Semnan University Press Progress in Physics of Applied Materials 2783-4794 6 4 2026 12 01 Numerical Analysis of Pulse Propagation in Optical Fibers Using Paraxial Wave Equations 293 303 10609 10.22075/ppam.2026.40741.1211 EN Zaman Hameed Kareem Center For Research On Environment and Renewable Energy, University of Kerbala 56001 Karbala, Iraq. Journal Article 2026 02 26 The study presented here presents a numerical analysis of Gaussian beam propagation in a square‑law inhomogeneous refractive‑index medium using the paraxial wave equation (PWE) and the split-step Fourier beam propagation method. In contrast to earlier studies, which have mostly relied on analytical approximations, the present work offers a computationally efficient framework for studying beam modulation in multimode graded-index optical fibers with varying initial conditions. Simulations were performed using a beam wavelength of 0.633 µm, with a core refractive index of n₁ = 1.5 and a cladding parameter of n₂ = 0.01. The width of the fundamental mode was calculated to be 1.419 mm and the modulation period was 47.123 m. The results of the study show that when the initial beam waist (ω₀) is smaller than the fundamental mode size (e.g. ω₀ = 1 mm), the beam initially defocuses before focusing. Similarly, when ω₀ is larger than the fundamental mode size (2 mm and 3 mm), the beam focuses before defocusing. The effects of refractive‑index variations in the core (n₁) and cladding (n₂) on diffraction patterns are evaluated and compared. The proposed PWE‑based model improves memory efficiency by about 60% compared with the FDTD method while maintaining reasonable accuracy for weakly guiding fiber systems. The results of this study provide practical design guidelines and optimization insights for optical fiber communication systems and medical instrumentation applications. https://ppam.semnan.ac.ir/article_10609_565a9761f376101733ac474ea7554f11.pdf