Issue:
Volume 1, Issue 2, June 2026
Pages:
54-63
Received:
10 October 2026
Accepted:
20 October 2026
Published:
31 October 2026
Abstract: Optical fibers carry most of the world’s long-distance data traffic, and reliable mathematical models are essential for designing, optimizing and teaching the systems built on them. This work presents a self-contained mathematical model of light propagation in single-mode optical fibers and its numerical implementation in Python. Starting from Maxwell’s equations, we derive the guided-mode eigenvalue problem of the step-index fiber, the frequency dependence of attenuation and chromatic dispersion from the Sellmeier equation and empirical loss models, and the nonlinear Schrödinger equation (NLSE) governing the slowly varying pulse envelope under the combined effects of loss, dispersion and the Kerr nonlinearity. Closed-form results for Gaussian pulse broadening, self-phase modulation (SPM) and soliton propagation are used as analytical benchmarks and combined with a symmetric split-step Fourier method (SSFM) for the numerical solution. The numerical scheme is validated against these analytical solutions to a relative accuracy better than 10-12 for linear propagation, reproduces the expected number of SPM spectral peaks, preserves fundamental and third-order solitons over two soliton periods, and demonstrates the expected second-order convergence with step size. A link-level simulation of a 2.5 Gb/s amplified system, including amplifier noise, a square-law receiver and the resulting Q-factor, shows an optimum launch power that decreases from approximately +11 dBm to +5 dBm as the number of 80 km spans increases from three to six, illustrating the trade-off between noise accumulation and nonlinear distortion. The results show how a compact, physics-based model, implemented in a few dozen lines of code, reproduces the main performance trade-offs of fiber-optic transmission and provides a validated basis for further studies including polarization effects, Raman scattering and multi-channel transmission.
Abstract: Optical fibers carry most of the world’s long-distance data traffic, and reliable mathematical models are essential for designing, optimizing and teaching the systems built on them. This work presents a self-contained mathematical model of light propagation in single-mode optical fibers and its numerical implementation in Python. Starting from Maxw...
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