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Spectrally modulated Stokes polarimeters use a pair of high-order crystal retarders to generate a spectrally dependent modulation of the polarization of light. In these systems, the detected intensity versus wavenumber spectrum is usually referred to as a channeled spectrum, and the Fourier inversion of this spectrum allows the determination of Stokes parameters of light without needing any other mechanical or active device for polarization control. This work proposes a spectrally modulated polarimeter beyond the concept of a channeled wavenumber spectrum, so effectively detaching the spectral modulation from the Fourier analysis technique. The wavelength domain analysis we use is best suited for dispersive spectrometers offering intensity versus wavelength measurements. The technique is illustrated with the measurement of very small optical rotations produced by sucrose solutions. The proposed technique is easily extendable to spectrally modulated Mueller polarimeters.

We advance an analytical model describing the polarimetric response of a depolarizing retarder whose retardance varies spatially in magnitude or in orientation. The variation of the retarder parameters may be either of deterministic or of random nature. The model provides both the mean values and the uncertainties of the parameters. Its application is illustrated on two experimental examples, respectively covering the deterministic and the random cases.

This work expands the use of spectroscopic ellipsometry to surfaces with roughness that is similar to or larger than the wavelength of the incident light. By using a custom-built spectroscopic ellipsometer and varying the angle of incidence, we were able to differentiate between the diffusely scattered and specularly reflected components. Our findings demonstrate that measuring the diffuse component at specular angles is highly beneficial for ellipsometry analysis, as its response is equivalent to that of a smooth material. This allows for accurate determination of the optical constants in materials with extremely rough surfaces. Our results have the potential to broaden the scope and utility of the spectroscopic ellipsometry technique.

The Fresnel–Arago laws of interference are five laws describing the interference of polarized light and published in 1819. The fifth law has been systematically forgotten in almost all available re...

This Letter shows the advantage of applying the complete temporal basis in polarimeters based on photoelastic modulators in lieu of the commonly used truncated temporal basis that results in a discrete selection of the Fourier harmonics used for data processing. Results are numerically and experimentally illustrated for a complete Mueller-matrix-based polarimeter on four photoelastic modulators.

The present erratum is intended to correct some typos as well as to complement Appendices B and C in our paper [J. Opt. Soc. Am. A 36, 403 (2019)JOAOD60740-323210.1364/JOSAA.36.000403].

In this work, we describe the design and implementation of a Mueller matrix imaging polarimeter that uses a polarization camera as a detector. This camera simultaneously measures the first three Stokes components, allowing for the top three rows of the Mueller matrix to be determined after only N = 4 measurements using a single rotating compensator, which is sufficient to fully characterize nondepolarizing samples. This setup provides the polarimetric analysis with micrometric resolution in about 3 seconds and can also perform live birefringence imaging at the camera frame rate by fixing the compensator at a static 45° angle. To further improve the conditioning of the setup, we also give the first experimental demonstration of an optimal elliptical retarder design.

International audience; Chirality is found at all length scales in nature, and chiral metasurfaces have recently attracted attention due to their exceptional optical properties and their potential applications. Most of these metasurfaces are fabricated by top-down methods or bottom-up approaches that cannot be tuned in terms of structure and composition. By combining grazing incidence spraying of plasmonic nanowires and nanorods and Layer-by-Layer assembly, we show that nonchiral 1D nano-objects can be assembled into scalable chiral Bouligand nanostructures whose mesoscale anisotropy is controlled with simple macroscopic tools. Such multilayer helical assemblies of linearly oriented nanowires and nanorods display very high circular dichroism up to 13 000 mdeg and giant dissymmetry factors up to g ≈ 0.30 over the entire visible and near-infrared range. The chiroptical properties of the chiral multilayer stack are successfully modeled using a transfer matrix formalism based on the experimentally determined properties of each individual layer. The proposed approach can be extended to much more elaborate architectures and gives access to template-free and enantiomerically pure nanocomposites whose structure can be finely tuned through simple design principles.

The emission of circularly polarized light is central to many applications, including data storage, optical quantum computation, biosensing, environmental monitoring, and display technologies. An emerging method to induce (chiral) circularly polarized (CP) electroluminescence from the active layer of polymer light-emitting diodes (polymer OLEDs; PLEDs) involves blending achiral polymers with chiral small-molecule additives, where the handedness/sign of the CP light is controlled by the absolute stereochemistry of the small molecule. Through the in-depth study of such a system we report an interesting chiroptical property: the ability to tune the sign of CP light as a function of active layer thickness for a fixed enantiomer of the chiral additive. We demonstrate that it is possible to achieve both efficient (4.0 cd/A) and bright (8000 cd/m2) CP-PLEDs, with high dissymmetry of emission of both left-handed (LH) and right-handed (RH) light, depending on thickness (thin films, 110 nm: gEL = 0.51, thick films, 160 nm: gEL = -1.05, with the terms "thick" and "thin" representing the upper and lower limits of the thickness regime studied), for the same additive enantiomer. We propose that this arises due to an interplay between localized CP emission originating from molecular chirality and CP light amplification or inversion through a chiral medium. We link morphological, spectroscopic, and electronic characterization in thin films and devices with theoretical studies in an effort to determine the factors that underpin these observations. Through the control of active layer thickness and device architecture, this study provides insights into the mechanisms that result in CP luminescence and high performance from CP-PLEDs, as well as demonstrating new opportunities in CP photonic device design.

We present a general method for redefining the permittivity and permeability tensors of a medium or structure exhibiting spatial dispersion (SD). The method effectively separates the electric and magnetic contributions that are intertwined in the traditional description of the SD-dependent permittivity tensor. The redefined material tensors are the ones to be used in the common methods for calculating the optical response of layered structures, thus enabling modeling of experiments in the presence of SD.

A complete formulation of the electromagnetic problem corresponding to the light incidence from a transparent to an absorbing medium (isotropic materials) is developed. According to the standard separation in s and p polarization cases, we explicitly obtain all the relevant formulas that relate the polarization and Poynting vectors of the reflected and transmitted beams with the incident ones. Overall, the procedure is compact since it is short and complete.

The dielectric function of V O x and V 2 O 5 thin films is determined with the use of a spectroscopic Mueller matrix ellipsometer from 1.5 to 5.0 eV. The complex dielectric function of the films is calculated using the measured Mueller matrices filtered with the Cloude decomposition. V O x shows high absorption in the UV region, a Tauc–Lorentz gap around 2.4 eV, and non-vanishing absorption in the visible. V 2 O 5 shows a high absorption band centered at 2.87 eV, an indirect optical band gap at 1.95 eV, and a direct optical band gap at 2.33 eV. The ellipsometric characterization is supported by Raman, x-ray photoelectron, and photoluminescence spectroscopy.

We study the scattering of polarized light by two equal corner stacked Au nanorods that exhibit strong electromagnetic coupling. In the far field, this plasmonic dimer manifests very prominent asymmetric scattering in the transverse direction. Calculations based on a system of two coupled oscillators, as well as simulations based on the boundary element method, show that, while in one configuration both vertical and horizontal polarization states are scattered to the detector, when we interchange the source and the detector, the scattered intensity of the horizontal polarization drops to zero. Following Perrin&rsquo, s criterion, it can be shown that this system, as well as any other linear system not involving magneto-optical effects, obeys the optical reciprocity principle. We show that the optical response of the plasmonic dimer, while preserving electromagnetic reciprocity, can be used for the non-reciprocal transfer of signals at a subwavelength scale.

Optical components based on Pancharatman-Berry phase feature a polarization-dependent diffraction that can be used to fabricate lenses and gratings with unique properties. In recent years, the great progress made in the fabrication of the metasurfaces required for these optical components has lowered their cost and has made them widely available. One of the often overlooked properties of optical components based on geometrical phases is that, contrary to dynamical phases, their phase can be measured using a polarimetric technique without need to resorting to interferometry methods. This is possible because the Pancharatnam-Berry phase is not controlled by an optical path difference; it results from a space variant polarization manipulation. In this work we apply Mueller matrix microscopy to measure the geometrical phase of GP lenses and polarization gratings. We show that a single space resolved Mueller matrix measurement with micrometric resolution is enough to obtain a full characterization phase-profile of these GP-based optical components and evaluate their performance.The analysis can be extended to multiple wavelengths to study the chromatic dependence of the optical parameters of the lens or the grating.

Polymer thin films that emit and absorb circularly polarised light have been demonstrated with the promise of achieving important technological advances; from efficient, high-performance displays, to 3D imaging and all-organic spintronic devices. However, the origin of the large chiroptical effects in such films has, until now, remained elusive. We investigate the emergence of such phenomena in achiral polymers blended with a chiral small-molecule additive (1-aza[6]helicene) and intrinsically chiral-sidechain polymers using a combination of spectroscopic methods and structural probes. We show that – under conditions relevant for device fabrication – the large chiroptical effects are caused by coupling of electric and magnetic transition dipole moments (natural optical activity), not structural chirality as previously assumed, and may occur because of local order in a cylinder blue phase-type organisation. This disruptive mechanistic insight into chiral polymer thin films will offer new approaches towards chiroptical materials development after almost three decades of research in this area.

Polymer thin films that emit and absorb circularly polarised light have been demonstrated with the promise of achieving important technological advances; from efficient, high-performance displays, to 3D imaging and all-organic spintronic devices. However, the origin of the large chiroptical effects in such films has, until now, remained elusive. We investigate the emergence of such phenomena in achiral polymers blended with a chiral small-molecule additive (1-aza[6]helicene) and intrinsically chiral-sidechain polymers using a combination of spectroscopic methods and structural probes. We show that – under conditions relevant for device fabrication – the large chiroptical effects are caused by coupling of electric and magnetic transition dipole moments (natural optical activity), not structural chirality as previously assumed, and may occur because of local order in a cylinder blue phase-type organisation. This disruptive mechanistic insight into chiral polymer thin films will offer new approaches towards chiroptical materials development after almost three decades of research in this area.

This report shows how the net supramolecular chirality that emerged by spontaneous mirror-symmetry breaking (SMSB) at the mesoscale level can be transferred towards asymmetric solution chemistry. The J-aggregates obtained by self-assembly of an achiral porphyrin act as chiral counteranions in an iminium-promoted Diels-Alder reaction, leading to enantiomeric imbalances in the final adducts.

Chirality 32(5), 619 - 631 (2020). doi:10.1002/chir.23213, An enantiomerically pure (R)‐2‐methylpyrrolidine‐based anilino squaraine crystallizes in two chiral polymorphs adopting a monoclinic C2 and an orthorhombic P212121 structure, respectively. By various thin‐film preparation techniques, a control of the polymorph formation is targeted. The local texture of the resulting textured thin films is connected to the corresponding optical properties. Special attention is paid to an unusual Davydov splitting, the anisotropic chiroptical response arising from preferred out‐of‐plane orientation of the crystallites, and the impact of the polymorph specific excitonic coupling., Published by Wiley Interscience, New York, NY [u.a.]

Methods used to compute the reflection or transmission Mueller matrix of stratified media assume light is a monochromatic plane wave, but measurements with spectroscopic devices invariably involve a finite distribution of wavelengths and incidence angles. Consequently, there can be stark disagreement between calculation and experiment, especially when the specimen includes a thick non-opaque layer. To accurately model specimens with a thick layer, it is sometimes necessary to explicitly include the coherence of the light in models. For anisotropic and/or optically active media, we distinguish between five regimes of coherence. Algebraic expressions valid for all regimes are given. Experimental data spanning multiple regimes is modeled.

The common mode of observation in an imaging Mueller matrix polarimeter is orthoscopic observation, where the front focal plane of the objective is focused onto the camera sensor. Different points on the camera sensor correspond to different points on the sample. But for certain applications, valuable complementary information is obtained when the back focal plane of the objective is focused onto the camera sensor. This observation mode informs about the directions distribution of light so that different points on the camera sensor correspond to different directions of light propagation through the specimen. We distinguish between two types of illumination; the sample can be illuminated with a large numerical aperture, such that what is measured corresponds to usual transmission or specular reflection ellipsometry (Mueller conoscopy), or the sample may be illuminated with collimated light, and what is measured corresponds to scattering or diffraction of light (Mueller diffractometry). A polarimeter suitable for back-focal measurements is described and illustrative examples of Mueller conoscopy and Mueller diffractometry are presented.

Experimental Mueller matrices contain certain amount of uncertainty in their elements and these uncertainties can create difficulties for decomposition methods based on analytic solutions. In an earlier paper [1] , we proposed a decomposition method for depolarizing Mueller matrices by using certain symmetry conditions. However, because of the experimental error, that method creates over-determined systems with non-unique solutions. Here we propose to use least squares minimization approach in order to improve the accuracy of our results. In this method, we are taking into account the number of independent parameters of the corresponding symmetry and the rank constraints on the component matrices to decide on our fitting model. This approach is illustrated with experimental Mueller matrices that include material media with different Mueller symmetries.

Liquid crystal variable retarders (LCVRs) will be used for the first time in a space instrument, the Solar Orbiter mission of the European Space Agency, as polarization states analyzers (PSAs). These devices will determine the Stokes parameters of the light coming from the Sun by temporal polarization modulation, using the so-called modulation matrix O. This is a matrix constituted by the first rows of properly selected PSA Mueller matrices. Calibrating a space instrument, in particular, finding O, is a critical point because in a spacecraft there is no possibility of physical access. Due to the huge difficulty in calibrating the complete instruments in all possible scenarios, a more complete calibration of the individual components has been done in ground in order to make extrapolations to obtain O in-flight. Nevertheless, apart from the individual calibrations, the experimental errors and nonideal effects that inhibit the system to reach the designed and theoretical values must be known. In this work, description and study of these effects have been done, focusing on the nonideal effects of the LCVRs and the azimuthal misalignments between the optical components of the PSA during the mechanical assembly. The Mueller matrix of a representative LCVR has been measured and mathematically decomposed by logarithm decomposition, looking for values of circular birefringence and fast axis angle variations as a function of voltage. These effects, in the absence of other nonidealities, affect the polarimetric performance, reducing the polarimetric efficiencies in some cases until 11%. Nevertheless, in this case, they are negligible if compared to the other nonideality studied, which are the azimuthal misalignments between the PSA optical components. The study presented in this work is key to extrapolate the PSA O matrix if the expected instrumental set-point temperatures are not reached in flight and can be used for the design and implementation of other polarimetric instruments.Liquid crystal variable retarders (LCVRs) will be used for the first time in a space instrument, the Solar Orbiter mission of the European Space Agency, as polarization states analyzers (PSAs). These devices will determine the Stokes parameters of the light coming from the Sun by temporal polarization modulation, using the so-called modulation matrix O. This is a matrix constituted by the first rows of properly selected PSA Mueller matrices. Calibrating a space instrument, in particular, finding O, is a critical point because in a spacecraft there is no possibility of physical access. Due to the huge difficulty in calibrating the complete instruments in all possible scenarios, a more complete calibration of the individual components has been done in ground in order to make extrapolations to obtain O in-flight. Nevertheless, apart from the individual calibrations, the experimental errors and nonideal effects that inhibit the system to reach the designed and theoretical values must be known. In this work, d...

7 pags., 6 figs., 1 app., A radial polarization converter is a super-structured optical retarder that converts a conventional linearly polarized light beam into a structured beam with radial or azimuthal polarization. We present a new type of these sophisticated optical elements, which is made of porous nanostructured sculptured single thin films or multilayers prepared by physical vapor deposition at an oblique angle. They are bestowed with an axisymmetric retardation activity (with the fast axis in a radial configuration). In particular, a Bragg microcavity multilayer that exhibits a tunable transmission peak in the visible range with a retardance of up to 0.35 rad has been fabricated using this methodology. Owing to the highly porous structure of this type of thin films and multilayers, their retardance could be switched off by liquid infiltration. These results prove the possibility of developing wavelength dependent (through multilayer optical design) and switchable (through vapor condensation or liquid infiltration within the pore structure) radial polarization converters by means of oblique angle physical vapor deposition., We acknowledge the support of the European Regional Development Funds program (EU-FEDER), the Spanish MinistryEconomy, Industry, and Competitiveness (projects 201560E055,MAT2016-79866-R, RECUPERA 2020 and Red CONSOLIDER MAT2015-69035-REDC).

We propose a novel, computationally efficient integral decomposition of depolarizing Mueller matrices allowing for the obtainment of a nondepolarizing estimate, as well as for the determination of the elementary polarization properties, in terms of mean values and variances-covariances of their fluctuations, of a weakly anisotropic depolarizing medium. We illustrate the decomposition on experimental examples and compare its performance to those of alternative decompositions.

Conventional generalized ellipsometry instrumentation is capable of measuring 12 out of the 16 elements of the Mueller matrix of the sample. The missing column (or row) of the experimental partial Mueller matrix can be analytically determined under additional assumptions. We identify the conditions necessary for completing the partial Mueller matrix to a full one. More specifically, such a completion is always possible if the sample is nondepolarizing; the fulfillment of additional conditions, such as the Mueller matrix exhibiting symmetries or being of a special two-component structure, are necessary if the sample is depolarizing. We report both algebraic and numerical procedures for completing the partial 12-element Mueller matrix in all tractable cases and validate them on experimental examples.

A spectroscopic Mueller matrix ellipsometer based on two rotating Fresnel rhomb compensators with a nearly achromatic response and optimal retardance is described. In this instrument, the compensators rotate in a discrete manner instead of continuously rotating, and this allows for a well-conditioned measurement even for low intensity samples. Moreover, in this configuration, the exposure time of the CCD detector can be varied within orders of magnitude without interfering with the dynamics of the compensator rotation. An optimization algorithm determines the optimal set of discrete angles that allows the determination of the Mueller matrix in the presence of noise. The calibration of the instrument is discussed, and examples of experimentally determined Mueller matrices are provided.

Chiral J-aggregates of achiral amphiphilic porphyrins (4-sulfonatophenyl and aryl meso-substituted porphyrins) show several effects under the hydrodynamic forces of common stirring. These effects can be classified as pure mechanic (e. g. elasticity, plasticity and breaking of the self-assembly non-covalent bonding) and chemically selective as detected in the formation/growth of the nanoparticles. Diastereoselective, enantioselective and, depending on the sign of chiral shear forces, even enantiospecific selections have been described. Some types of these effects have been reported in other type of J-aggregates. Reversible and irreversible structural effects have been studied by atomic force imaging. The determination of the optical polarization properties (linear and circular) of their solutions is best done using Mueller matrix polarimetry methods.

This work compares the reflection optical response of a homogeneous sample with natural optical activity with the Bragg reflection from an inhomogeneous system consisting of a periodic helicoidal structure. Examples of periodic helicoidal systems are cholesteric liquid crystals and the cuticle of some beetles. For transmitted light natural optical activity and Bragg reflection essentially lead to the same type of optical response, but there are fundamental differences on how they reflect circularly polarized light. The Mueller matrix symmetries for the two types of media are theoretically deduced and experimentally verified with ellipsometry measurements.

The complex optical constants and the subsurface damage layer of uniaxial doped 6H-SiC wafers are measured using Mueller matrix spectroscopic ellipsometry. A comparison is made between measurements on a single-sided polished wafer that can be treated as a semi-infinite substrate and on a double-sided polished wafer that is studied with the partial-wave theory. The refractive indices and extinction coefficients for ordinary and extraordinary directions are determined below the bandgap after point-by-point fitting of experimental Mueller matrices. The thickness of the subsurface damage layer caused by mechanical polishing and chemical mechanical polishing determined by ellipsometry is consistent with the result of transmission electron microscope. The ellipsometry results show that the analysis based on a double-sided polished wafer is more informative about the optical properties of 6H-SiC than that of the single-sided polished wafer as it renders information properties about the bulk properties of the material, for example, allowing the determination of the very weak absorption coefficient ( k ≈ 10 − 4) due to doping.

We show that an incomplete, nine-element Mueller matrix with a row and a column missing, obtained in a partial polarimetry experiment, can be completed to a full, 16-element Mueller matrix, provided depolarization is absent experimentally. There exist exactly two solutions for the missing row and column, differing from one another only by the signs of the respective row and column elements. To select the correct solution, additional information on the sample properties, such as weak anisotropy or special symmetry, is needed. We provide analytical and numerical procedures for completing the partial Mueller matrix for the cases of practical interest and illustrate the approach on an experimental example.

The authors report on an algebraic procedure, allowing for the completion of an experimental nondepolarizing Mueller matrix with a column or a row missing to a full 16-element one. The method provides a closed-form solution for the missing column or row and is illustrated on single-wavelength, spectroscopic, and imaging experimental examples.The authors report on an algebraic procedure, allowing for the completion of an experimental nondepolarizing Mueller matrix with a column or a row missing to a full 16-element one. The method provides a closed-form solution for the missing column or row and is illustrated on single-wavelength, spectroscopic, and imaging experimental examples.

International audience; Two coherent waves carrying orthogonal polarizations do not interfere when they superpose, but an interference pattern is generated when the two waves share a common polarization. This well-known principle of coherence and polarization is exploited for the experimental demonstration of a novel method for performing circular dichroism measurements whereby the visibility of the interference fringes is proportional to the circular dichroism of the sample. Our proof-of-concept experiment is based upon an analog of Young's double-slit experiment that continuously modulates the polarization of the probing beam in space, unlike the time modulation used in common circular dichroism measurement techniques. The method demonstrates an accurate and sensitive circular dichroism measurement from a single camera snapshot, making it compatible with real-time spectroscopy.

In this work, we derive closed-form expressions for determination of the linear birefringence and linear dichroism of uniaxial crystals utilizing transmission ellipsometry measurements at small angles of incidence in c -cut crystal substrates. The model-free method we use is an algebraic generalization of the method reported in Appl. Opt. 44, 3153 (2005).APOPAI0003-693510.1364/AO.44.003153 The optical anisotropy of substrates of sapphire, 4H-SiC, and 6H-SiC single crystals is measured for illustration.

In 1822 Augustin Fresnel discovered the circular polarization of light with an experiment in which a plane polarized beam was resolved into its left- and right- circularly polarized components after refraction at slightly different angles at the interface between two different species of quartz that formed a composite prism, called the Fresnel triprism. Fresnel’s landmark experiment, once popular, remains today a very little known method for producing circularly polarized light.

Nanostructures with chiral geometries exhibit strong polarization rotation. However, achieving reversible modulation of chirality and polarization rotation in device-friendly solid-state films is difficult for rigid materials. Here, we describe nanocomposites, made by conformally coating twisted elastic substrates with films assembled layer-by-layer from plasmonic nanocolloids, whose nanoscale geometry and rotatory optical activity can be reversibly reconfigured and cyclically modulated by macroscale stretching, with up to tenfold concomitant increases in ellipticity. We show that the chiroptical activity at 660 nm of gold nanoparticle composites is associated with circular extinction from linear effects. The polarization rotation at 550 nm originates from the chirality of nanoparticle chains with an S-like shape that exhibit a non-planar buckled geometry, with the handedness of the substrate's macroscale twist determining the handedness of the S-like chains. Chiroptical effects at the nexus of mechanics, excitonics and plasmonics open new operational principles for optical and optoelectronic devices from nanoparticles, carbon nanotubes and other nanoscale components.

This work reports the conversion of a commercial polarization microscope (Zeiss Jenaval) into an automatized Mueller matrix microscope. A Mueller matrix measurement provides the value of all the optical properties of a specimen (linear dichroism, linear birefringence, circular dichroism etc.) at a specific wavelength. In contrast to traditional polarization microscopes, which use white light and crossed polarizers to generate colored interference patterns that are analyzed by the microscope user and give only semi-quantitative results, here we demonstrate that it is possible to convert a polarization microscope into a Mueller microscope by only adding two motorized rotating compensators into the optical path without altering the optics or other opto-mechanical elements of the microscope. To our knowledge this is the most compact, fast and handy Mueller microscope ever developed. The performance of this new Mueller matrix microscope is illustrated with some birefringence measurements on textile fibers Este trabajo describe la conversión de un microscopio de polarización comercial (Zeiss Jenaval) en un microscopio de matriz de Mueller automatizado. Una medida de la matriz de Mueller proporciona todas las propiedades ópticas de una muestra (dicroísmo lineal, birrefringencia lineal, dicroísmo circular, etc) para una longitud de onda dada. Los microscopios de polarización tradicionales usan luz blanca y polarizadores cruzados para generar un patrón de colores interferencia que debe ser interpretado por el usuario del microscopio y proporciona resultados sólo semi-cuantitativos. En este trabajo demostramos que añadiendo dos compensadores rotatorios actuados por sendos motores es posible convertir un microscopio de polarización en un microscopio de matriz de Mueller sin alterar la óptica u otros elementos opto-mecánicos del microscopio. Creemos que este es el microscopio de matriz de Mueller más compacto, rápido y práctico que se ha desarrollado. El funcionamiento de este microscopio se demuestra con algunas medidas de birrefringencia en fibras textiles

International audience; We study the optical response of two coupled oriented dipoles with the dimer axis perpendicular to the wave vector of light by analyzing how their scattering matrix can be decomposed. The scattering matrix can be written as a linear combination of three terms with a clear physical meaning: one for each particle and another that is responsible for the coupling and that vanishes for noninteracting or distant particles. We show that the interaction term may generate optical activity for certain scattering directions and that this effect manifests itself mostly in the near field. This simple and intuitive theory based on matrix and vector states of oriented dipoles also describes hybridization processes and Fano resonances. The decomposition method can be also formulated in terms of a hybrid basis that allows us to quantitatively determine the individual contribution of the in-phase and out-of-phase coupling modes to the overall intensity. Our method can help to understand the optical response of more complex nanostructures that can be decomposed into dipole terms. The results are illustrated in gold nanoantenna dimers which exhibit a strong dipolar resonance.