This thematic day focuses on the analysis and discretization of partial differential equations modelling plasmonic problems. Its objective is to present the numerical and theoretical difficulties of these problems to an audience of applied mathematicians that are not specialist of this topic.
This meeting is:
organized by Florian Monteghetti and Thomas Ourmières-Bonafos from the Applied Analysis team of I2M.
made possible thanks to the financial support of FRUMAM and I2M.
What is "plasmonics"?
Plasmonics is a sub-field of photonics that studies surface plasmons, which are a family of electromagnetic surface waves. The defining characteristic of these waves is that they are localized at surfaces that separate a material with positive dielectric permittivity from a material with negative dielectric permittivity. This change of sign of the dielectric permittivity is a source of theoretical and numerical challenges.
Registration
If you would like to receive a Zoom link for the conference, please register (click on "My registration" on the left column and submit the form).
Speakers
Stephen P. Shipman Louisiana State University homepage
11:45 - 13:15 Buffet lunch (2nd floor of the FRUNAM building, bâtiment 7)
13:15 - 14:15 Lucas Chesnel
14:15 - 15:15 Matias Ruiz
15:15 - 15:35 Coffee break
15:35 - 16:35 Luiz Faria
16:35 - 17:35 Stephen P. Shipman
Abstracts
Lucas Chesnel: An introduction to transmission problems in presence of negative materials
In this talk, we will study transmission problems involving physical parameters that change sign over the domain of interest. These problems arise in particular in the analysis of wave propagation phenomena in electromagnetism in presence of metals for certain range of frequencies, or in presence of certain metamaterials. Due to the change of sign of the coefficients in the principal part of the underlying operators, classical tools cannot be used, for example due to loss of coercivity properties, and it is necessary to develop new approaches. In this introductory presentation, we will look at some surprising results for these problems and describe different methods for studying them, both from a theoretical and numerical point of view.
Matias Ruiz: The plasmonic eigenvalue problem beyond the quasi-static limit
Plasmonic resonances in nanoparticles can be understood in the quasi-static limit as solutions to the plasmonic eigenvalue problem, i.e. solutions to the quasi-static homogeneous Maxwell's equations when considering the permittivity as the eigenvalue; this formulation makes the modes material-independent. In this talk I will consider analogous versions of the plasmonic eigenvalue problem in two scenarios. First, the full wave regime in 2D where the subwavelength assumption on the size of the nanoparticle is abandoned and the wave scattering problem has to be modelled by the Helmholtz equation. Second (time permitting), the nonlocal hydrodynamic Drude model, which describes, qualitatively, the light-matter interactions at scales where the quantum nature of matter becomes apparent. I will present a rigorous spectral analysis of the plasmonic eigenvalue problem in these two scenarios. The main results are the completeness of the material-independent modes for the Helmholtz equation, and the regularizing properties of nonlocality in the nonlocal hydrodynamic Drude model.
Luiz Faria: Complex-scaled boundary integral equations for complex resonances
Stephen P. Shipman: Embedded eigenvalues of the Neumann-Poincaré operator
Loading... 
