Variational approach to multimode nonlinear optical fibers

2025/01/19 by Lorenzi, Francesco, Salasnich, Luca
#FOS: Physical sciences #Optics (physics.optics) #Pattern Formation and Solitons (nlin.PS) #Quantum Gases (cond-mat.quant-gas)

paper · doi:10.48550/arxiv.2501.11058

Abstract

We analyze the spatiotemporal solitary waves of a graded-index multimode optical fiber with a parabolic transverse index profile. Using the nonpolynomial Schrödinger equation approach, we derive an effective one-dimensional Lagrangian associated with the Laguerre-Gauss modes with a generic radial mode number p and azimuthal index m. We show that the form of the equations of motion for any Laguerre-Gauss mode is particularly simple, and we derive the critical power for the collapse for every mode. By solving the nonpolynomial Schrödinger equation, we provide a comparison of the stationary mode profiles in the radial and temporal coordinates.

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