Evaluation of few propagation parameters for single-mode nonlinear graded index profile fibers in low V-region: a simplified analytical framework

This paper presents accurate analytical expressions for propagation constant, modal dispersion parameters and group delay in graded index optical fibers operating in the fundamental mode, especially tailored for the low V number region. Utilizing a power series-based representation of the fundamental mode field derived using the analytical Chebyshev formalism, we investigate the behaviour of typical index profiles-step, parabolic, and triangular under both linear and Kerr nonlinear conditions. The impact of nonlinearity is incorporated through an iterative method, enabling efficient prediction of propagation characteristics. Our results demonstrate excellent agreement with exact numerical solutions as obtained using the finite element method, while requiring significantly less computational effort. The proposed model proves to be a reliable and practical tool for researchers and system engineers working in nonlinear fiber optics, particularly in regimes where low V numbers are critical.