due to the intramode coupling imposed by the external Bragg resonators. CRIGFs are composed of a grating coupler (guided-mode resonance filter, GMRF) put between two distributed Bragg reflectors (DBRs). They form a cavity box in which the excited guided mode is confined. This confinement provides resonances with small spectral width (smaller than 1 nm for optical wavelengths) and extraordinary wide angular acceptance (several degrees). At a first glance, one may think that similar performances could be obtained while putting the GMRF and the DBR one above the other, forming a so-called "doubly periodic" grating, as in this configuration also the DBR confines the mode. Yet, the angular acceptance of CRIGFs is an order of magnitude greater than in classical gratings, even with complex pattern. The aim of the present paper is to identify the phenomenon responsible for the extraordinary large angular acceptance of CRIGFs. We numerically calculate, for the first time to the best of our knowledge, the dispersion curve of the mode excited in the CRIGF. The dispersion curve shows a flat part, where the resonance wavelength is quasi-independent of the angle of incidence, and the flattening grows with the width of the Bragg reflector. We develop an approximate coupled four-wave model, which predicts the extraordinary flattening as a consequence of an additional coupling of the waveguide modes of the GMRF provided by the Bragg grating, that does not exist in the "doubly periodic" gratings

Transmission properties of slanted annular aperture arrays. Giant energy deviation over sub-wavelength distance

International audienceThis paper is devoted to the study of the transmission properties of Slanted Annular Aperture Arrays made in perfectly conducting metal. More precisely, we consider the transmission based on the excitation of the cutoff-less guided mode, namely the TEM mode. We numerically and analytically demonstrate some intrinsic properties of the structure showing a transmission coefficient of at least 50% of an unpolarized incident beam independently of the illumination configuration (angle and plane of incidence). The central symmetry exhibited by the structure is analytically exploited to demonstrate the existence of a polarization state for which all the incident energy is transmitted through the sub-wavelength apertures when the eigenmode is excited, whatever are the illumination and the geometrical parameters. For this state of polarization, the laminar flow of the energy through the structure can exhibit giant deviation over very small distances. An example of energy flow deviation of 220 degrees per wavelength is presented for illustration. The results presented in this paper could be considered as an important contribution to the understanding of the enhanced transmission phenomenon based on the excitation of guided modes. (C) 2015 Optical Society of Americ

Avoided Crossing Patterns and Spectral Gaps of Surface Plasmon Modes in Gold Nano-Structures

The transmission of ultrashort (7 fs) broadband laser pulses through periodic gold nano-structures is studied. The distribution of the transmitted light intensity over wavelength and angle shows an efficient coupling of the incident p-polarized light to two counter-propagating surface plasmon (SP) modes. As a result of the mode interaction, the avoided crossing patterns exhibit energy and momentum gaps, which depend on the configuration of the nano-structure and the wavelength. Variations of the widths of the SP resonances and an abrupt change of the mode interaction in the vicinity of the avoided crossing region are observed. These features are explained by the model of two coupled modes and a coupling change due to switching from the high frequency dark mode to the low frequency bright mode for increasing wavelength of the excitation light. PACS numbers: 73.20.Mf, 42.70.Qs, 42.25.-p,Comment: 17 pages, 4 figure

Réseaux résonnants à Bande Interdite Photonique, nouveaux filtres pour le D.W.D.M.

Dense wavelength division multiplexing (D.W.D.M.) significantly increases the optical telecommunicationtransmission rates. To separate the channels, narrow band spectral filters are necessary.Resonant gratings, composed with a grating engraved on a planar waveguide, are apotential solution. These structures support eigenmodes, which can be excited by a wave comingout of an optical fiber. The excitation creates a resonance peak in the reflected beam,for a given wavelength and incidence angle. In general, the peak does not exhibit the qualitiesrequired for the D.W.D.M.: at oblique incidence, the angular and spectral tolerances are weak,and the line shapes are polarization dependent. Combining photonic crystals concepts, a rigorousphenomenological theory, and a perturbative theory, we design a filter that meet all theconditions imposed by the D.W.D.M..Key words: D.W.D.M., filters, resonance, grating,Les débits des télécommunications optiques sont considérablement accrus par le multiplexagedense en longueur d'onde (D.W.D.M.). Pour séparer les différents canaux, des filtres fréquentielsultra-sélectifs sont nécessaires. Les réseaux résonnants, formés d'un réseau gravé sur un guided'onde plan, sont une solution potentielle. Ces structures supportent des modes propres pouvantêtre excités par une onde issue d'une fibre optique. L'excitation produit un pic de résonance enréflexion à une longueur d'onde et un angle d'incidence donnés. Le pic ne présente en généralpas les qualités requises pour le D.W.D.M. : en incidence oblique, les tolérances angulaire etspectrale sont faibles et les profils dépendent de la polarisation. En conjuguant les concepts descristaux photoniques, une théorie phénoménologique rigoureuse et une théorie perturbative, nousconcevons un filtre répondant à toutes les contraintes imposées par le D.W.D.M.. Nos résultatssont validés par des exemples numériques