Splice Loss of Graded-Index Fibers: Accurate Semianalytical Descriptions Using Nelder-Mead Nonlinear Unconstrained Optimization with Three-Parameter Fundamental Modal Field

A faster and accurate semianalytical formulation with a robust optimization solution for estimating the splice loss of graded-index fibers has been proposed. The semianalytical optimization of modal parameters has been carried out by Nelder-Mead method of nonlinear unconstrained minimization suitable for functions which are uncertain, noisy, or even discontinuous. Instead of normally used Gaussian function, as the trial field for the fundamental mode of graded-index optical fiber a novel sinc function with exponentially and ( is the normalized radius of the optical fiber) decaying trailing edge has been used. Due to inclusion of three parameters in the optimization of fundamental modal solution and application of an efficient optimization technique with simple analytical expressions for various modal parameters, the results are found to be accurate and computationally easier to find than the standard numerical method solution. 1. Introduction Single mode fiber is considered as the most important broadband transmission media for optical communication system. Achieving accurate values of modal field distribution in such fiber is very essential, as it can provide basic solutions for wave equation and many useful properties like splice loss, microbending loss, fiber coupling, and the prediction of intramodal dispersion [1]. However, the various expressions for the fundamental modal field that have been reported so far are not able to predict propagation constant and modal parameters exactly in all regions of single mode operation [2]. The Gaussian approximation shows poor accuracy for lower normalized frequency region although this region may involve single mode fiber operation [2]; however, it can perform satisfactorily only for higher normalized frequency region and give good result near the cut-off frequency of next higher mode [3]. Besides, it is also equally important that the approximation should describe the field in the cladding accurately, as it is useful in the study of evanescent coupling problem. To overcome these inefficiencies, an exponentially and decaying trailing edge fundamental modal field solution in core-cladding interface region has been considered. To achieve higher accuracy compared to Gaussian function, the Gaussian-Hankel [2], the generalized Gaussian [4], the extended Gaussian [5], and the Laguerre-Gauss/Bessel expansion approximation [6, 7] have been proposed so far. An approximate analytical description with no requirement for optimization has also been presented [8]. But such analytical expression may not work for all