arXiv subjects

Frédéric Zolla

Publications and source records attributed to Frédéric Zolla.

16 recordsLinked to original sources

arXiv2026

Nonlocal Optical Response and Surface Susceptibilities: A Systematic Derivation via Spatial Moment Expansion

We present a systematic theory connecting the nonlocal response kernel of a homogeneous medium to its effective surface susceptibilities for an arbitrary curved interface. Starting from the most general tensorial nonlocal constitutive relation and combining a spatial moment expansion with a distributional thin-layer limit, we show that the full complexity of the interfacial response condenses, at leading order, into a single scalar: the surface susceptibility $χ^s$, equal for the tangential and normal components of the electric field. These quantities provide a constructive generalization of the Feibelman $d$-parameters to interfaces of arbitrary curvature, and the curvature corrections, proportional to the geometric invariants $H$ (mean curvature) and $K$ (Gaussian curvature), are derived explicitly. The formalism is illustrated on a comprehensive set of analytically tractable cases (planar, spherical, cylindrical, and ellipsoidal interfaces) for several kernel choices (Gaussian, Yukawa, tensorial Lorentz). Generalized Maxwell boundary conditions are established and compared with the classical Fresnel results.

physics.optics↗

arXiv2026

A generalized perturbative approach for the computation of nonlinear scattering problems

We present a perturbative technique for modeling the scattering of light by a nonlinear material. This approach eliminates the need for an iterative algorithm to solve the fully coupled nonlinear problem. We demonstrate its effectiveness in the cases of a nonlinear anisotropic slab and a nonlinear periodic crystal, both illuminated by a plane wave under conical incidence and arbitrary polarization. Quantitative comparisons of the accuracy and computational time with our previously published rigorous model are provided.

physics.optics↗

arXiv2025

Scattering modeling by a nonlinear slab: exact solution of the full vector problem

We investigate the scattering of light by a nonlinear, anisotropic slab under conical incidence and arbitrary polarization, within the framework of Maxwell's equations, where the nonlinearities are described by nonlinear susceptibility tensors. We develop a fully tensorial numerical method, free from standard simplifications such as the undepleted pump approximation or scalar field assumptions, based on an iterative scheme where each step is solved via the finite element method. The two-dimensional problem is reduced to one dimension by exploiting symmetry arguments. Energy considerations are also addressed. Several numerical experiments involving a potassium titanyl phosphate (KTP) slab and a lithium niobate (LiNbO3) photonic crystal are presented, including cases with incident TE and TM waves, as well as a rotation-based study highlighting the anisotropic capabilities of our numerical model. This work provides a practical and general tool to help the optics research community overcome the limitations of existing models. It may facilitate the design of more advanced experiments to test nonlinear optical theories or improve nonlinear devices.

physics.optics↗

arXiv2024

Physically Agnostic Quasinormal Mode Expansion in Time Dispersive Structures:from Mechanical Vibrations to Nanophotonic Resonances

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.

physics.optics↗

arXiv2023

Dispersive Perfectly Matched Layer and high order Absorbing Boundary Conditions for the computation of Quasinormal modes of open electromagnetic structures

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.

physics.optics↗

arXiv2023

Electrodynamics of an oscillating particle without cheating PART I : In vacuo. PART II : Near a dispersive bulk

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.

physics.optics↗

arXiv2022

Open source models for the parametric study of diffraction gratings in 2D/2.5D/3D with ONELAB/Gmsh/GetDP

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

physics.optics↗

arXiv2020

A 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.

physics.optics↗

arXiv2018

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 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.

physics.optics↗

arXiv2016

Extracting an accurate model for permittivity from experimental data : Hunting complex poles from the real line

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.

physics.optics↗

arXiv2014

Transmission enhancement through square coaxial apertures arrays in metallic film: when leaky modes filter infrared light

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.

physics.optics↗

arXiv2014

Resonant metamaterial absorbers for infrared spectral filtering: quasimodal analysis, design, fabrication and characterization

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.

physics.optics↗

arXiv2013

Quasimodal expansion of electromagnetic fields in open two-dimensionnal structures

A quasimodal expansion method (QMEM) is developed to model and understand the scattering properties of arbitrary shaped two-dimensional (2-D) open structures. In contrast with the bounded case which have only discrete spectrum (real in the lossless media case), open resonators show a continuous spectrum composed of radiation modes and may also be characterized by resonances associated to complex eigenvalues (quasimodes). The use of a complex change of coordinates to build Perfectly Matched Layers (PMLs) allows the numerical computation of those quasimodes and of approximate radiation modes. Unfortunately, the transformed operator at stake is no longer self-adjoint, and classical modal expansion fails. To cope with this issue, we consider an adjoint eigenvalue problem which eigenvectors are bi-orthogonal to the eigenvectors of the initial problem. The scattered field is expanded on this complete set of modes leading to a reduced order model of the initial problem. The different contributions of the eigenmodes to the scattered field unambiguously appears through the modal coefficients, allowing us to analyze how a given mode is excited when changing incidence parameters. This gives new physical insights to the spectral properties of different open structures such as nanoparticles and diffraction gratings. Moreover, the QMEM proves to be extremely efficient for the computation of Local Density Of States (LDOS).

physics.optics↗

arXiv2013

Finite Element Method (Chapter from "Gratings: Theory and Numeric Applications")

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.

physics.optics↗

arXiv2010

Homogenization of nonlocal wire metamaterial via a renormalization approach

It is well known that defining a local refractive index for a metamaterial requires that the wavelength be large with respect to the scale of its microscopic structure (generally the period). However, the converse does not hold. There are simple structures, such as the infinite, perfectly conducting wire medium, which remain non-local for arbitrarily large wavelength-to-period ratios. In this work we extend these results to the more realistic and relevant case of finite wire media with finite conductivity. In the quasi-static regime the metamaterial is described by a non-local permittivity which is obtained analytically using a two-scale renormalization approach. Its accuracy is tested and confirmed numerically via full vector 3D finite element calculations. Moreover, finite wire media exhibit large absorption with small reflection, while their low fill factor allows considerable freedom to control other characteristics of the metamaterial such as its mechanical, thermal or chemical robustness.

physics.optics↗

arXiv2009

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.

physics.optics↗