Designing the Mode solving of the photonic crystal fiber via BPM and   Exploring the Single-Mode Properties
  Microstructured optical fibers (MOFs) are one of the most exciting recent developments in fiber optics. A MOF usually consists of a hexagonal arrangement of air holes running down the length of a silica fiber surrounding a central core of solid silica or, in some cases air. MOFs can exhibit a number of unique properties, including zero dispersion at visible wavelengths and low or high effective nonlinearity [3]-[17], By varying the size of the holes and their number and position, one can also design MOFs with carefully controlled dispersive and modal properties. In this paper, we analyze and modeling the behavior of the photonic crystal fiber (PCF) by using in the first step a propagator method based on the BPM method. With our BPM software, the electric field contour of the fundamental mode of PCF was demonstrated. We also used it to see the variation of the effective index; an effective index model confirms that such a fiber can be single mode for any wavelength. It would make a study of photonic crystal fibers, and a study of the numerical simulation methods allow the simulation of optical properties and has modeled the propagation of light in this fiber type. After that we use the V-parameter because it offers a simple way to design a photonic crystal fiber (PCF), by basing in a recent formulation of this parameter of a PCF, we provide numerically based empirical expression for this quantity only dependent on the two structural parameters, the air hole diameter and the hole-to-hole center spacing. 
Mohammed Debbal, Mohamed Chikh-Bled
cs.OH physics.optics