Composition law for polarizers

The polarization process when polarizers act on an optical field is studied. We give examples for two kinds of polarizers. The first kind presents an anisotropic absorption - as in a polaroid film - and the second one is based on total reflection at the interface with a birefringent medium. Using the Stokes vector representation, we determine explicitly the trajectories of the wave light polarization during the polarization process. We find that such trajectories are not always geodesics of the Poincar\'e sphere as it is usually thought. Using the analogy between light polarization and special relativity, we find that the action of successive polarizers on the light wave polarization is equivalent to the action of a single resulting polarizer followed by a rotation achieved for example by a device with optical activity. We find a composition law for polarizers similar to the composition law for noncollinear velocities in special relativity. We define an angle equivalent to the relativistic Wigner angle which can be used to quantify the quality of two composed polarizers.Comment: 23 pages, 9 figures, accepted for publication in Physical Review

Constructing Fresnel reflection coefficients by ruler and compass

A simple and intuitive geometical method to analyze Fresnel formulas is presented. It applies to transparent media and is valid for perpendicular and parallel polarizations. The approach gives a graphical characterization particularly simple of the critical and Brewster angles. It also provides an interpretation of the relation between the reflection coefficients for both basic polarizations as a symmetry in the plane

Pressure in a tank due to water–ice phase transformation

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Mesure de l’épaisseur et analyse de la composition des revêtements d’alliage d’or et des éventuelles sous-couches par microfluorescence X

Aujourd’hui, les applicateurs de traitements de surface et les donneurs d’ordres s’équipent de spectromètres de microfluorescence X afin de mesurer les épaisseurs des revêtements notamment pour valider leur conformité à la réglementation sur les revêtements de métaux précieux ou au cahier des charges. Les spectromètres de microfluorescence X de nouvelle génération, équipés de logiciels proposant la détermination des épaisseurs et de la composition des revêtements, favorisent la diffusion de cette technologie. Cette utilisation complique les relations clients – fournisseurs à cause des divergences sur l’utilisation des équipements et l’interprétation des résultats obtenus. L’étude présente porte sur la comparaison des valeurs obtenues par spectrométrie de microfluorescence X avec des mesures réalisées sur coupe micrographique, considérée comme la méthode de référence. Plusieurs gammes de traitements, habituelles sur les produits décoratifs, sont étudiées. L’étude montre la réelle difficulté et les limites dans la détermination de l’épaisseur des revêtements d'or par microfluorescence X

Radiative and non-radiative decay of a single molecule close to a metallic nanoparticle

We study the spontaneous emission of a single emitter close to a metallic nanoparticle, with the aim to clarify the distance dependence of the radiative and non-radiative decay rates. We derive analytical formulas based on a dipole-dipole model, and show that the nonradiative decay rate follows a R-6 dependence at short distance, where R is the distance between the emitter and the center of the nanoparticle, as in Forster's energy transfer. The distance dependence of the radiative decay rate is more subtle. It is chiefly dominated by a R-3 dependence, a R-6 dependence being visible at plasmon resonance. The latter is a consequence of radiative damping in the effective dipole polarizability of the nanoparticle. The different distance behavior of the radiative and non-radiative decay rates implies that the apparent quantum yield always vanishes at short distance. Moreover, non-radiative decay is strongly enhanced when the emitter radiates at the plasmon-resonance frequency of the nanoparticle