We have investigated light propagation and Anderson localization in one-dimensional dispersive random metamaterials,
focusing on the effects disorder correlation. We analyze and compare the cases where disorder is
uncorrelated, totally correlated and anticorrelated. We show that the photonic gaps of the corresponding periodic
structure are not completely destroyed by the presence of disorder, which leads to minima in the localization
length. We demonstrate that, in the vicinities of a gap of the corresponding periodic structure, the behavior of
the localization length depends crucially on the physical origin of the gap (Bragg or non-Bragg gaps).
The photonic modes of Thue-Morse and Fibonacci lattices with generating layers A and B, of positive and negative
indices of refraction, are calculated by the transfer-matrix technique. For Thue-Morse lattices, as well for periodic
lattices with AB unit cell, the constructive interference of reflected waves, corresponding to the zero<sup>th</sup>-order gap, takes
place when the optical paths in single layers A and B are commensurate. In contrast, for Fibonacci lattices of high order,
the same phenomenon occurs when the ratio of those optical paths is close to the golden ratio. In the long wavelength
limit, analytical expressions defining the edge frequencies of the zeroth order gap are obtained for both quasi-periodic
lattices. Furthermore, analytical expressions that define the gap edges around the zeroth order gap are shown to
correspond to the < ε > =0 and <μ> = 0 conditions.
The band-structure properties of a photonic two-dimensional honeycomb lattice formed by cylindrical semiconductor
shell rods with dielectric permitivities ε<sub>1</sub> and
and embedded in a background with permitivity ε<sub>3</sub>,
is studied by
using an standard plane-wave expansion. The properties of bandgaps and density of states, considering dispersive
dielectric responses, are investigated together with the possibility of fabricating systems with tunable photonic bandgaps,
due to the Voigt magneto-optical effect, under the influence of an external magnetic field.
We have investigated the propagation of plane waves through one-dimensional superlattices
composed of alternate layers characterized by two di.erent refractive indexes, which may take on
positive as well as negative values. For both indices of refraction positive we have found null-gap
points for commensurate values of the optical path lengths of each layer at which the superlattice
becomes transparent. We have determined the symmetry properties of the electromagnetic field
demonstrating the degeneracy of the solutions at these points. Furthermore, we have been able
to characterize non-Bragg gaps that show up in frequency regions in which the average refractive
index is null, by obtaining analytically the non-Bragg gap width which depends only on the ratio <sup>b</sup>/<sub>a</sub>
of the layer widths.