Cladding mode coupling in long-period gratings in index-guided microstructured optical fibers

To inscribe the long-period gratings (LPGs) in an index-guiding (or the solid-core) microstructured optical fiber (MOF), the opto-geometrical parameters of the fiber have to be determined, at first. Using our earlier developed analytical field model, we have evaluated the effective index for the fundamental core mode of the triangular lattice-based MOF, and the effective index of the fundamental cladding mode is obtained by approximating hexagonal unit cell by a circular unit cell. We demonstrate that the grating period of the LPGs obtained using the radius of the equivalent circular unit cell of Λ/2 and Λ32π1/2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varLambda \left( {{{\sqrt 3 } \mathord{\left/ {\vphantom {{\sqrt 3 } {2\pi }}} \right. \kern-0pt} {2\pi }}} \right)^{1/2}$$\end{document}, which are the two widely accepted radii for evaluating the effective index of the fundamental cladding mode, do not match well with the available experimental results. Therefore, to achieve better agreement in the results, we have proposed the linear combination of these two radii. Comparisons with available experimental results have also been included.