Semi-analytical formulation of modal dispersion parameter of an optical fiber with Kerr nonlinearity and using a novel fundamental modal field approximation

Abstract

To characterize nonlinear optical fiber, a semi-analytical formulation using variational principle and the Nelder–Mead Simplex method for nonlinear unconstrained minimization is proposed. The number of optimizing parameters in order to optimize core parameter U has been increased to incorporate more flexibility in the formulation of an innovative form of fundamental modal field. This formulation provides accurate analytical expressions for modal dispersion parameter (g ) of optical fiber with Kerr nonlinearity. The minimization of core parameter (U ), which involves Kerr nonlinearity through the nonstationary expression of propagation constant, is carried out by the Nelder–Mead Simplex method of nonlinear unconstrained minimization, suitable for problems with nonsmooth functions as the method does not require any derivative information. This formulation has less computational burden for calculation of modal parameters than full numerical methods.