Abstract
It is crucial to be time and resource-efficient when enabling and optimizing novel applications and functionalities of optical fibers, as well as accurate computation of the vectorial field components and the corresponding propagation constants of the guided modes in optical fibers. To address these needs, a novel full-vectorial fiber mode solver based on a discrete Hankel transform is introduced and validated here for the first time for rotationally symmetric fiber designs. It is shown that the effective refractive indices of the guided modes are computed with an absolute error of less than 10−4 with respect to analytical solutions of step-index and graded-index fiber designs. Computational speeds in the order of a few seconds allow to efficiently compute the relevant parameters, e.g., propagation constants and corresponding dispersion profiles, and to optimize fiber designs.
Highlights
Two different modes of operation are compared in Figure 2c: (i) For each N the implicitly restarted Lanczos method (IRLM) solver uses random noise as a guess or (ii) the solver uses the previous solution as a guess
A full-vectorial fiber mode solver based on a discrete Hankel transform (DHT) has been developed and discussed
It has been demonstrated that the effective refractive indices of the guided modes are computed with an absolute error of less than 10−4 with respect to analytical solutions at a reasonably low number of Fourier–Bessel coefficients
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. For example and in combination with the split-step approach [1] or the frequency-domain Runge–Kutta approach [2], the nonlinear pulse propagation can be analyzed numerically Such studies allow us to understand and tailor effects such as the pulse broadening for supercontinuum generation either in the fundamental mode [2] or even in higher-order modes (HOMs) [3]. To numerically compute the guided fiber modes of a given refractive index profile, a transversal discretization concept has to be chosen [14] This can be a local strategy such as a finite element [15] or a finite difference [16,17,18] approach for which a discretization i.e., mesh (either uniform or non-uniform) is used to linearize the differential operators in the corresponding wave equation(s). Computation of the guided vector modes and their propagation constants in rotationally symmetric fibers
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