We present a systematic study of group-velocity-dispersion properties in photonic crystal fibers (PCF's). This analysis includes a thorough description of the dependence of the fiber geometrical dispersion on the structural parameters of a PCF. The interplay between material dispersion and geometrical dispersion allows us to established a well-defined procedure to design specific predetermined dispersion profiles. We focus on flattened, or even ultraflattened, dispersion behaviors both in the telecommunication window (around 1.55 microm) and in the Ti-Za laser wavelength range (around 0.8 microm}. We show the different possibilities of obtaining normal, anomalous, and zero dispersion curves in the above frequency domains and discuss the limits for the existence of the above dispersion profiles.

We present a procedure for achieving photonic crystal fibers with nearly zero ultraflattened group-velocity dispersion. Systematic knowledge of the special guiding properties of these fibers permits the achievement of qualitatively novel dispersion curves. Unlike the behavior of conventional fibers, this new type of dispersion behavior permits remarkably improved suppression of third-order dispersion, particularly in the low-dispersion domain.

We analyze the guiding problem in a realistic photonic crystal fiber using a novel full-vector modal technique, a biorthogonal modal method based on the nonselfadjoint character of the electromagnetic propagation in a fiber.Dispersion curves of guided modes for different fiber structural parameters are calculated along with the 2D transverse intensity distribution of the fundamental mode. Our results match those achieved in recent experiments, where the feasibility of this type of fiber was shown.

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We extensively study the propagation features of higher-order modes in a photonic crystal fiber (PCF). Our analysis is based on a full-vector modal technique specially adapted to accurately describe light propagation in PCF's. Unlike conventional fibers, PCF's exhibit a somewhat unusual mechanism for the generation of higher-order modes. Accordingly, PCF's are characterized by the constancy of the number of modes below a wavelength threshold. An explicit verification of this property is given through a complete analysis of the dispersion relations of higher-order modes in terms of the structural parameters of this kind of fiber. The transverse irradiance distributions for some of these higher-order modes are also presented, showing an excellent agreement with recent experimental measurements. In the same way, the full-vector nature of our approach allows us to analyze the rich polarization structure of the PCF mode spectrum.

We consider layered heterostructures combining ordinary positive index materials and dispersive metamaterials. We show that these structures can exhibit a new type of photonic gap near frequencies where either the magnetic permeability µ or the electric permittivity ǫ of the metamaterial change signs. Although the interface of a medium with zero refractive index (a condition attained either when µ = 0 or when ǫ = 0) is known to give full reflectivity for all incident polarizations, here we show that a gap corresponding to µ = 0 occurs only for TE polarized waves, whereas a gap corresponding to ǫ = 0 occurs only for TM polarized waves. These band gaps are scale-length invariant and very robust against disorder, although they may disappear for the particular case of propagation along the stratification direction. *

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We report on an analytical formulation, based on the concept of effective Fresnel number, to evaluate in a simple way the relative focal shift of rotationally nonsymmetric scalar fields that have geometrical focus and moderate Fresnel number. To illustrate our approach, certain previously known results and also some new focusing setups are analytically examined.