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Resonances, also known as quasi normal modes (QNM) in the non-Hermitian case, play an ubiquitous role in all domains of physics ruled by wave phenomena, notably in continuum mechanics, acoustics, electrodynamics, and quantum theory. In this paper, we present a QNM expansion for dispersive systems, recently applied to photonics but based on sixty year old techniques in mechanics. The resulting numerical algorithm appears to be physically agnostic, that is independent of the considered physical problem and can therefore be implemented as a mere toolbox in a nonlinear eigenvalue computation library., Comment: 23 pages, 6 figures, dedicated to Natasha and Sasha Movchan on the occasion of their jubilee

A topology optimization method is presented and applied to a blazed diffraction grating in reflection under conical incidence. This type of gratings is meant to disperse the incident light on one particular diffraction order and this property is fundamental in spectroscopy. Conventionally, a blazed metallic grating is made of a sawtooth profile designed to work with the +/-1st diffraction order in reflection. In this paper, we question this intuitive triangular pattern and look for optimal opto-geometric characteristics using topology optimization based on Finite Element modelling of Maxwell's equations. In practical contexts, the grating geometry is mono-periodic but it is enlightened by a 3D plane wave with a wavevector outside of the plane of invariance. Consequently, this study deals with the resolution of a direct and inverse problem using the Finite Element Method in this intermediate state between 2D and 3D: the so-called conical incidence. A multi-wavelength objective is used in order to obtain a broadband blazed effect. Finally, several numerical experiments are detailed. The results show that it is possible to reach a 98% diffraction efficiency on the -1st diffraction order if the optimization is performed on a single wavelength, and that the reflection integrated over the [400,1500]nm wavelength range can be 29% higher in absolute terms, 56% in relative terms, than that of the sawtooth blazed grating when using a multi-wavelength optimization criterion (from 52% to 81%)., Comment: 26 pages (20 for the main paper, 6 for the appendix after the references), 10 figures (8 in the main paper), 8 sections in the main paper, 4 (A,B,C,D) in the appendix

Multi-dielectric coated coverslip can be designed to reach large optical field enhancements when working under proper illumination conditions and in total internal reflection. In an objective-based total internal reflection fluorescence microscopy (TIRF-M), we propose to use the resulting large field enhancement supported in such coverslip to improve TIRF-M sensitivity by amplifying the collected fluorescence signal. We present here the optimization, realization and testing in TIRF-M of resonant coverslips designed to take into account the experimental constraints. The latter's are due to the inverted configuration of TIRF-M together with the use of a high numerical aperture objective. The challenge is therefore to find the best coating design compromising between the angular tolerance and the field enhancement. We will report here enhanced-TIRF-M imaging over model samples but the ultimate goal here is to be able to monitor and quantify dynamics of pathogens at the membrane of living cells., Comment: 2023 23rd International Conference on Transparent Optical Networks (ICTON), Jul 2023, Bucharest, Romania

Optically active achiral metasurfaces offer a promising way to detect chiral molecules based on chiroptic methods. The combination of plasmonic enhanced circular dichroism and reversible optical activity would boost the sensitivity and provide enantiomerselective surfaces while using a single sensing site. In this work, we use metasurfaces containing arrays of U-shaped resonators as a benchmark for analyzing the optical activity of achiral materials. Although the peculiar optical activity of these metasurfaces has 1 been quite well described, we present here an experimental and numerical quantitative determination of the different contributions to the measured optical activity. In particular, it is shown that linear birefringence and retardance contribute, but only marginally, to the apparent circular dichroism of the metasurface associated with the excitation of magnetoelectric modes. We then numerically demonstrate the peculiar near-field properties of the magneto-electric modes and explain how these properties could be reflected in the far-field polarimetric properties in the presence of chiral molecules. This work provides alternatives for the detection scheme of chiral molecules using plasmonic resonators., Comment: ACS Applied Optical Materials, 2023

We revisit the design of cloaks, without resorting to any geometric transform. Cancellation techniques and anomalous resonances have been applied for this purpose. Instead of a deductive reasoning, we propose a novel mono-objective optimization algorithm, namely a ternary grey wolf algorithm, and we adapt a bi-objective optimization algorithm. Firstly, the proposed chaotic ternary grey wolf algorithm searches three-valued spaces for all permittivity values in the cloak while minimizing the summation of a protection criterion and an invisibility criterion. Secondly, a bi-objective genetic algorithm is adapted to find pairs of optimal values of invisibility and protection.

Resonances, also known as quasinormal modes (QNM) 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. Dispersive perfectly matched layers and absorbing boundary conditions are studied.

In this paper, the electromagnetic radiation from an oscillating particle placed in the vicinity of an object of size comparable to the wavelength is studied. Although this problem may seem academic at first sight, the details of the calculations are presented throughout without any detail left under the carpet. A polyharmonic decomposition of the radiation sources allows the diffraction problem to be fully characterised while satisfying energy conservation. Finally, the source expressions obtained are suitable for use in a numerical code. A 3D illustration using finite elements is provided., Comment: 40 pages

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.

In this paper, a general methodology to study rigorously 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 to retrieve most of the results of this paper are provided., Comment: The GetDP/Gmsh scripts allowing to retrieve the results are attached

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

Photonic crystals are periodic structures which prevent light propagation along one or more directions in certain frequency intervals. Their band spectrum is usually analyzed using Floquet-Bloch decomposition. This spectrum is located on the real axis, and it enters the complex plane when absorption and dispersion is considered in the dielectric permittivity of material constituents. Here, we review fundamental definition and properties of dispersion law and group velocity in photonic crystals and we illustrate them with numerical examples., Comment: book chapter

We present a framework to solve non-linear eigenvalue problems suitable for a Finite Element discretization. The implementation is based on the open-source finite element software GetDP and the open-source library SLEPc. As template examples, we propose and compare in detail different ways to address the numerical computation of the electromagnetic modes of frequency-dispersive objects. This is a non-linear eigenvalue problem involving a non-Hermitian operator. A classical finite element formulation is derived for five different solutions and solved using algorithms adapted to the large size of the resulting discrete problem. The proposed solutions are applied to the computation of the dispersion relation of a diffraction grating made of a Drude material. The important numerical consequences linked to the presence of sharp corners and sign-changing coefficients are carefully examined. For each method, the convergence of the eigenvalues with respect to the mesh refinement and the shape function order, as well as computation time and memory requirements are investigated. The open-source template model used to obtain the numerical results is provided. Details of the implementation of polynomial and rational eigenvalue problems in GetDP are given in appendix., Comment: An open-source model showing the implementation of all the method is available at the following address https://gitlab.onelab.info/doc/models/tree/master/NonLinearEVP

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 an ellipsoid, 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.

This document aims at presenting both theoretical and practical aspects of the grating2D.pro and grating3D.pro [1] ONELAB [2] models. The 2D model grating2D.pro applies to so-called mono-dimensional gratings, i.e. structures having one direction of invariance. Various geometries and materials can be handled or easily added. The two classical scalar polarization cases, denoted here E// and H//, are addressed as well as the conical vector case. The output consists in a full energy balance of the problem computed from the field maps. The 3D vector model grating3D.pro applies to crossed-gratings. These models are based on free the open source software Gmsh, GetDP and their interface ONELAB. [1] https://gitlab.onelab.info/doc/models/-/wikis/Diffraction-gratings [2] https://onelab.info, Comment: arXiv admin note: text overlap with arXiv:1302.1032

In this letter, we describe a very general procedure to obtain a causal fit of the permittivity of materials from experimental data with very few parameters. Unlike other closed forms proposed in the literature, the particularity of this approach lies in its independence towards the material or frequency range at stake. Many illustrative numerical examples are given and the accuracy of the fitting is compared to other expressions in the literature., Comment: The python code and datasets used to obtain the numerical results in this paper can be found at : https://git.io/v14Jb

Numerical calculation of modes in dispersive and absorptive systems is performed using the finite element method. The dispersion is tackled in the frame of an extension of Maxwell's equations where auxiliary fields are added to the electromagnetic field. This method is applied to multi-domain cavities and photonic crystals including Drude and Drude-Lorentz metals. Numerical results are compared to analytical solutions for simple cavities and to previous results of the literature for photonic crystals, showing excellent agreement. The advantages of the developed method lie on the versatility of the finite element method regarding geometries, and in sparing the use of tedious complex poles research algorithm. Hence the complex spectrum of resonances of non-hermitian operators and dissipative systems, like two-dimensional photonic crystal made of absorbing Drude metal, can be investigated in detail. The method is used to reveal unexpected features of their complex band structures., Comment: to be submitted for publication

We consider arrays of square coaxial apertures in a gold layer and study their diffractive behavior in the far infrared region. These structures exhibit a resonant transmission enhancement that is used to design tunable bandpass filters. We provide a study of their spectral features and show by a modal analysis 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 up to 30 degrees of the fabricated filters., Comment: 4 pages, 3 figures

We present a modal analysis of metal-insulator-metal (MIM) based metamaterials in the far infrared region. These structures can be used as resonant reflection bandcut spectral filters that are independent of the polarization and direction of incidence because of the excitation of quasimodes (modes associated with a complex frequency) leading to quasi-total absorption. We fabricated large area samples made of chromium nanorod gratings on top of Si/Cr layers deposited on silicon substrate and measurements by Fourier Transform spectrophotometry show good agreement with finite element simulations. A quasimodal expansion method is developed to obtain a reduced order model that fits very well full wave simulations and that highlights excitation conditions of the modes., Comment: 8 pages, 7 figures

In this chapter, we demonstrate a general formulation of the Finite Element Method allowing to calculate the diffraction efficiencies from the electromagnetic field diffracted by arbitrarily shaped gratings embedded in a multilayered stack lightened by a plane wave of arbitrary incidence and polarization angle. It relies on a rigorous treatment of the plane wave sources problem through an equivalent radiation problem with localized sources. Bloch conditions and a new Adaptative Perfectly Matched Layer have been implemented in order to truncate the computational domain. We derive this formulation for both mono-dimensional gratings in TE/TM polarization cases (2D or scalar case) and for the most general bidimensional or crossed gratings (3D or vector case). The main advantage of this formulation is its complete generality with respect to the studied geometries and the material properties. Its principle remains independent of both the number of diffractive elements by period and number of stack layers. The flexibility of our approach makes it a handy and powerful tool for the study of metamaterials, finite size photonic crystals, periodic plasmonic structures., Comment: Finite Element Method (in "Gratings:Theory and Numeric Applications") This document contains 47 pages and 23 figures. A version of this chapter with high resolution figures is available online: http://www.fresnel.fr/files/gratings/Chapter5.pdf The full book is available online: http://www.fresnel.fr/numerical-grating-book Title: Gratings:Theory and Numeric Applications ISBN: 2-85399-860-4

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., Comment: 6 pages, 4 figures