Theoretical Studies of Optical Metamaterials

Optical metamaterials are artificial media that exhibit new properties from structuring on the nanometric scale. One of the main researches in metamaterials investigates materials with negative refractive index, which can allow the development of perfect lens and other exciting potential applications. In this thesis, we theoretically study the properties of negative-index optical fishnet metamaterials, especially the origin of their negative-valued refractive index, and also associated theoretical problems. The thesis can be divided into 4 parts. In the first part we study the light scattering at an interface between air and a semi-infinite fishnet metamaterial. With a fully-vectorial numerical method, we calculate the scattering coefficients of the interface and find that the energy transport inside the fishnet is due to a single Bloch mode, the fundamental one. Based on the single-interface scattering coefficients and the effective index of this Bloch mode we propose a new algorithm for retrieving effective optical parameters of the metamaterial. The approach emphasizes the key role played by the fundamental Bloch mode and provides retrieved parameters that are more accurate or stable than those obtained by classical methods based only on light reflection and transmission through finite-thickness metamaterial slabs. Due to the importance of the fundamental Bloch mode in the light transport in metamaterials, in the second part, based on the Bloch mode orthogonality we derive closed-form expressions for the scattering coefficients at an interface between two periodic media with slightly different geometrical parameters, which is a computationally demanding electromagnetic problem. We show that the analytical expressions are very accurate for various geometries, including dielectric waveguides and metallic metamaterials. Thus they can be useful for designing and engineering stacks of periodic structures. As shown in the first part, the fundamental Bloch mode is central to explain the negative refraction phenomenon in fishnet metamaterials. In the third part, we derive an accurate semi-analytical model for the complex propagation constant of the fishnet fundamental Bloch mode. This is achieved by analyzing light propagation and scattering inside the fishnet. The model shows that the origin of broad-band negative index of fishnets can be mainly understood as a plasmon resonance in the transversal metal-insulator-metal (MIM) channels. The plasmon resonance enhances the ‘magnetic’ response of fishnet and the losses associated to this resonance can be compensated by including gain in the dielectric layers of the fishnet. Furthermore, the model allows an easy and precise geometrical tailoring of fishnet metamaterials. As shown in the third part, it is the plasmon resonance in metal-insulator-metal (MIM) structures that induces the negative index of fishnet metamaterials. In the last part, we study the asymptotic behavior of 3D MIM nanoresonators, as the resonator size is shrunk below the diffraction limit. In particular we show that the quality factor increases from 10 to 100 when the resonator volume is scaled down from (λ/2n)3 to (λ/50)3. We provide a comprehensive study with a semi-analytical Fabry-Perot model. The model remains accurate over the whole size scale even in the quasi-static regime for which retardation effects are not expected. This important and counterintuitive result indicates that both localized plasmon resonances in nanoparticles and delocalized resonance in elongated plasmonic nanowires can be possibly understood as a wave-retardation based antenna problem.