37 citations · 137 across the 29 of their papers we have counts for
37 papers
Trapped modes in electromagnetic waveguides
Anne-Sophie Bonnet-Ben Dhia, Lucas Chesnel, Sonia Fliss
We consider the Maxwell's equations with perfect electric conductor boundary conditions in three-dimensional unbounded domains which are the union of a bounded resonator and one or…
A few techniques to achieve invisibility in waveguides
Lucas Chesnel
The aim of this lecture is to consider a concrete problem, namely the identification of situations of invisibility in waveguides, to present techniques and tools that may be useful…
Eigenvalue falls in thin broken quantum strips
Lucas Chesnel, Sergei A. Nazarov
We are interested in the spectrum of the Dirichlet Laplacian in thin broken strips with angle . Playing with symmetries, this leads us to investigate spectral problems for the L…
Examples of non-scattering inhomogeneities
Lucas Chesnel, Houssem Haddar, Hongjie Li +1
We consider the scattering of waves by a penetrable inclusion embedded in some reference medium. We exhibit examples of materials and geometries for which non-scattering frequencie…
On the breathing of spectral bands in periodic quantum waveguides with inflating resonators
Lucas Chesnel, Sergei A. Nazarov
We are interested in the lower part of the spectrum of the Dirichlet Laplacian in a thin waveguide obtained by repeating periodically a pattern, its…
Generalized impedance boundary conditions with vanishing or sign-changing impedance
Lucas Chesnel, Laurent Bourgeois
We consider a Laplace type problem with a generalized impedance boundary condition of the form on a flat part of the boundary. Here …
Maxwell's equations with hypersingularities at a negative index material conical tip
Anne-Sophie Bonnet-Ben Dhia, Lucas Chesnel, Mahran Rihani
We study a transmission problem for the time harmonic Maxwell's equations between a classical positive material and a so-called negative index material in which both the permittivi…
Spectrum of the Laplacian with mixed boundary conditions in a chamfered quarter of layer
Lucas Chesnel, Sergei A. Nazarov, Jari Taskinen
We investigate the spectrum of a Laplace operator with mixed boundary conditions in an unbounded chamfered quarter of layer. This problem arises in the study of the spectrum of the…
Spectrum of the Dirichlet Laplacian in a thin cubic lattice
Lucas Chesnel, Sergei A. Nazarov
We give a description of the lower part of the spectrum of the Dirichlet Laplacian in an unbounded 3D periodic lattice made of thin bars (of width ) which have a s…
Acoustic waveguide with a dissipative inclusion
Lucas Chesnel, Jérémy Heleine, Sergei A. Nazarov +1
We consider the propagation of acoustic waves in a waveguide containing a penetrable dissipative inclusion. We prove that as soon as the dissipation, characterized by some coeffici…
Acoustic passive cloaking using thin outer resonators
Lucas Chesnel, Jérémy Heleine, Sergei A. Nazarov
We consider the propagation of acoustic waves in a 2D waveguide unbounded in one direction and containing a compact obstacle. The wavenumber is fixed so that only one mode can prop…
Design of a mode converter using thin resonant ligaments
Lucas Chesnel, Jérémy Heleine, Sergei A. Nazarov
The goal of this work is to design an acoustic mode converter. More precisely, the wave number is chosen so that two modes can propagate. We explain how to construct geometries suc…
Design of an acoustic energy distributor using thin resonant slits
Lucas Chesnel, Sergei A. Nazarov
We consider the propagation of time harmonic acoustic waves in a device with three channels. The wave number is chosen such that only the piston mode can propagate. The main goal o…
Maxwell's equations with hypersingularities at a conical plasmonic tip
Anne-Sophie Bonnet-Ben Dhia, Lucas Chesnel, Mahran Rihani
In this work, we are interested in the analysis of time-harmonic Maxwell's equations in presence of a conical tip of a material with negative dielectric constants. When these const…
Abnormal acoustic transmission in a waveguide with perforated screens
Lucas Chesnel, Sergei A. Nazarov
We consider the propagation of the piston mode in an acoustic waveguide obstructed by two screens with small holes. In general, due to the features of the geometry, almost no energ…
Qualitative indicator functions for imaging crack networks using acoustic waves
Lorenzo Audibert, Lucas Chesnel, Houssem Haddar +1
We consider the problem of imaging a crack network embedded in some homogeneous background from measured multi-static far field data generated by acoustic plane waves. We propose t…
A continuation method for building invisible obstacles in waveguides
Antoine Bera, Antoine-Sophie Bonnet-BenDhia, Lucas Chesnel
We consider the propagation of acoustic waves at a given wavenumber in a waveguide which is unbounded in one direction. We explain how to construct penetrable obstacles characteriz…
Surface waves in a channel with thin tunnels and wells at the bottom: non-reflecting underwater tomography
Lucas Chesnel, Sergei A. Nazarov, Jari Taskinen
We consider the propagation of surface water waves in a straight planar channel perturbed at the bottom by several thin curved tunnels and wells. We propose a method to construct n…
Exact zero transmission during the Fano resonance phenomenon in non symmetric waveguides
Lucas Chesnel, Sergei A. Nazarov
We investigate a time-harmonic wave problem in a waveguide. We work at low frequency so that only one mode can propagate. It is known that the scattering matrix exhibits a rapid va…
On quasi-reversibility solutions to the Cauchy problem for the Laplace equation: regularity and error estimates
Laurent Bourgeois, Lucas Chesnel
We are interested in the classical ill-posed Cauchy problem for the Laplace equation. One method to approximate the solution associated with compatible data consists in considering…
Inside-outside duality with artificial backgrounds
Lorenzo Audibert, Lucas Chesnel, Houssem Haddar
We use the inside-outside duality approach proposed by Kirsch-Lechleiter to identify transmission eigenvalues associated with artificial backgrounds. We prove that for well chosen…
From zero transmission to trapped modes in waveguides
Lucas Chesnel, Vincent Pagneux
We consider the time-harmonic scattering wave problem in a 2D waveguide at wavenumber such that one mode is propagating in the far field. In a first step, for a given , play…
On well-posedness of time-harmonic problems in an unbounded strip for a thin plate model
Laurent Bourgeois, Lucas Chesnel, Sonia Fliss
We study the propagation of elastic waves in the time-harmonic regime in a waveguide which is unbounded in one direction and bounded in the two other (transverse) directions. We as…
Non reflection and perfect reflection via Fano resonance in waveguides
Lucas Chesnel, Sergei A. Nazarov
We investigate a time-harmonic wave problem in a waveguide. By means of asymptotic analysis techniques, we justify the so-called Fano resonance phenomenon. More precisely, we show…