The observation of ideal four-wave mixing dynamics is notoriously difficult to implement experimentally due to the generation of higher-order sidebands and optical loss, which limit the potential interaction distance. Here, we overcome this problem with an experimental technique that uses programmable phase and amplitude shaping to iterate the wave mixing initial conditions injected into an optical fiber. This extends the effective propagation distance by two orders of magnitude, allowing idealized Kerr-driven dynamics to be seen over 50 km of fiber using only one short fiber segment of 500 m. Our experiments reveal the full phase space topology, showing characteristic features of multiple Fermi–Pasta–Ulam recurrence, stationary wave existence, and the system separatrix representing the boundary between two distinct regimes of spatiotemporal evolution. Experiments are in excellent quantitative agreement with numerical solutions of the differential equation system describing the wave evolution. This experimental approach can be readily adapted to study other wave mixing and nonlinear propagation phenomena in optics.

中文翻译：

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非线性薛定谔方程光纤系统中的理想化四波混频动力学

由于高阶边带和光损耗的产生，限制了潜在的相互作用距离，理想的四波混合动力学的观察是出了名的难以通过实验实现。在这里，我们通过一种实验技术克服了这个问题，该技术使用可编程相位和幅度整形来迭代注入光纤的波混合初始条件。这将有效传播距离延长了两个数量级，仅使用一个 500 m 的短光纤段，就可以在 50 km 的光纤上看到理想化的 Kerr 驱动动力学。我们的实验揭示了全相空间拓扑结构，显示了多次 Fermi-Pasta-Ulam 递归、驻波存在、系统分界线表示两种不同的时空演化机制之间的边界。实验与描述波浪演化的微分方程系统的数值解具有极好的定量一致性。这种实验方法可以很容易地适用于研究光学中的其他波混合和非线性传播现象。