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Asymptotics of plasmonic resonnances of rectangular cavities

Abstract : 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 grooves with 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 these 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 tothe 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.
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Abdelfatah Gtet. Asymptotics of plasmonic resonnances of rectangular cavities. General Mathematics [math.GM]. Université Grenoble Alpes, 2017. English. ⟨NNT : 2017GREAM096⟩. ⟨tel-01885548⟩

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