41 citations · 66 across the 14 of their papers we have counts for
17 papers
Broadband quasistatic passive cloaking: bounds and limitations in the near-field regime
Maxence Cassier, Graeme W. Milton, Aaron Welters
We consider here several aspects of the following challenging question: is it possible to use a passive cloak to make invisible a dielectric inclusion on a finite frequency interva…
Geometric spectral properties of electromagnetic waveguides
Philippe Briet, Maxence Cassier, Thomas Ourmières-Bonafos +1
Consider a reference homogeneous and isotropic electromagnetic waveguide with a simply connected cross-section embedded in a perfect conductor. In this setting, when the waveguide…
An operator approach to the analysis of electromagnetic wave propagation in dispersive media. Part 1: general results
Maxence Cassier, Patrick Joly
We investigate in this chapter the mathematical models for electromagnetic wave propagation in dispersive isotropic passive linear media for which the dielectric permittivity $\var…
An operator approach to the analysis of electromagnetic wave propagation in dispersive media. Part 2: transmission problems
Maxence Cassier, Patrick Joly
In this second chapter, we analyse transmission problems between a dielectric and a dispersive negative material. In the first part, we consider a transmission problem between two…
Long time behaviour of the solution of Maxwell's equations in dissipative generalized Lorentz materials (II) A modal approach
Maxence Cassier, Patrick Joly, Luis Alejandro Rosas Martínez
This work concerns the analysis of electromagnetic dispersive media modelled by generalized Lorentz models. More precisely, this paper is the second of two articles dedicated to th…
Long time behaviour of the solution of Maxwell's equations in dissipative generalized Lorentz materials (I) A frequency dependent Lyapunov function approach
Maxence Cassier, Patrick Joly, Luis Alejandro Rosas Martínez
It is well-known that electromagnetic dispersive structures such as metamaterials can be modelled by generalized Drude-Lorentz models. The present paper is the first of two article…
Active exterior cloaking for the 2D Helmholtz equation with complex wavenumbers and application to thermal cloaking
Maxence Cassier, Trent DeGiovanni, Sébastien Guenneau +1
We design sources for the two-dimensional Helmholtz equation that can cloak an object by cancelling out the incident field in a region, without the sources completely surrounding t…
Spectral theory for Maxwell's equations at the interface of a metamaterial. Part II: Limiting absorption, limiting amplitude principles and interface resonance
Maxence Cassier, Christophe Hazard, Patrick Joly
This paper is concerned with the time-dependent Maxwell's equations for a plane interface between a negative material described by the Drude model and the vacuum, which fill, respe…
High contrast elliptic operators in honeycomb structures
Maxence Cassier, Michael I. Weinstein
We study the band structure of self-adjoint elliptic operators , where has the symmetries of a honeycomb tiling of . W…
Active Thermal Cloaking and Mimicking
Maxence Cassier, Trent DeGiovanni, Sébastien Guenneau +1
We present an active cloaking method for the parabolic heat (and mass or light diffusion) equation that can hide both objects and sources. By active we mean that it relies on desig…
Electromagnetic waves in photonic crystals: laws of dispersion, causality and analytical properties
Boris Gralak, Maxence Cassier, Guillaume Demésy +1
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…
Imaging small polarizable scatterers with polarization data
Patrick Bardsley, Maxence Cassier, Fernando Guevara Vasquez
We present a method for imaging small scatterers in a homogeneous medium from polarization measurements of the electric field at an array. The electric field comes from illuminatin…
Mathematical models for dispersive electromagnetic waves: an overview
Maxence Cassier, Patrick Joly, Maryna Kachanovska
In this work, we investigate mathematical models for electromagnetic wave propagation in dispersive isotropic media. We emphasize the link between physical requirements and mathema…
Bounds on Herglotz functions and fundamental limits of broadband passive quasi-static cloaking
Maxence Cassier, Graeme W. Milton
Using a sum rule, we derive new bounds on Herglotz functions that generalize those given in (Gustafson and Sjöberg 2010) and (Bernland, Luger and Gustafson 2011). These bounds appl…
Spectral theory for Maxwell's equations at the interface of a metamaterial. Part I: Generalized Fourier transform
Maxence Cassier, Christophe Hazard, Patrick Joly
We explore the spectral properties of the time-dependent Maxwell's equations for a plane interface between a metamaterial represented by the Drude model and the vacuum, which fill…
A rigorous approach to the field recursion method for two-component composites with isotropic phases
Maxence Cassier, Aaron Welters, Graeme W. Milton
In this chapter of the book entitled, "Extending the Theory of Composites to Other Areas of Science" [edited by Graeme W. Milton, 2016] we give a rigorous derivation of the field e…
Analyticity of the Dirichlet-to-Neumann map for the time-harmonic Maxwell's equations
Maxence Cassier, Aaron Welters, Graeme W. Milton
In this chapter of the book entitled, "Extending the Theory of Composites to Other Areas of Science" [edited by Graeme W. Milton, 2016] we derive the analyticity properties of the…