Albert Ferrando

Designing the properties of dispersion-flattened photonic crystal fibers.

We present a systematic study of group-velocity-dispersion properties in photonic crystal fibers (PCFs). 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.

Nearly zero ultraflattened dispersion in photonic crystal fibers

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.

Full-vector analysis of a realistic photonic crystal fiber

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

Vector description of higher-order modes in photonic crystal fibers

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 PCFs. Unlike conventional fibers, PCFs exhibit a somewhat unusual mechanism for the generation of higher-order modes. Accordingly, PCFs 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.

Spatial soliton formation in photonic crystal fibers.

We demonstrate the existence of spatial soliton solutions in photonic crystal fibers (PCFs). These guided localized nonlinear waves appear as a result of the balance between the linear and nonlinear diffraction properties of the inhomogeneous photonic crystal cladding. The spatial soliton is realized self-consistently as the fundamental mode of the effective fiber defined simultaneously by the PCF linear and the self-induced nonlinear refractive indices. It is also shown that the photonic crystal cladding is able to stabilize these solutions, which would be unstable otherwise if the medium was entirely homogeneous.

Vortex solitons in photonic crystal fibers.

We demonstrate the existence of vortex soliton solutions in photonic crystal fibers. We analyze the role played by the photonic crystal fiber defect in the generation of optical vortices. An analytical prediction for the angular dependence of the amplitude and phase of the vortex solution based on group theory is also provided. Furthermore, all the analysis is performed in the non-paraxial regime.

Analysis of dielectric-loaded cavities using an orthonormal-basis method

An orthonormal-basis method to analyze dielectric-loaded cavities is proposed. Resonant frequencies and fields are obtained by solving an eigenvalue problem in which the modes of an auxiliary problem define the orthonormal-basis that is used to expand the fields of the original problem. The merit of our approach is to take advantage of some mathematical properties to develop a computationally efficient and versatile method. The accuracy of the method is demonstrated by comparing our results with other results available in the literature.

Single-polarization single-mode intraband guidance in supersquare photonic crystals fibers

We present a two-dimensional (2D) photonic crystal structure exhibiting appealing guiding properties as an optical fiber. The structure can be regarded as a dislocation of a variant from a 2D square photonic crystal and shows a large photonic band gap for on-axis illumination. The introduction of an off-lattice hole in the structure acts as a defect and generates a highly anisotropic intraband guidance. The combination of very strong anisotropy and intraband guidance gives rise to a mechanism of polarization discrimination in optical fiber propagation that enables this guiding structure to operate as a single-polarization single-mode fiber over a wide wavelength window.

Donor and acceptor guided modes in photonic crystal fibers.

We present a triangular photonic-crystal-fiber structure that exhibits guided modes simultaneously above and below the first conduction band. We achieve this configuration by decreasing the size of one of the airholes (the defect) in a specific triangular lattice. More generally, we analyze the behavior of guided modes that depends on the size of the defect. Defects generated by decreasing or increasing the size of one of the holes produce donor or acceptor guided modes, respectively, in analogy with impurity levels in solid-state crystals. We conclude that the guiding mechanism for both donor and acceptor modes is produced by a unique phenomenon of multiple interference by a periodic structure.

Analysis of inhomogeneously filled waveguides using a bi-orthonormal-basis method

A general theoretical formulation to analyze inhomogeneously filled waveguides with lossy dielectrics is presented in this paper. The wave equations for the tranverse-field components are written in terms of a nonself-adjoint linear operator and its adjoint. The eigenvectors of this pair of linear operators define a biorthonormal-basis, allowing for a matrix representation of the wave equations in the basis of an auxiliary waveguide. Thus, the problem of solving a system of differential equations is transformed into a linear matrix eigenvalue problem. This formulation is applied to rectangular waveguides loaded with an arbitrary number of dielectric slabs centered at arbitrary points. The comparison with theoretical results available in the literature gives good agreement.