Asymptotic Analysis of Plasmonic Resonances of some Metallic Structures

Keywords :

• resonances
• electromagntic resonances

Rough metallic surfaces with subwavelength structurations possess extraordinary diffractive properties: at certain frequencies, one may observe fine localization and very large enhancement of the electromagnetic fields. The discovery of these phenomena has raised considerable interest as potential applications are numerous (optical switches, sensors, devices for microscopy). This behavior results from the combination of very complex interaction between the incident excitation, the geometry and the material properties of the scatterer. The main goal of this thesis is to better understand these phenomena from the mathematical point of view. In mathematical terms, the localization and concentration of the fields is the mark of a resonance phenomenon. In our context, the corresponding resonant field may be surface plasmons, i.e., waves that propagate along the interface of the grating, and that decay exponentially away from it. Another type of resonance is due to possible cavity modes. Thus, the study of these phenomena pertains to eigenvalue problems for the  solutions of the Maxwell system, in geometric configurations where in the whole of a dielectric (generally air) and a metal are separated by an infinite rough interface. We are interested in particular micro-structured devices, namely metallic surfaces that contain rectangular grooveswith sub-wavelength apertures, and thin plane layers. Configurations of this type can be manufactured quite precisely and have been subject to many experimental works. The simple geometry of the structures allows us to transform the eigenvalue problem for the Maxwell system into a nonlinear eigenvalue problem for an integral operator that depends on a small parameter, which, using tools from analytic perturbation of operators theory, lends itself to a precise asymptotic analysis. Precisely we showed that the resonances of these structures converge to the zeros of some explicit dispersion equations when the ratio between the roughness parameter and the wavelength tends to zero. These asymptotic models provide a precise localization of the resonances in the complex plane, and are suited for numerical approximation, shape and material optimization. 

Directors:

• Mr Eric Bonnetier (Professeur - Université Grenoble Alpes )
• Mr Faouzi Triki (Professeure - Université Grenoble Alpes )

Raporteurs:

• Mr Mourad Sini (Directeur de recherche - Académie autrichienne des sciences )
• Mr Lim Mikyoung (Professor - KAIST - Corée du Sud )

Examinators:

• Mr Gregory Vial (Professeur - Ecole Centrale de Lyon )
• Mr Sebastien Tordeaux (Maître de conférénces - Université de Pau et des pays de l'Adour )
• Mr Fernando Guevera Vasquez (Professeur - Université d'Utah, Etats-Unis )