arXiv subjects

Benjamin Vial

Publications and source records attributed to Benjamin Vial.

15 recordsLinked to original sources

arXiv2025

Fabry-P\'erot quasinormal modes for topological edge states

Topological waveguides supporting quantum valley Hall interfacial states confine waves to interfaces and, due to topological protection, are resistant to backscattering even in the presence of defects. These topological insulators are typically studied by means of an infinite spectral problem. However, practical implementations are necessarily finite. In this work, we propose an alternative framework for analysing topologically non-trivial states in open, finite systems. Our approach is based on a Quasinormal Modal Expansion Method (QMEM), which directly characterizes the existence and excitation of these modes within the open system. The resulting spectrum is complex and discrete and fully describes the topologically non-trivial states, revealing an analogy of topological mode steering as a dispersive Fabry-P\'erot cavity, with a dispersion relation closely related to that of the corresponding infinite (Floquet-Bloch) ribbon problem. Our results illustrate how topologically protected waveguiding can be understood in terms of leaky cavity modes and offers a powerful framework for analysing finite topological devices.

physics.app-ph↗

arXiv2025

Quasinormal modes of Floquet media slabs

Exploiting non-Hermitian wave-matter interactions in time-modulated media to enable the dynamic control of electromagnetic waves requires advanced theoretical tools. In this article we bridge concepts from photonic quasinormal modes (QNMs) and time-varying metamaterials providing the foundation for designing dynamic optical devices with prescribed scattering properties. Establishing the QNM framework for slabs with time-periodic permittivity, and solving the associated nonlinear eigenvalue problem, allows us to derive the QNM expansion capturing the resonant features of the system. This reduced-order model enables highly efficient computation of scattered fields while revealing insight into how modulation couples to resonant modes, creating tailored gain-loss engineering. Our approach is validated through numerical experiments on time-modulated systems, and we design strategies to engineer tailored excitations selectively amplifying or suppressing specific modal contributions.

physics.optics↗

arXiv2025

On the Practicability of Ceramic-Tiled Walls for Sound Absorption by Tuning Cavities

We present the practicality of structuring ceramic tiles for enhancing sound absorption on rigid walls. The cornerstone of our methodology is to structure walls with cavities so that walls effectively behave as heterogeneous absorbing surfaces over a large frequency bandwidth. Using this approach, ceramic tiled walls are developed by integrating tuned cavity structures based on Helmholtz resonators. Such a design leverages the empty joints between tiles to form resonator necks, while the space between the ceramic tiles and the wall acts as the resonator chambers. By arranging these resonators in a spatially graded array, we achieve broadband sound absorption which targets low-frequency noise generated by impacts, footsteps and ambient sources. This makes the system highly suitable for practical architectural applications. The study encompasses the entire process, from numerical modeling and analytical formulation to the fabrication and mounting of resonant tiles, followed by experimental validation, clearly demonstrating the effectiveness of the proposed solution in real-world conditions. The findings highlight the strong potential of this approach for practical tiled room acoustic treatment and noise mitigation.

physics.app-ph↗

arXiv2025

The MACIV multiscale seismic experiments in the French Massif Central (2023-2027): deployment, data quality and availability

In the framework of the MACIV project, a consortium of French laboratories has deployed a temporary seismic network of 100 broadband stations in the French Massif Central (FMC) for 3-4 years (2023-2027). The project aims at imaging the crust and upper mantle of the FMC to better assess the sources of volcanism, and the impacts of the Variscan inheritance or the Cenozoic rift system on volcanic systems. A large-scale array of 35 broadband stations covers the entire FMC and complements the permanent networks to reach a homogeneous coverage with ~35 km spacing. This network, with XP code, is the French contribution to AdriaArray. The XP array is complemented with 3 quasi-linear north-south, east-west and northwest-southeast profiles with inter-station spacing of 5-20 km, making up the XF network of 65 stations. The profiles cross volcanic areas and the main Variscan structures. We describe the experimental setup designed to optimize the performance/cost ratio and minimize the number of field visits, the deployment, the state-of-health monitoring, the data management and the data quality control strategies, outcomes of our 15-years' experience with major temporary seismic experiments in France and neighboring countries, including AlpArray. We also show some preliminary results including hypocenter locations and receiver function analysis. The 2 broadband arrays will be supplemented in 2025 by a month-long deployment of 3 large-N dense arrays of 625 3-C short-period nodes. These dense arrays will complete our multi-scale seismic experiment and illuminate active faults and possible plumbing systems of the youngest volcanoes.

physics.ins-det↗

arXiv2024

Platonic quasi-normal modes expansion

Elastic wave manipulation using large arrays of resonators is driving the need for advanced simulation and optimization methods. To address this we introduce and explore a robust framework for wave control: Quasi-normal modes (QNMs). Specifically we consider the problem for thin elastic plates, where the Green's function formalism is well known and readily exploited to solve multiple scattering problems. By studying the associated nonlinear eigenvalue problem we derive a dispersive QNM expansion, providing a reduced-order model for efficient forced response computations which reveals physical insight into the resonant mode excitation. Furthermore, we derive eigenvalue sensitivities with respect to resonator parameters and apply a gradient-based optimization to design quasi-bound states in the continuum and position eigenfrequencies precisely in the complex plane. Scattering simulations validate our approach in structures such as graded line arrays and quasi-crystals. Drawing on QNM concepts from electromagnetism we demonstrate significant advances in elastic metamaterials, highlighting their potential for tailored wave manipulation.

cond-mat.mtrl-sci↗

arXiv2023

Isospectral open cavities and gratings

Open cavities are often an essential component in the design of ultra-thin subwavelength metasurfaces and a typical requirement is that cavities have precise, often low frequency, resonances whilst simultaneously being physically compact. To aid this design challenge we develop a methodology to allow isospectral twinning of reference cavities with either smaller or larger ones, enforcing their spectra to coincide so that open resonators are identical in terms of their complex eigenfrequencies. For open systems the spectrum is not purely discrete and real, and we pay special attention to the accurate twinning of leaky modes associated with complex valued eigenfrequencies with an imaginary part orders of magnitude lower than the real part. We further consider twinning of 2D gratings, and model these with Floquet-Bloch conditions along one direction and perfectly matched layers in the other one; complex eigenfrequencies of special interest are located in the vicinity of the positive real line and further depend upon the Bloch wavenumber. The isospectral behaviour is illustrated, and quantified, throughout by numerical simulation using finite element analysis.

physics.app-ph↗

arXiv2023

High-frequency homogenization for periodic dispersive media

High-frequency homogenization is used to study dispersive media, containing inclusions placed periodically, for which the properties of the material depend on the frequency (Lorentz or Drude model with damping, for example). Effective properties are obtained near a given point of the dispersion diagram in frequency-wavenumber space. The asymptotic approximations of the dispersion diagrams, and the wavefields, so obtained are then cross-validated via detailed comparison with finite element method simulations in both one and two dimensions.

physics.class-ph↗

arXiv2018

Enhanced tunability in ferroelectric composites through local field enhancement and the effect of disorder

We investigate numerically the homogenized permittivities of composites made of low index dielectric inclusions in a ferroelectric matrix under a static electric field. A refined model is used to take into account the coupling between the electrostatic problem and the electric field dependent permittivity of the ferroelectric material, leading to a local field enhancement and permittivity change in the ferroelectric. Periodic and pseudo-random structures in two dimensions are investigated and we compute the effective permittivity, losses, electrically induced anisotropy and tunability of those metamaterials. We show that the tunability of such composites might be substantially enhanced in the periodic case, whereas introducing disorder in the microstructure weaken the effect of enhanced local permittivity change. Our results may be useful to guide the synthesis of novel composite ceramics with improved characteristics for controllable microwave devices.

physics.app-ph↗

arXiv2016

A class of invisible inhomogeneous media and the control of electromagnetic waves

We propose a general method to arbitrarily manipulate an electromagnetic wave propagating in a two-dimensional medium, without introducing any scattering. This leads to a whole class of isotropic spatially varying permittivity and permeability profiles that are invisible while shaping the field magnitude and/or phase. In addition, we propose a metamaterial structure working in the infrared that demonstrates deep sub-wavelength control of the electric field amplitude and strong reduction of the scattering. This work offers an alternative strategy to achieve invisibility with isotropic materials and paves the way for tailoring the propagation of light at the nanoscale

physics.optics↗

arXiv2016

A coupling model for quasi-normal modes of photonic resonators

We develop a model for the coupling of quasi-normal modes in open photonic systems consisting of two resonators. By expressing the modes of the coupled system as a linear combination of the modes of the individual particles, we obtain a generalized eigenvalue problem involving small size dense matrices. We apply this technique to dielectric rod dimmer of rectangular cross section for Transverse Electric (TE) polarization in a two-dimensional (2D) setup. The results of our model show excellent agreement with full-wave finite element simulations. We provide a convergence analysis, and a simplified model with a few modes to study the influence of the relative position of the two resonators. This model provides interesting physical insights on the coupling scheme at stake in such systems and pave the way for systematic and efficient design and optimization of resonances in more complicated systems, for applications including sensing, antennae and spectral filtering.

physics.optics↗

arXiv2015

Adaptive perfectly matched layer for Wood's anomalies in diffraction gratings

We propose an Adaptive Perfectly Matched Layer (APML) to be used in diffraction grating modeling. With a properly tailored co-ordinate stretching depending both on the incident field and on grating parameters, the APML may efficiently absorb diffracted orders near grazing angles (the so-called Wood's anomalies). The new design is implemented in a finite element method (FEM) scheme and applied on a numerical example of a dielectric slit grating. Its performances are compared with classical PML with constant stretching coefficient.

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↗