Dispersive perfectly matched layers and high-order absorbing boundary conditions for electromagnetic quasinormal modes.

Resonances, also known as quasinormal modes (QNMs) in the non-Hermitian case, play a ubiquitous role in all domains of physics ruled by wave phenomena, notably in continuum mechanics, acoustics, electrodynamics, and quantum theory. The non-Hermiticity arises from the system losses, whether they are material (Joule losses in electromagnetism) or linked to the openness of the problem (radiation losses). In this paper, we focus on the latter delicate matter when considering bounded computational domains mandatory when using, e.g., finite elements. We address the important question of whether dispersive perfectly matched layer (PML) and high-order absorbing boundary conditions offer advantages in QNM computation and modal expansion of the optical responses compared with nondispersive PMLs.

Design and analysis of chiral and achiral metasurfaces with the finite element method.

The rise of metasurfaces to manipulate the polarization states of light motivates the development of versatile numerical methods able to model and analyze their polarimetric properties. Here we make use of a scattered-field formulation well suited to the Finite Element Method (FEM) to compute the Stokes-Mueller matrix of metasurfaces. The major advantage of the FEM lies in its versatility and its ability to compute the optical properties of structures with arbitrary and realistic shapes, and rounded edges and corners. We benefit from this method to design achiral, pseudo-chiral, and chiral metasurfaces with specific polarimetric properties. We compute and analyze their Mueller matrices. The accuracy of this method is assessed for both dielectric and metallic scatterers hosting Mie and plasmonic resonances.

Complete design of a fully integrated graphene-based compact plasmon coupler for the mid-infrared.

A fully integrated waveguide-based, efficient surface plasmon coupler composed of a realistic non-tapered dielectric waveguide with graphene patches and sheet is designed and optimized for the infrared. The coupling efficiency can reach nearly 80% for a coupler as short as 700 nm for an operating wavelength of 12 µm. This work is carried out using rigorous numerical models based on the finite element method taking into account 2D materials as surface conductivities. The key numerical results are supported by physical arguments based on modal approach or resonance condition.

Surface Functionalization with Polymer Membrane or SEIRA Interface to Improve the Sensitivity of Chalcogenide-Based Infrared Sensors Dedicated to the Detection of Organic Molecules.

Priority substances likely to pollute water can be characterized by mid-infrared spectroscopy based on their specific absorption spectral signature. In this work, the detection of volatile aromatic molecules in the aqueous phase by evanescent-wave spectroscopy has been optimized to improve the detection efficiency of future in situ optical sensors based on chalcogenide waveguides. To this end, a hydrophobic polymer was deposited on the surface of a zinc selenide prism using drop and spin-coating methods. To ensure that the water absorption bands will be properly attenuated for the selenide waveguides, two polymers were selected and compared: polyisobutylene and ethylene/propylene copolymer coating. The system was tested with benzene, toluene, and ortho-, meta-, and para-xylenes at concentrations ranging from 10 ppb to 40 ppm, and the measured detection limit was determined to be equal to 250 ppb under these analytical conditions using ATR-FTIR. The polyisobutylene membrane is promising for pollutant detection in real waters due to the reproducibility of its deposition on selenide materials, the ease of regeneration, the short response time, and the low ppb detection limit, which could be achieved with the infrared photonic microsensor based on chalcogenide materials. To improve the sensitivity of future infrared microsensors, the use of metallic nanostructures on the surface of chalcogenide waveguides appears to be a relevant way, thanks to the plasmon resonance phenomena. Thus, in addition to preliminary surface-enhanced infrared absorption tests using these materials and a functionalization via a self-assembled monolayer of 4-nitrothiophenol, heterostructures combining gold nanoparticles/chalcogenide waveguides have been successfully fabricated with the aim of proposing a SEIRA microsensor device.

Continuous family of exact Dispersive Quasi-Normal Modal (DQNM) expansions for dispersive photonic structures.

In photonics, Dispersive Quasi-Normal Modes (DQNMs) refer to optical resonant modes, solutions of spectral problems associated with Maxwell's equations for open photonic structures involving dispersive media. Since these DQNMs are the constituents determining optical responses, studying DQNM expansion formalisms is the key to model the physical properties of a considered system. In this paper, we emphasize the non-uniqueness of the expansions related to the over-completeness of the set of modes and discuss a family of DQNM expansions depending on continuous parameters that can be freely chosen. These expansions can be applied to dispersive, anisotropic, and even non-reciprocal materials. As an example, we particularly demonstrate the modal analysis on a 2-D scattering model where the permittivity of a silicon object is drawn directly from actual measurement data.

Discontinuities in photonic waveguides: rigorous Maxwell-based 3D modeling with the finite element method.

In this paper, a general methodology to study rigorous discontinuities in open waveguides is presented. It relies on a full vector description given by Maxwell's equations in the framework of the finite element method. The discontinuities are not necessarily small perturbations of the initial waveguide and can be very general, such as plasmonic inclusions of arbitrary shapes. The leaky modes of the invariant structure are first computed and then injected as incident fields in the full structure with obstacles using a scattered field approach. The resulting scattered field is finally projected on the modes of the invariant structure making use of their bi-orthogonality. The energy balance is discussed. Finally, the modes of open waveguides periodically structured along the propagation direction are computed. The relevant complex propagation constants are compared to the transmission obtained for a finite number of identical cells. The relevance and complementarity of the two approaches are highlighted on a numerical example encountered in infrared sensing. Open source models allowing us to retrieve most of the results of this paper are provided.

Photonics in highly dispersive media: the exact modal expansion.

We present exact modal expansions for photonic systems including highly dispersive media. The formulas, based on a simple version of the Keldys theorem, are very general since both permeability and permittivity can be dispersive, anisotropic, and even possibly nonreciprocal. A simple dispersive test case where both plasmonic and geometrical resonances strongly interact exemplifies the numerical efficiency of our approach.

Scattering matrix of arbitrarily shaped objects: combining finite elements and vector partial waves.

We demonstrate the interest of combining finite element calculations with the vector partial wave formulation (used in T-matrix and Mie theory) in order to characterize the electromagnetic scattering properties of isolated individual scatterers. This method consists of individually feeding the finite element problem with incident vector partial waves in order to numerically determine the T-matrix elements of the scatterer. For a sphere and a spheroid, we demonstrate that this method determines the scattering matrix to high accuracy. Recurrence relations for a fast determination of the vector partial waves are given explicitly, and an open-source code allowing the retrieval of the presented numerical results is provided.

Two-dimensional grating for narrow-band filtering with large angular tolerances.

A two-dimensional periodic sub-wavelength array of vertical dielectric cylinders on a glass substrate is studied numerically using three different electromagnetic approaches. It is shown that such structure can present a narrow-band spectral resonance characterized by large angular tolerances and 100% maximum in reflection. In particular, in a two-nanometer spectral bandwidth the reflectivity stays above 90% within angles of incidence exceeding 10 degrees for unpolarized light. Bloch modal analysis shows that these properties are due to the excitation of a hybrid mode that is created in the structure by a guided-like mode and a localized cavity mode. The first one is due to the collective effect of the array, while the second one comes from the mode(s) of a single step-index fiber.

Surface plasmon hurdles leading to a strongly localized giant field enhancement on two-dimensional (2D) metallic diffraction gratings.

An extensive numerical study of diffraction of a plane monochromatic wave by a single gold cone on a plane gold substrate and by a periodical array of such cones shows formation of curls in the map of the Poynting vector. They result from the interference between the incident wave, the wave reflected by the substrate, and the field scattered by the cone(s). In case of a single cone, when going away from its base along the surface, the main contribution in the scattered field is given by the plasmon surface wave (PSW) excited on the surface. As expected, it has a predominant direction of propagation, determined by the incident wave polarization. Two particular cones with height approximately 1/6 and 1/3 of the wavelength are studied in detail, as they present the strongest absorption and field enhancement when arranged in a periodic array. While the PSW excited by the smaller single cone shows an energy flux globally directed along the substrate surface, we show that curls of the Poynting vector generated with the larger cone touch the diopter surface. At this point, their direction is opposite to the energy flow of the PSW, which is then forced to jump over the vortex regions. Arranging the cones in a two-dimensional subwavelength periodic array (diffraction grating), supporting a specular reflected order only, resonantly strengthens the field intensity at the tip of cones and leads to a field intensity enhancement of the order of 10 000 with respect to the incident wave intensity. The enhanced field is strongly localized on the rounded top of the cones. It is accompanied by a total absorption of the incident light exhibiting large angular tolerances. This strongly localized giant field enhancement can be of much interest in many applications, including fluorescence spectroscopy, label-free biosensing, surface-enhanced Raman scattering (SERS), nonlinear optical effects and photovoltaics.

Transmission enhancement through square coaxial aperture arrays in metallic film: when leaky modes filter infrared light for multispectral imaging.

The diffractive behavior of arrays of square coaxial apertures in a gold layer is studied. These structures exhibit a resonant transmission enhancement that is used to design tunable bandpass filters for multispectral imaging in the 7-13 µm wavelength range. A modal analysis is used for this design and the study of their spectral features. Thus we show that the resonance peak is due to the excitation of leaky modes of the open photonic structure. Fourier transform infrared (FTIR) spectrophotometry transmission measurements of samples deposited on Si substrate show good agreement with numerical results and demonstrate angular tolerance of up to 30 degrees of the fabricated filters.

All-purpose finite element formulation for arbitrarily shaped crossed-gratings embedded in a multilayered stack.

We propose a novel formulation of the finite element method adapted to the calculation of the vector field diffracted by an arbitrarily shaped crossed-grating embedded in a multilayered stack and illuminated by an arbitrarily polarized plane wave under oblique incidence. A complete energy balance (transmitted and reflected diffraction efficiencies and losses) is deduced from field maps. The accuracy of the proposed formulation has been tested using classical cases computed with independent methods. Moreover, to illustrate the independence of our method with respect to the shape of the diffractive object, we present the global energy balance resulting from the diffraction of a plane wave by a lossy thin torus crossed-grating. Finally, computation time and convergence as a function of the mesh refinement are discussed. As far as integrated energy values are concerned, the presented method shows a remarkable convergence even for coarse meshes.

Versatile full-vectorial finite element model for crossed gratings.

We demonstrate the accuracy of the finite-element method to calculate the diffraction efficiencies of an arbitrarily shaped crossed grating in a multilayered stack illuminated by an arbitrarily polarized plane wave under oblique incidence. The method has been validated by using classical cases found in the literature. Finally, to illustrate the independence of our method with respect to the shape of the diffractive object, we present the global energy balance resulting from the diffraction of a plane wave by a lossy thin torus crossed grating.

Revolution analysis of three-dimensional arbitrary cloaks.

We extend the design of radially symmetric three-dimensional invisibility cloaks through transformation optics to cloaks with a surface of revolution. We derive the expression of the transformation matrix and show that one of its eigenvalues vanishes on the inner boundary of the cloaks, while the other two remain strictly positive and bounded. The validity of our approach is confirmed by finite edge-elements computations for a non-convex cloak of varying thickness.

The finite element method as applied to the diffraction by an anisotropic grating.

The main goal of the method proposed in this paper is the numerical study of various kinds of anisotropic gratings deposited on isotropic substrates, without any constraint upon the diffractive pattern geometry or electromagnetic properties. To that end we propose a new FEM (Finite Element Method) formulation which rigorously deals with each infinite issue inherent to grating problems. As an example, 2D numerical experiments are presented in the cases of the diffraction of a plane wave by an anisotropic aragonite grating on silica substrate (for the two polarization cases and at normal or oblique incidence). We emphasize the interesting property that the diffracted field is non symmetric in a geometrically symmetric configuration.