极值波的拓扑控制
Topological Control of Extreme Waves
摘要：
从光学到流体力学，冲击波和异常波广泛存在。虽然它们看起来是不同的现象，但新的理论指出，极端波之间的过渡是允许的。然而，由于缺乏控制策略，这些从未被实验观察到。利用Riemann θ函数的非线性薛定谔方程解所对应的环面亏格与波包振荡相数之间的一一对应关系，提出了一种新的非线性波拓扑控制的概念.我们证明了它的实验报告的第一个观察监督过渡极端波与不同的属，如连续过渡从色散冲击流氓波。具体来说，我们使用一个参数的时间依赖的非线性形状的渐近波属。我们考虑了聚焦类克尔光折变介质中的盒问题，通过调整非线性和色散随时间变化的传播系数，来探索状态图中的每个区域，并包含了非线性波传播的所有动力学相位。我们的结果是可积非线性波拓扑控制的第一个例子。这种新技术使色散冲击波和流氓波的产生，并可以扩展到其他非线性现象，从经典的量子。这一结果不仅对极端非线性波的基础研究和控制具有重要意义，而且在显微镜、医学、光谱学等领域的空间光束整形以及宽带相干光的产生等方面也具有重要的应用价值。
英文摘要：
From optics to hydrodynamics, shock and rogue waves are widespread. Although they appear as distinct phenomena, new theories state that transitions between extreme waves are allowed. However, these have never been experimentally observed because of the lack of control strategies. We introduce a new concept of nonlinear wave topological control, based on the one-to-one correspondence between the number of wave packet oscillating phases and the genus of toroidal surfaces associated with the nonlinear Schrödinger equation solutions by the Riemann theta function. We prove it experimentally by reporting the first observation of supervised transitions between extreme waves with different genera, like the continuous transition from dispersive shock to rogue waves. Specifically, we use a parametric time-dependent nonlinearity to shape the asymptotic wave genus. We consider the box problem in a focusing Kerr-like photorefractive medium and tailor time-dependent propagation coefficients, as nonlinearity and dispersion, to explore each region in the state-diagram and include all the dynamic phases in the nonlinear wave propagation. Our result is the first example of the topological control of integrable nonlinear waves. This new technique casts light on dispersive shock waves and rogue wave generation, and can be extended to other nonlinear phenomena, from classical to quantum ones. The outcome is not only important for fundamental studies and control of extreme nonlinear waves, but can be also applied to spatial beam shaping for microscopy, medicine and spectroscopy, and to the broadband coherent light generation.
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