Calculations of Photonic Crystal Fibers by the Galerkin Method with Sine Functions without a Refractive Index Approximation

TL;DR

This paper presents a precise computational method for photonic crystal fibers using the Galerkin approach with sine functions, accurately accounting for the refractive index distribution without approximations.

Contribution

It introduces a novel calculation technique that considers the exact refractive index distribution and arbitrary hole shapes in photonic crystal fibers.

Findings

Accurate calculation of fiber characteristics with two rings of holes.

Formulae for arbitrary-shaped holes using rotated rectangles.

Method accounts for exact refractive index distribution.

Abstract

Results from the calculation of the basic characteristics of the photonic crystal fiber with two rings of holes are presented by the approach which takes into account the exact distribution of the refractive index over the cross section of the photonic crystal fiber. Formulae are theoretically derived for the calculation of holes with arbitrary shapes by dividing the material within them into rotated at different angles rectangles. Keywords: photonic crystal fibre, Galerkin method, a set of sine functions, local coordinate systems.