Two-dimensional hexagonal photonic crystals can be recorded using the simple superimposition of two interference patterns rotated by 60°. 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.

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.

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.

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.

The finite element method (FEM) and the genetic algorithm (GA) have been used to solve the inverse problem involving absolute photonic band gap (PBG) searching and optimization. Square and triangular lattices composed by Tellurium (anisotropic material) and air have been analyzed. In order to avoid the requirements of high computational efforts and resources needed in these kind of tasks, the PBGs have been computed only at key positions along the first region of Brillouin and we obtained absolute midgap ratio, considering PBGs between the TE 1-2 and TM 3-4 modes, of 18.00% and 23.49% for the square and triangular lattices, respectively.

Finite-element analysis in time and frequency domains using perfectly matched layers and isoparametric curvilinear elements for finite-size photonic-crystal (PC) cavities is presented in this paper. The time-domain approach includes current sources, the full band scheme, and the slowly varying envelope approximation; consequently, bigger time steps can be used independent of the size of the elements. The resonant frequency, quality factor, effective modal area, and field distribution for each mode can be obtained in a single simulation. A strategy to compute the higher resonant modes by using only a quarter of the cavity and adequate boundary conditions is also presented.