Espectros fractais em sistemas nanoestruturados e cristais fotônicos

The study of the elementary excitations such as photons, phonons, plasmons, polaritons, polarons, excitons and magnons, in crystalline solids and nanostructures systems are nowdays important active field for research works in solid state physics as well as in statistical physics. With this aim in mind, this work has two distinct parts. In the first one, we investigate the propagation of excitons polaritons in nanostructured periodic and quasiperiodic multilayers, from the description of the behavior for bulk and surface modes in their individual constituents. Through analytical, as well as computational numerical calculation, we obtain the spectra for both surface and bulk exciton-polaritons modes in the superstructures. Besides, we investigate also how the quasiperiodicity modifies the band structure related to the periodic case, stressing their amazing self-similar behavior leaving to their fractal/multifractal aspects. Afterwards, we present our results related to the so-called photonic crystals, the eletromagnetic analogue of the electronic crystalline structure. We consider periodic and quasiperiodic structures, in which one of their component presents a negative refractive index. This unusual optic characteristic is obtained when the electric permissivity and the magnetic permeability µ are both negatives for the same range of angular frequency ω of the incident wave. The given curves show how the transmission of the photon waves is modified, with a striking self-similar profile. Moreover, we analyze the modification of the usual Planck´s thermal spectrum when we use a quasiperiodic fotonic superlattice as a filter.