Abstract

We present a general framework capable of describing the nonlinear propagation of pulsed optical beams of arbitrary shapes and phase fronts inside a graded-index (GRIN) fiber. The main assumption made is that the spatial self-imaging features of the beam are not affected by the temporal evolution of optical pulses. A propagation kernel known from the work done in the 1970s is used to obtain a distance-dependent nonlinear coefficient that captures all spatial effects within an effective nonlinear Schrödinger equation. We consider three specific beam shapes (Gaussian, circular, and square) to study the impact of the shape, position, and curvature of optical beams on the complex spatiotemporal dynamics specific to GRIN fibers. In particular, we focus on the impact of an input beam’s shape on the modulation-instability sidebands and the generation of multiple dispersive waves when higher-order solitons form inside a GRIN fiber. The results of our numerical analysis indicate that for beam widths chosen to yield the same value of the effective mode area at the input end of the fiber, the nonlinear effects are pronounced considerably when a Gaussian beam is launched into the fiber. We also found that even though the self-imaging period is doubled when an off-centered Gaussian beam is launched into a GRIN fiber, it does not affect the nonlinear evolution because the effective beam area still maintains the same periodicity, as long as the shift in the beam’s center is not so large that it does not remain confined to the fiber’s core.

© 2020 Optical Society of America

Vector modulation instability in birefringent graded-index multimode fibers

Amira S. Ahsan and Govind P. Agrawal
J. Opt. Soc. Am. B 38(1) 201-208 (2021)

Nonlinear beam self-imaging and self-focusing dynamics in a GRIN multimode optical fiber: theory and experiments

Tobias Hansson, Alessandro Tonello, Tigran Mansuryan, Fabio Mangini, Mario Zitelli, Mario Ferraro, Alioune Niang, Rocco Crescenzi, Stefan Wabnitz, and Vincent Couderc
Opt. Express 28(16) 24005-24021 (2020)

Spatial beam narrowing in Raman amplifiers made with graded-index multimode fibers: a semi-analytic approach

Govind P. Agrawal
J. Opt. Soc. Am. B 40(4) 715-720 (2023)

Spatial beam self-cleaning accompanied by self-similar propagation in few-mode graded-index fiber

Leila Graini and Bülend Ortaç
J. Opt. Soc. Am. B 40(8) 2139-2145 (2023)

Evolution of the Bessel–Gaussian beam modeled by the fractional Schrödinger equation

Yagang Zhang, Zhenkun Wu, Jingmin Ru, Feng Wen, and Yuzong Gu
J. Opt. Soc. Am. B 37(11) 3414-3421 (2020)