Fibonacci sequences constructed from high-index-contrast GaAs and
Al<sub>2</sub>O<sub>3</sub> quarter-wavelength layers are used as unit cells in a novel multilayer system. Quasi-periodic heterostructures, formed by concatenating repeated Fibonacci sequences of different order, have properties markedly different from classic Fabry-Perot bilayer systems. We employ the transfer matrix method, including imaginary components of the refractive index, to extract transmission and reflection spectra, and consider their sensitivity to material and geometrical variation. We find that these quasi-periodic heterostructures may have a very high quality factor and deep extinction in reflection. By contrast, bilayer structures of similar dimension are so strongly evanescently damped that the coupling to the cavity is negligible. Due to the coupled geometric resonances in the Fibonacci-based heterostructure, the spectral properties are easily tuned by altering the imaginary component of the refractive index in a single layer. We discuss the viability of possible technological applications.
The optical propagation of a pulse through one dimensional finite
gratings and photonic crystals is discussed. In the case of shallow
gratings the light transport properties are derived within the frame
of the Coupled Mode Theory, while the Transfer Matrix Method is used
for investigating photonic crystal (PC) structures. The so-called
superluminal tunneling of wave-packets through the band-gap region is investigated, and the dwell time is computed. Because of the
analyticity of the wave equation, the Einstein causality principle is
not violated, although the group velocity can exceed the speed of the
light in vacuum. We show that the dwell time is a propagation
phenomenon and not a quasi-static process in which the incident pulse
envelope modulates the amplitude of an exponentially decaying standing wave. Nevertheless, the group velocity cannot be always used to compute the transmission group delay, because the latter does not represent the time spent by the energy to propagate through the band-gap.