Simple Empirical Relation for Effective Cladding Index of an Index-Guiding Photonic Crystal Fiber and Estimation of its Beam Divergence and Far-Field Intensity

Abstract

A new empirical relation is formulated for effective cladding index of solid-core photonic crystal fibers (PCF) with a triangular lattice of uniform air holes in the cladding region, which involves only the operating wavelength and two fundamental geometrical parameters of the PCF: the air-hole diameter and the hole-pitch. This relation is valid in the endlessly single-mode (ESM) region of the PCF, defined by an upper limit of the normalized air-hole diameter of the same PCF. The empirical relation is simple, user-friendly, and consisting of a few optimization parameters, which are independent of wavelength and the PCF parameters. In addition, it takes many wide ranges of all the opto-geometrical parameters of PCFs into account. The accuracy of the proposed relation is depicted by comparing the results obtained from it with those found previously from rigorous full-vector finite element method (FEM) data. The empirical relation can be used to easily predict various propagation characteristics of PCFs, entirely dependent on their effective cladding indices, with tolerable accuracy. For instance, the beam divergence and the far-field intensity distribution of PCFs are studied here.