Near Field and Propagation Constant of Nonlinear Single-mode Optical Fibers: A Simple Numerical Technique

Abstract

Near field distribrution and propagation constant of nonlinear single-mode optical fibers have been investigated. The shooting method technique is used and implemented into a computer code for the case of step index and graded index fibers. Some reasonable and accurate approximations were made to match the cylindrical geometry. An error function is defined to estimate the discrepancy between the expected boundary values and the computed ones obtained by numerical integration through the use of Runge-Kutta method. More accurate values are then depicted using the secant method. The accuracy and convergence of the results have been considered by performing these methods in a two-path iterative manner. The effects of various guiding parameters and the nonlinear Kerr coefficient on the modal field distribution and on the effective index are studied. Typical b-V curves for both linear and nonlinear fibers are presented. The cutoff value of the normalized frequency is investigated and approximate relations with the Kerr coefficient are deduced for both fiber types.