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arXiv · 2501.11058

Variational approach to multimode nonlinear optical fibers

Francesco Lorenzi·Luca Salasnich
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Abstract

We analyze the spatiotemporal solitary waves of a graded-index multimode optical fiber with a parabolic transverse index profile. Using the nonpolynomial Schr\"odinger 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 Schr\"odinger equation, we provide a comparison of the stationary mode profiles in the radial and temporal coordinates.

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Francesco Lorenzi, Luca Salasnich. 2025-01-19. Variational approach to multimode nonlinear optical fibers. https://doi.org/10.1515/nanoph-2024-0591

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