Metamaterials and periodic structures in optics
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This thesis studies periodic structures in optics, ranging from metamaterials, that are subwavelength structures, to periodic claddings of waveguides where the lattice parameter is comparable to the wavelength. The work can be divided into two parts, where, in causal order, the first part concerns the dispersion properties of a symmetric 1D Bragg waveguide, and the second part concerns active electromagnetic metamaterials. For the Bragg waveguide we developed new methods for finding the band gap diagram and propagating modes. We found that the dispersion picture is dominated by standard waveguide dispersion similar to that of a metallic waveguide, even with a chirped cladding periodicity. We also investigated cladding defects and found that the waveguide dispersion can be tailored to some extent, and negative dispersion can be achieved in a limited bandwidth. The influence of negative index materials in the cladding grating is also investigated. It is found that a strongly dispersive material causes a more chaotic band diagram, and that such materials in Bragg waveguides could be used to tailor the dispersion properties of the waveguide. We have studied the fundamental properties of active right-handed metamaterials with negative refractive index, and found a possible realizable material, concretized in a lumped circuit model example. Furthermore, we show by analytical arguments and simulations how the sign of the refractive index must be chosen for active materials. We have developed a theory for active electromagnetic materials and put it in context with theory on instabilities in active materials from plasma science. It is shown that the uniqueness theorem in its usual form cannot be applied to active materials, and that any refractive index function can be realized in a finite bandwidth. Also there exist no fundamental, maximal gain for active, stable materials. As a special case it is argued that lossless left-handed negative refractive index can be achieved.