Abstract
We provide a systematic analysis of geometric parametric instabilities in nonlinear graded-index multimode fibers. Our approach implicitly accounts for self-focusing effects and considers dispersion processes to all orders. It is shown that the resulting parametric problem takes the form of a Hill’s equation that can be systematically addressed using a Floquet approach. The theory developed indicates that the unstable spectral domains associated with such geometric parametric instabilities can be significantly altered as the power levels injected in a parabolic multimode fiber increase. These predictions are in excellent agreement with experimental data gathered from graded-index multimode structures.
Highlights
The landscape of fiber optic technologies has been dominated by single-mode fibers (SMFs)
We provide a systematic analysis of geometric parametric instabilities in nonlinear graded-index multimode fibers
We present a rigorous analysis of geometric parametric instabilities (GPIs) effects in multimode fibers (MMFs) that includes dispersion effects to all orders, while at the same time, it accounts for spatial self-focusing oscillations
Summary
The landscape of fiber optic technologies has been dominated by single-mode fibers (SMFs). MMFs can provide a versatile platform to investigate altogether new nonlinear propagation phenomena such as spatiotemporal dynamics, spatial beam self-cleaning, rogue waves, and spatiotemporal mode-locking to mention a few In this respect, graded-index (GRIN) MMFs play a prominent role due to the fact that the differential group delay between modes can be considerably suppressed.. Nonlinear light propagation in a MMF is a complex problem to analyze since it involves coupled spatial and temporal effects between hundreds or thousands of modes Along these lines, several numerical studies have been carried out to describe the space-time dynamics in parabolic MMFs based on perturbative schemes.. We present a rigorous analysis of GPI effects in MMFs that includes dispersion effects to all orders, while at the same time, it accounts for spatial self-focusing oscillations Note that under these conditions, a perturbative treatment is no longer valid. Analytical results supported by numerical simulations indicate that as the input power is increased, the generated GPI sidebands in GRIN MMFs tend to move closer to the pump wavelength, experiencing higher amplification rates
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