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.
An accurate three parameter approximate solution of fundamental mode, to describe different propagation parameter of graded-index optical fiber has been presented. Due to three parameter optimization of the fundamental modal solution, the results are much more accurate for a wide range of optical fiber specifications. Employing variational technique, an estimation of effective area and effective index with proposed fundamental modal field are carried out. It has been shown that the results match identically with the exact available results for step and parabolic refractive index profile optical fiber. The accurate analytical expressions for the evaluation of effective area and effective index are formulated. Optimization of three parameters has been carried out for a wide range of normalized frequencies. Data for these parameters are also provided, which can be used directly while calculating different design parameters of an optical fiber.
Variational principle has been incorporated in the proposed semi analytical formulation to characterize graded index optical fiber and optimization process is being carried out by NelderMead Simplex method for nonlinear unconstrained minimization. By introducing increased optimizing parameters in the formulation of fundamental modal field, more flexibility to refine a design and thus achieving a greater accuracy for a particular requirement, has been presented. Employing variational technique, effective index, normalized propagation constant, normalized group delay and modal dispersion parameter of an optical fiber have been evaluated analytically, by using the proposed formulation of fundamental field. The calculations show excellent agreement to the exact results, over a wide range of normalized frequency. Optimized values of three parameters, incorporated in the fundamental modal field have been presented for various values of normalized frequencies. This approximation can be used in the analysis of doped and nonlinear fiber amplifier, or in the case of dispersion-shifted fiber with large effective area.
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