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

Raja Roy Choudhury,Arundhati Roy Choudhury,Mrinal Kanti Ghose

doi:10.1155/2013/168923

Raja Roy Choudhury, Arundhati Roy Choudhury + Show 1 more

Open Access

https://doi.org/10.1155/2013/168923

Copy DOI

Abstract

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 R-3/2 (R 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.

Highlights

Single mode fiber is considered as the most important broadband transmission media for optical communication system
The proposed approximation of fundamental field involving three optimizing parameters incorporates more flexibility to modify the fundamental modal solution of optical fibers having different specifications. Optimized values of these parameters for different normalized frequencies are given in Tables 1 and 2 for a particular specification of optical fiber having trapezoidal and triangular index profiles, respectively
Values for other normalized frequencies having different specification of optical fiber can be obtained by using Nelder-Mead method of nonlinear unconstrained minimization

Summary

Introduction

Single mode fiber is considered as the most important broadband transmission media for optical communication system. Using the proposed three-parameter fundamental modal solution coupled with Nelder-Mead method of nonlinear unconstrained minimization, the algorithm becomes comparatively easier to be implemented on an ordinary personal computer, which provides computationally more efficient result [14, 15] than standard numerical method and yields excellent agreement with exact solutions. This is achieved due to the fact that requisite analytical formulae are deduced beforehand and parameters of those analytical expressions are found by optimization using Nelder-Mead simplex method for nonlinear unconstrained minimization. The proposed semianalytical model can be used in the study of nonlinear fiber [21]

R6 cos

Results and Discussions

Conclusions