  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.
