Aspectos da transmissão de ondas eletromagnéticas em filmes de multicamadas. - Nascimento, Elton Malta (2009)
In this thesis, we study some aspects of the transmission of a monochromatic electromagnectic plane wave inciding into some configurations of multilayered films. Using a transfer matrix formalism, we firstly investigate the case of a binary sequence of N dielectric layers distributed in a random way, where the layer parameters follow the Bragg condition (nAdA = nBdB). We could observe that the mode for which the optical thickness of the layers corresponds to half-wavelength is insensitive to disorder and fully transparent. The average transmission in a frequency range around this resonance decays as 1/N1/2, and the localization length diverges quadratically as this resonance mode is approached. In the vicinity of the quarter-wavelength, the localization length diverges logarithmically and the frequency averaged transmission exhibits an stretched exponential dependence on the total thickness. At the quarter-wavelength resonance, the Lyapunov exponent for different realizations of disorder has a Gaussian distribution leading to distinct scaling laws for the geometric and arithmetic averages of the transmission. The scaling laws for the half-and quarter-wavelength modes are analogous to those found in electronic onedimensional Anderson models with random dimers and pure off-diagonal disorder, respectively, which are known to display similar violations of the usual exponential Anderson localization. These scale behavior were compared with the case of a disordered structure where one kind of constituint material is a metamaterial. We observe that the spectrally averaged transmission in a frequency range around the fully transparent resonant mode is shown to decay faster as the number of layer increases (1/N). The interplay of strong localization and the emergence of resonant modes within the gap leads to a non-monotonous disorder dependence of the transmission that reaches a minimum at an intermediate disorder strength. Using the same layer parameters of the first case, we investigate the influence of a binary aperiodic incommensurated sequence of layers. The aperiodicity is introduced by considering the sequence of refractive indices to follow a sinusoidal function whose phase ϕ varies as a power-law of the layer index (ϕ ∝ jν). For ν > 1 the resulting sequence is effectivelly uncorrelated leading to the usual Anderson localization of light. The crossover from a uniform structure at ν = 0 to a quasi-periodic structure at ν = 1 is signaled by a minimum at the spectrally averaged transmission. We perform a spectral analysis of the refractive index sequence to show its close connection to the main features exhibited by the averaged optical transmittance. The last case studied is about the inclusion of a cholesteric liquid crystal (ChLC) in the film composition. We considered a single-pitched ChLC multilayered system with quasiperiodic Fibonaccian phase defects as well as an alternate sequence of single-pitched ChLC and isotropic dielectric layers. Using the Berreman 4 × 4 matrix formalism, we numerically obtain the reflection spectrum and the chromaticity diagram of these structures. The associated chromaticity is shown to depend on the incidence angle. However, for the ChLC Fibonaccian phase defect system, the color shift can be controlled by the defect angle α. For the F4 generation and α = π/3, the chromaticity of the reflected light remains close to the white color region for a wide range of incidence angles, followed by a blue-shift at intermediate incidence angles. This is the setup that produces the nearest omnidirectional red-green-blue condition for the reflection spectrum. On the other hand, the structure with alternate ChLC and isotropic layers exhibits a complex sequence of color shifts when the incidence angle is increased.