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

Abstract

The spectral parameter power series (SPPS) method is a recently introduced technique (Kravchenko 2008 Complex Var. Elliptic Equ. 53 775–89, Kravchenko and Porter 2010 Math. Methods Appl. Sci. 33 459–68) for solving linear differential equations and related spectral problems. In this 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 for 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.