Abstract

Modulation instability (MI) refers to a process where a weak periodic perturbation of an intense continuous wave (CW) grows exponentially as a result of the interplay between dispersion and nonlinearity. In its most basic manifestation, it can be observed in homogeneous optical fibers in the anomalous dispersion regime. Another kind of MI, named parametric instability (PI), is induced by the periodic variation of some parameters during the evolution [1]. Parametric instability can be produced by an external forcing (like Faraday instability of fluids) or by some collective oscillations. In the latter case it is called geometric-type parametric instability (GPI) [2]. A system that experiences a natural collective oscillation is a multimode graded-index (GRIN) fibre. GRIN fibers are now experiencing a new spring in nonlinear optics community due to their complex spatiotemporal dynamics [3]. The objective of this work is to study GPI in a GRIN fibre with a z-periodic core diameter, which represents an external forcing applied to the system.

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