Birefringence Analysis of Photonic-Bandgap Fibers Using the Hexagonal Yee's Cell

Abstract

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> A full-vectorial finite-difference scheme utilizing the hexagonal Yee's cell is used in this paper to analyze the modes of photonic-bandgap fibers with <formula formulatype="inline"><tex Notation="TeX">${\rm C}_{6v}$</tex> </formula> symmetry. Because it respects the fiber's native symmetry, this method is free from any numerical birefringence. We also incorporate in it techniques for reducing the memory requirement (up to 3 to 4 times) and computational time, in particular by exploiting some of the symmetry properties of these fibers. Using sub-pixel averaging, we demonstrate quadratic convergence for the fundamental mode's effective index dependence on spatial resolution. We show that this method can be used to calculate the beat length of PBFs in which a birefringence is introduced by applying a small unidirectional stretch to the fiber cross section along one of its axes. Abrupt variations of the modeled fiber geometries with spatial resolution lead to oscillatory beat length convergence behavior. We can obtain a better estimate for beat length by averaging these oscillations. We apply a strong perturbation analysis to the fiber's unperturbed mode, calculated by our finite-difference method, to perform this averaging in a rigorous way. By fitting a polynomial to the predicted beat lengths as a function of grid spacing, we obtain an accurate estimate of the beat length at zero grid spacing. Reasonable convergence for the beat length is observed using a single processor with 8 GB of memory. </para>