We develop a formalism for the calculation of the macroscopic dielectric response of composite systems made of particles of one material embedded periodically within a matrix of another material, each of which is characterized by a well-defined dielectric function. The nature of these dielectric functions is arbitrary, and could correspond to dielectric or conducting, transparent or opaque, absorptive and dispersive materials. The geometry of the particles and the Bravais lattice of the composite are also arbitrary. Our formalism goes beyond the long-wavelength approximation as it fully incorporates retardation effects. We test our formalism through the study of the propagation of electromagnetic waves in two-dimensional photonic crystals made of periodic arrays of cylindrical holes in a dispersionless dielectric host. Our macroscopic theory yields a spatially dispersive macroscopic response which allows the calculation of the full photonic band structure of the system, as well as the characterization of its normal modes, upon substitution into the macroscopic field equations. We can also account approximately for the spatial dispersion through a local magnetic permeability and analyze the resulting dispersion relation, obtaining a region of left handedness.
We present a spectroscopic ellipsometry study of Mo-doped VO2 thin films deposited on silicon substrates for the mid-infrared range. The dielectric functions and conductivity were extracted from analytical fittings of Ψ and Δ ellipsometric angles showing a strong dependence on the dopant concentration and the temperature. Insulator-to-metal transition (IMT) temperature is found to decrease linearly with increasing doping level. A correction to the classical Drude model (termed Drude-Smith) has been shown to provide excellent fits to the experimental measurements of dielectric constants of doped/undoped films and the extracted parameters offer an adequate explanation for the IMT based on the carriers backscattering across the percolation transition. The smoother IMT observed in the hysteresis loops as the doping concentration is increased, is explained by charge density accumulation, which we quantify through the integral of optical conductivity. In addition, we describe the physics behind a localized Fano resonance that has not yet been demonstrated and explained in the literature for doped/undoped VO2 films.
We report the reflectivity of one-dimensional finite and semi-infinite photonic crystals, computed through the coupling to Bloch modes (BM) and through a transfer matrix method (TMM), and their comparison to the experimental spectral line shapes of porous silicon (PS) multilayer structures. Both methods reproduce a forbidden photonic bandgap (PBG), but slowly-converging oscillations are observed in the TMM as the number of layers increases to infinity, while a smooth converged behavior is presented with BM. The experimental reflectivity spectra is in good agreement with the TMM results for multilayer structures with a small number of periods. However, for structures with large amount of periods, the measured spectral line shapes exhibit better agreement with the smooth behavior predicted by BM.
We report the design, fabrication, and characterization of a porous silicon-based omnidirectional mirror for the near infrared range. The structure consists of 300 porous silicon chirped dielectric layers, optimized to have omnidirectional reflectivity response from 1000 to 2000 nm wavelength range. Measurements of reflectivity spectra are presented for non-polarized light at several incident angles (range 8°–65°) with a reflectivity >95% covering a 1μm band-width. Transfer matrix method calculations were carried out to show the complete angular range for both TM and TE polarizations including a simple model to illustrate the interface scattering effects.
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