Hugo E. Hernandez-Figueroa

Highly efficient generation of broadband cascaded four-wave mixing products

We propose a novel way to efficiently generate broadband cascaded Four-Wave Mixing (FWM) products. It consists of launching two strong pump waves near the zero-dispersion wavelength of a very short (of order a few meters) optical fiber. Simulations based on Split Step Fourier Method (SSFM) and experimental data demonstrate the efficiency of our new approach. Multiple FWM products have been investigated by using conventional fibers and ultra-flattened dispersion photonic crystal fibers (UFD-PCFs). Measured results present bandwidths of 300 nm with up to 118 FWM products. We have also demonstrated a flat bandwidth of 110 nm covering the C and L bands, with a small variation of only 1.2 dB between the powers of FWM products, has been achieved using highly nonlinear fibers (HNLFs). The use of UFD-PCFs has been shown interesting for improving the multiple FWM efficiency and reducing the separation between the pump wavelengths.

Propagation speed of evanescent modes

The group velocity of evanescent waves (in undersized waveguides, for instance) was theoretically predicted, and has been experimentally verified, to be superluminal (v(g)>c). By contrast, it is known that the precursor speed in vacuum cannot be larger than c. In this paper, by computer simulations based on Maxwell equations only, we show the existence of both phenomena. In other words, we verify the actual possibility of superluminal group velocities, without violating the so-called (naive) Einstein causality.

Improved vectorial finite-element BPM analysis for transverse anisotropic media

An efficient finite-element vector beam propagation formulation for dielectric media with transverse anisotropy is thoroughly presented. This formulation is expressed in terms of the magnetic fields transverse components and includes perfectly matched layers at the truncated boundaries and the wide-angle Pade approach. Several key examples demonstrate the usefulness and effectiveness of the present scheme.

Integral localized approximation description of ordinary Bessel beams and application to optical trapping forces

Ordinary Bessel beams are described in terms of the generalized Lorenz-Mie theory (GLMT) by adopting, for what is to our knowledge the first time in the literature, the integral localized approximation for computing their beam shape coefficients (BSCs) in the expansion of the electromagnetic fields. Numerical results reveal that the beam shape coefficients calculated in this way can adequately describe a zero-order Bessel beam with insignificant difference when compared to other relative time-consuming methods involving numerical integration over the spherical coordinates of the GLMT coordinate system, or quadratures. We show that this fast and efficient new numerical description of zero-order Bessel beams can be used with advantage, for example, in the analysis of optical forces in optical trapping systems for arbitrary optical regimes.

Band gap of hexagonal 2D photonic crystals with elliptical holes recorded by interference lithography

Two-dimensional hexagonal photonic crystals can be recorded using the simple superimposition of two interference patterns rotated by 60 masculine. Such process generates high contrast masks, however, it generates elliptical cross section structures instead of cylinders. We study the PBG properties of the experimentally feasible geometries, using this technique and we demonstrate that the effect of this asymmetric shape is a reduction in the PBG map area, for TE polarization, in comparison with cylindrical structures. On the other hand, it appears a PBG for TM polarization.

Pade/spl acute/ boundary conditions for the finite-element modeling of arbitrary planar junctions

Novel boundary conditions based on Pade/spl acute/ approximations for the frequency domain two-dimensional/finite element (2-D/FE) simulation of planar optical junctions of arbitrary geometry and number of accessing waveguides are presented and described in detail. This efficient formulation is straightforwardly implemented within the 2-D/FE framework and also can easily be used in finite difference schemes. Three examples show the applicability and reliability of the present method: a waveguide step discontinuity, waveguide transverse displacement and T-shaped beam splitter.

Novel numerical method for the analysis of 2D photonic crystals: the cell method

The Cell Method, a new efficient numerical method suitable for working with periodic structures having anisotropic inhomogeneous media with curved shapes, is proposed in order to calculate the band gap of 2D photonic crystals for in-plane propagation of TM and TE waves. Moreover some numerical comparisons with other numerical methods will be provided.

Ge-Doped Defect-Core Microstructured Fiber Design by Genetic Algorithm for Residual Dispersion Compensation

A special microstructured optical fiber, which may be used in a wavelength-division-multiplexing (WDM) optical fiber transmission system for residual chromatic dispersion compensation, is designed and analyzed. The proposed structure is obtained by introducing a small Ge-doped core at the center of a conventional photonic crystal fiber. The behavior of the resulting geometry has been optimized by a genetic algorithm in conjunction with an efficient vectorial finite element formulation. Numerical results show that the designed photonic crystal fiber exhibits flattened negative dispersion over E + S + C + L + U wavelength bands with an average dispersion of - 212 ps ·km-1 ·nm-1.

General formulation for the analysis of scalar diffraction-free beams using angular modulation: Mathieu and Bessel beams

In this paper, we start from the well known Durnins experimental setup, finding general analytical formulae to investigate generation and propagation of nondiffracting beams. Our general formula makes possible considering any kind of angular modulation. As an example we discuss the Mathieu beams. Moreover, in the study of Bessel beams we consider the width of the slit to compare with the ideal case represented by a Dirac d transmittance function. 2003 Elsevier Science B.V. All rights reserved.

Novel time-domain step-by-step scheme for integrated optical applications

A novel time-domain scheme, based on the slow-wave variation approach and computation of the second time derivative for the scalar two-dimensional wave equation, is presented. This scheme permits the simulation of problems involving very wide bandwidth spectra and allows one to use coarser spatial meshes and larger time steps than other reported approaches.