Vectorial wave analysis of a dual shape core optical fibre with a parabolic centre core

Abstract

To calculate the propagation characteristics of a graded-index optical fibre with a parabolic core, such as a dual-shape core optical fibre having a parabolic-index centre core, one needs to solve a vector wave equation in the inhomogeneous core region. The paper derives a coupled second-order differential equation with respect to the radial functions linking to the transverse electric fields through the refractive-index distribution, and solve it by the perturbation method. Analytical results show that the first-order perturbed solution plays a dominant role in the vector wave solution, especially for the fundamental mode. In fact, normalised frequencies and waveguide dispersions calculated using the first-order solution hold at least seven significant figures in the single-mode region. Comparison between cutoff frequencies of the conventional square-law optical fibre calculated here and those obtained by the numerical methods also guarantees the accuracy of the first-order solution. Using the first-order solution, the paper examines the waveguide dispersion and the mode field distribution of the dual-shape core optical fibre. Results show that the fibre with a parabolic-index centre core is one of the best dispersion-shifted optical fibres. The waveguide dispersion can be flattened over a relatively wide range of the waveguide parameters, and the confinement of modal power is good.