Rare events in optical fibers

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Abstract

This thesis examines the topic of rogue waves and interacting quasi-solitons in optical fibers. We demonstrate a simple cascade mechanism that drives the formation and emergence of rogue waves in the generalized non-linear Schrödinger equation with third-order dispersion. Such generation mechanism is based on inelastic collisions of quasi-solitons and is well described by a resonant-like scattering behavior for the energy transfer in pair-wise quasi-soliton collisions. Our theoretical and numerical results demonstrate a threshold for rogue wave emergence and the existence of a period of reduced amplitudes — a "calm before the storm" — preceding the arrival of a rogue wave event. Using long time window simulations we observe the statistics of rogue waves in optical fibers with an unprecedented level of detail and accuracy, unambiguously establishing the long-ranged character of the rogue wave probability density function over seven orders of magnitude. The same cascade mechanism also generates rogue waves in the generalized non-linear Schrödinger equation with Raman term.

To comprehend the physics governing rogue wave formation, we propose an experimental setup where soliton amplification is induced without third order dispersion or Raman term. In an optical fiber with anomalous dispersion, we replace a small region of the fiber with a normal dispersion fiber. We show that solitons colliding in this region are able to exchange energy. Depending on the relative phase of the soliton pair, we find that the energy transfer can lead to an energy gain in excess of 20% for each collision. A sequence of such events can be used to enhance the energy gain even further, allowing the possibility of considerable soliton amplification.

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