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Experimental realization of Fermi-Pasta-Ulam-Tsingou recurrence in a long-haul optical fiber transmission system
摘要： The integrable nonlinear Schr?dinger equation (NLSE) is a fundamental model of nonlinear science which also has important consequences in engineering. The powerful framework of the periodic inverse scattering transform (IST) provides a description of the nonlinear phenomena modulational instability and Fermi-Pasta-Ulam-Tsingou (FPUT) recurrence in terms of exact solutions. It associates the complex nonlinear dynamics with invariant nonlinear spectral degrees of freedom that may be used to encode information. While optical fiber is an ideal testing ground of its predictions, maintaining integrability over sufficiently long distances to observe recurrence, as well as synthesizing and measuring the field in both amplitude and phase on the picosecond timescales of typical experiments is challenging. Here we report on the experimental realization of FPUT recurrence in terms of an exact space-time-periodic solution of the integrable NLSE in a testbed for optical communication experiments. The complex-valued initial condition is constructed by means of the finite-gap integration method, modulated onto the optical carrier driven by an arbitrary waveform generator and launched into a recirculating fiber loop with periodic amplification. The measurement with an intradyne coherent receiver after a predetermined number of revolutions provides a non-invasive full-field characterization of the space-time dynamics. The recurrent space-time evolution is in close agreement with theoretical predictions over a distance of 9000 km. Nonlinear spectral analysis reveals an invariant nonlinear spectrum. The space-time scale exceeds that of previous experiments on FPUT recurrence in fiber by three orders of magnitude.
关键词： finite-gap solutions,nonlinear Schr?dinger equation,nonlinear spectral analysis,Fermi-Pasta-Ulam-Tsingou recurrence,optical fiber transmission
更新于2025-09-12 10:27:22
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[IEEE 2019 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) - Munich, Germany (2019.6.23-2019.6.27)] 2019 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) - Fermi-Pasta-Ulam-Tsingou Recurrence in Spatial Optical Dynamics
摘要： Celebrated as the Fermi-Pasta-Ulam-Tsingou (FPUT) problem, the reappearance of initial conditions in unstable and chaotic systems is one of the most controversial phenomena in nonlinear dynamics. Integrable models predict recurrence as exact solutions [1], but the difficulties involved in upholding integrability for a long dynamics has not allowed a quantitative experimental validation. Evidences of the recurrence of states have been reported from deep water waves [2] to optical fibers [3]. However, the observation of the FPUT dynamics as predicted by exact solutions of an underlying integrable model remains an open challenge. Here, we report the observation of the FPUT recurrence in spatial nonlinear optics and provide evidence that the recurrent behavior is ruled by the exact solution of the Nonlinear Schrodinger Equation [4]. We exploit a three-waves interferometric setup [Fig. 1(a)] to finely tune amplitude and phase of the single-mode input perturbation propagating in a pumped photorefractive medium [5]. We reveal how the unstable mode manifests the Akhmediev breathers (AB) profile [Fig.1(c)] and undergoes several growth and decay cycles [Fig. 1(b)] whose partial-period and phase-shift are determined by the initial excitation in remarkable agreement with the analytic NLSE theory [Fig.1(d-e)]. The deterministic properties of the return cycle allows us to achieve one of the basic aspirations of nonlinear dynamics: the reconstruction, after several return cycles, of the exact initial condition of the system [Fig. 1(f)], ultimately proving that the complex evolution can be accurately predicted in experimental conditions. This results extends predictive approaches to unstable wave regimes and maps a strategy to achieve the control of rogue waves [6] in environmental conditions. In general, our findings shed light on the foundations of the FPUT problem and represent a unique test for nonlinear wave theory, with broad implications in nonlinear optics, hydrodynamics and beyond.
关键词： Nonlinear Schrodinger Equation,spatial optical dynamics,Akhmediev breathers,Fermi-Pasta-Ulam-Tsingou recurrence,nonlinear dynamics
更新于2025-09-11 14:15:04