Camille Carvalho

Camille Carvalho
University of California, Merced | UCM · Department of Applied Mathematics

PhD
Maîtresse de conférence à l'INSA de Lyon et à l'Université de Californie Merced.

About

19
Publications
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109
Citations
Introduction
Modeling and simulation for electromagnetic phenomena in plasmonics structures Personal Webpage http://camillecarvalho.org/

Publications

Publications (19)
Article
Full-text available
The limiting amplitude principle states that the response of a scatterer to a harmonic light excitation is asymptotically harmonic with the same pulsation. Depending on the geometry and nature of the scatterer, there might or might not be an established theoretical proof validating this principle. In this paper, we investigate a case where the theo...
Article
When using boundary integral equation methods, we represent solutions of a linear partial differential equation as layer potentials. It is well-known that the approximation of layer potentials using quadrature rules suffer from poor resolution when evaluated closed to (but not on) the boundary. To address this challenge, we provide modified represe...
Preprint
Full-text available
We study scattering by a high aspect ratio particle using boundary integral equation methods. This problem has important applications in nanophotonics problems, including sensing and plasmonic imaging. Specifically, we consider scattering in two dimensions by a sound-hard, high aspect ratio ellipse. For this problem, we find that the boundary integ...
Preprint
Full-text available
It is well-known that optical cavities can exhibit localized phenomena responsible for numerical instabilities in approximating scattering problems. In classic optical cavities, those localized phenomena concentrate at the inner boundary of the cavity and are called whispering gallery modes. In this paper we consider cavities made of Negative-Index...
Article
Full-text available
We present a simple and effective method for evaluating double- and single-layer potentials for Laplace's equation in three dimensions close to the boundary. The close evaluation of these layer potentials is challenging because they are nearly singular integrals. The method we propose is based on writing these layer potentials in spherical coordina...
Preprint
Full-text available
When using boundary integral equation methods, we represent solutions of a linear, partial differential equation as layer potentials. It is well-known that the approximation of layer potentials using quadrature rules suffer from poor resolution when evaluated closed to (but not on) the boundary. To address this challenge, we establish new layer pot...
Article
We present a novel fully fourth order in time and space finite difference method for the time domain Maxwell's equations in metamaterials. We consider a Drude metamaterial model for the material response to incident electromagnetic fields. We consider the second order formulation of the system of partial differential equations that govern the evolu...
Preprint
We present a novel fully fourth order in time and space finite difference method for the time domain Maxwell's equations in metamaterials. We consider a Drude metamaterial model for the material response to incident electromagnetic fields. We consider the second order formulation of the system of partial differential equations that govern the evolu...
Preprint
When using the boundary integral equation method to solve a boundary value problem, the evaluation of the solution near the boundary is challenging to compute because the layer potentials that represent the solution are nearly-singular integrals. To address this close evaluation problem, we apply an asymptotic analysis of these nearly singular inte...
Preprint
We present a simple and effective method for computing double- and single-layer potentials for Laplace's equation in three dimensions close to the boundary. The close evaluation of these layer potentials is challenging because they are nearly singular integrals. The method is comprised of three steps: (i) rotate the spherical coordinate system so t...
Article
Full-text available
Transmission problems with sign-changing coefficients occur in electromagnetic theory in the presence of negative materials surrounded by classical materials. For general geometries, establishing Fredholmness of these transmission problems is well-understood thanks to the \(\mathtt {T}\)-coercivity approach. Moreover, for a plane interface, there e...
Article
Full-text available
Accurate evaluation of layer potentials near boundaries is needed in many applications, including fluid-structure interactions and near-field scattering in nano-optics. When numerically evaluating layer potentials, it is natural to use the same quadrature rule as the one used in the Nystr\"om method to solve the underlying boundary integral equatio...
Article
Full-text available
We consider a class of eigenvalue problems involving coefficients changing sign on the domain of interest. We describe the main spectral properties of these problems according to the features of the coefficients. Then, under some assumptions on the mesh, we explain how one can use classical finite element methods to approximate the spectrum as well...
Thesis
Full-text available
Dans cette thèse, nous nous intéressons à la propagation d’ondes électromagnétiques dans des structures plasmoniques, composées d’un diélectrique et d’un métal. Les métaux exhibent aux fréquences optiques des propriétés électromagnétiques inhabituelles comme une permittivité diélectrique négative, alors que les diélectriques possèdent une permittiv...
Article
We investigate in a $2$D setting the scattering of time-harmonic electromagnetic waves by a plasmonic device, represented as a non dissipative bounded and penetrable obstacle with a negative permittivity. Using the $\textrm{T}$-coercivity approach, we first prove that the problem is well-posed in the classical framework $H^1_{\text{loc}} $ if the n...
Article
We study a 2D dielectric cavity with a metal inclusion and we assume that, in a given frequency range, the metal permittivity ε = ε(ω) is a negative real number. We look for the plasmonic cavity resonances by studying the linearized eigenvalue problem (dependence in ω of ε frozen). When the inclusion is smooth, the linearized problem operator has a...

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