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.

在光纤中，弱调制可能会以强大的泵浦为代价而增长，以形成边带对的三角梳，直到过程相反。这种转换和反向转换的重复周期构成了普遍的非线性现象的表现，即费米-帕斯塔-乌拉姆复发。然而，由于这种现象的自发对称破坏性质，观察不同类型的复发并存仍然是一个重大挑战。在这里，我们实现了一种新颖的非破坏性技术，该技术可以通过对光纤的反向散射光进行后处理来重构频率模式的振幅和相位的演化。我们清楚地观察到，对输入调制种子的控制是如何导致自发地打破对称性所指示的相空间结构中出现不同的递归行为的。所提出的技术是表征光纤中其他混合过程以及流氓波形成和波湍流的新机制的重要工具。