Generalised Closed-Form Model for Super-Gaussian Pulse Propagation in Single-Mode Optical Fibre

Abstract

Linear and nonlinear effects degrade the pulses propagated through single-mode optical fibre at high bit rates. Their numerical simulation by methods such as the inverse fast Fourier transform (IFFT) is accurate but computationally expensive, whereas existing closed-form models are restricted to Gaussian pulses, which poorly reproduce the quasi-rectangular waveform delivered by real optical transmitters. This work presents a generalised closed-form analytical model for the propagation of super-Gaussian pulses of arbitrary order m in single-mode fibre. Using the method of moments, closed-form expressions are derived for the propagated chirp, the pulse width and the RMS broadening factor, together with a correction factor that guarantees exact continuity with the Gaussian case. The model is validated against a numerical IFFT reference over an ITU-T G.652b fibre at $\lambda=1320 \mathrm{~nm}$ for different values of m, yielding RMS-width errors below $10^{-4} \%$ for all tested $m \leq 10$, with a computational speed-up between roughly $650 \times$ and $1.6 \times 10^{5}$ over the IFFT. Extended validation over $z=10-100 \mathrm{~km}$ and at $\lambda=1550 \mathrm{~nm}$ confirms the same accuracy, and a closed-form leading-order estimate shows this error is intrinsically independent of both propagation distance and operating wavelength, making the model suitable for real-time parametric sweeps and the interactive design of high-speed optical links.