Analysis of graded-index optical fibers by the spectral parameter power series method

TL;DR

This paper introduces a spectral parameter power series (SPPS) method for analyzing graded-index optical fibers, providing an accurate and efficient way to compute guided modes and dispersion parameters.

Contribution

It develops an analytical SPPS-based approach for solving the eigenvalue problem in optical fibers, improving accuracy over existing methods.

Findings

SPPS method yields higher accuracy in eigenvalue calculations.

The approach simplifies the computation of guided modes.

Dispersion parameters are effectively analyzed using the method.

Abstract

Spectral parameter power series (SPPS) method is a recently introduced technique for solving linear differential equations and related spectral problems. In the present work we develop an approach based on the SPPS for analysis of graded-index optical fibers. The characteristic equation of the eigenvalue problem for calculation of guided modes is obtained in an analytical form in terms of SPPS. Truncation of the series and consideration in this way of the approximate characteristic equation gives us a simple and efficient numerical method for solving the problem. Comparison with the results obtained by other available techniques reveals clear advantages of the SPPS approach, in particular, with regards to accuracy. Based on the solution of the eigenvalue problem, parameters describing the dispersion are analyzed as well.