In optical fibres, weak modulations can grow at the expense of a strong pump to form a triangular comb of sideband pairs, until the process is reversed. Repeated cycles of such conversion and back-conversion constitute a manifestation of the universal nonlinear phenomenon known as Fermi–Pasta–Ulam recurrence. However, it remains a major challenge to observe the coexistence of different types of recurrences owing to the spontaneous symmetry-breaking nature of such a phenomenon. Here, we implement a novel non-destructive technique that allows the evolution in amplitude and phase of frequency modes to be reconstructed via post-processing of the fibre backscattered light. We clearly observe how control of the input modulation seed results in different recursive behaviours emerging from the phase-space structure dictated by the spontaneously broken symmetry. The proposed technique is an important tool to characterize other mixing processes and new regimes of rogue-wave formation and wave turbulence in fibre optics.

https://hal.archives-ouvertes.fr/hal-02385106/document

Fibre multi-wave mixing combs reveal the broken symmetry of Fermi-Pasta-Ulam recurrence

One of the most controversial phenomena in nonlinear dynamics is the recurrence of initial conditions. New optical experiments reveal the origin of this enigma and demonstrate the ability to reconstruct the initial condition of an unstable system.

Observation of Fermi-Pasta-Ulam-Tsingou Recurrence and Its Exact Dynamics

The double-periodic solutions of the focusing nonlinear Schr\"odinger equation have been previously obtained by the method of separation of variables. We construct these solutions by using an algebraic method with two eigenvalues. Furthermore, we characterize the Lax spectrum for the double-periodic solutions and analyze rogue waves arising on the background of such solutions. Magnification of the rogue waves is studied numerically.

Rogue waves on the double-periodic background in the focusing nonlinear Schrödinger equation

We report an optical fiber experiment in which we study the nonlinear stage of modulational instability of a plane wave in the presence of a localized perturbation. Using a recirculating fiber loop as the experimental platform, we show that the initial perturbation evolves into an expanding nonlinear oscillatory structure exhibiting some universal characteristics that agree with theoretical predictions based on integrability properties of the focusing nonlinear Schrodinger equation. Our experimental results demonstrate the persistence of the universal evolution scenario, even in the presence of small dissipation and noise in an experimental system that is not rigorously of an integrable nature.

Nonlinear Evolution of the Locally Induced Modulational Instability in Fiber Optics

The Physics of the one-dimensional nonlinear Schrödinger equation in fiber optics: rogue waves, modulation instability and self-focusing phenomena

Instabilities are common phenomena frequently observed in nature, sometimes leading to unexpected catastrophes and disasters in seemingly normal conditions. One prominent form of instability in a distributed system is its response to a harmonic modulation. Such instability has special names in various branches of physics and is generally known as modulation instability (MI). The MI leads to a growth-decay cycle of unstable waves and is therefore related to Fermi-Pasta-Ulam (FPU) recurrence since breather solutions of the nonlinear Schrodinger equation (NLSE) are known to accurately describe growth and decay of modulationally unstable waves in conservative systems. Here, we report theoretical, numerical and experimental evidence of the effect of dissipation on FPU cycles in a super wave tank, namely their shift in a determined order. In showing that ideal NLSE breather solutions can describe such dissipative nonlinear dynamics, our results may impact the interpretation of a wide range of new physics scenarios.

/pdf/modulation-instability-and-phase-shifted-fermi-pasta-ulam-49x8ksok3g.pdf

Modulation Instability and Phase-Shifted Fermi-Pasta-Ulam Recurrence.

Instabilities are common phenomena frequently observed in nature, sometimes leading to unexpected catastrophes and disasters in seemingly normal conditions. The simplest form of instability in a distributed system is its response to a harmonic modulation. Such instability has special names in various branches of physics and is generally known as modulation instability (MI). The MI is tightly related to Fermi-Pasta-Ulam (FPU) recurrence since breather solutions of the nonlinear Schrodinger equation (NLSE) are known to accurately describe growth and decay of modulationally unstable waves in conservative systems. Here, we report theoretical, numerical and experimental evidence of the effect of dissipation on FPU cycles in a super wave tank, namely their shift in a determined order. In showing that ideal NLSE breather solutions can describe such dissipative nonlinear dynamics, our results may impact the interpretation of a wide range of new physics scenarios.

/pdf/modulation-instability-and-phase-shifted-fermi-pasta-ulam-19sighozsz.pdf

M. S. Li

Papers

Modulation Instability and Phase-Shifted Fermi-Pasta-Ulam Recurrence.

Modulation Instability and Phase-Shifted Fermi-Pasta-Ulam Recurrence