Statistical study on rogue waves in Gaussian light field in saturated nonlinear media

The concept of rogue waves originated in oceanography, and refers to high-intensity waves with great destructive power that suddenly appear and disappear in the sea. Ocean-going ships, offshore drilling platforms and other facilities have records of being damaged by rogue waves. It is extremely difficult to study rogue waves in water environments such as oceans or tanks due to their unpredictable nature and numerous excitation conditions.

In 2007, time-domain rogue waves in nonlinear optical fibers were discovered for the first time, and the research on rogue waves entered the field of optics. Since optical experiments are repeatable and each parameter can be quantitatively analyzed, researchers can better explore the excitation conditions and characteristics of rogue waves through the study of optical rogue waves.

In 2019, C. Hermann-Avigliano statistically studied nonlinear spatial rogue waves induced by tightly focused beams, and concluded that the rogue wave excitation probability is positively correlated with nonlinearity. However, the excitation conditions of the wide-area spatial frequency distribution of the input tightly focused Gaussian light cannot directly reflect the role of modulation instability in the excitation of rogue waves.

Recently, the team of Professor Lou Cibo from the College of Physical Science and Technology of Ningbo University conducted a statistical study on the spatial rogue waves in saturated nonlinear medium, and found that under the condition of wide beam incidence. The excitation probability of the spatial rogue waves appears to the maximum when the optical splitting filament is induced by the saturated nonlinear modulation instability. The irregular change of the spatial rogue waves excitation probability with the nonlinear intensity is also observed experimentally，as shown in Fig. 1.

Relevant research results were published in Chinese Optics Letters Vol. 20, Issue 8 in 2022 under the title of "Statistical study on rogue waves in Gaussian light field in saturated nonlinear media", and was selected as the cover.

The study found that with the increase of nonlinearity, the beam undergoes a Gauss-corrosion like region-splitting process, and the excitation probability of rogue waves reaches the highest when the beam is just splitting, and then the excitation probability of rogue waves fluctuates. It is also found that the rogue wave excitation probability has the same trend as the flicker index, as show in Fig. 2(a), which provides another parametric perspective for people to study rogue waves. In addition, the corresponding numerical simulation supports the experimental results well, as show in Fig. 2(b).

The researchers further verified the rogue waves characteristics of the high-amplitude light spot in the experiment by observing the spatial spectrum. The appearance of the high-order spectrum is an important feature of the rogue wave. As shown in Fig.3, when the voltage of 400 V reaches the critical point of splitting, the spectrum is obviously broadened, and the discrete high-order spectrum appears, which can further prove that the high-amplitude light spot in the experiment conforms to the rogue wave characteristic.

In summary, the mechanism of wide Gaussian light excitation of spatial rogue waves under saturated nonlinearity is much more complicated than generally believed. With the increase of nonlinearity, splitting of high-intensity filaments and the increase of the overall filament number will causes the change of the rogue wave excitation probability. In the follow-up research, the researchers will also study the influence of different perturbation intensities and incident light gradients on the excitation of rogue waves, and incorporate diffusion effects into statistics to explore the excitation mechanism of rogue waves under higher nonlinearity.

高斯光激发铌酸锶钡晶体，破解怪波的又一视角

怪波的概念最早起源于海洋学，指在海中突然出现又突然消失的、具有极大破坏力的高强度海浪。远洋船舶、海上钻井平台等设施都有被怪波破坏的记录。由于怪波无法预测且影响因素众多，在海洋或水箱等水体环境中对怪波进行研究极其困难。

2007年，非线性光纤中的时域怪波首次被发现，对怪波的研究也进入了光学领域。由于光学实验的可重复性和各参量可定量分析的特性，研究者可通过对光怪波的研究来更好地探究怪波的激发条件和特性。

2019年，C. Hermann-Avigliano对紧聚焦光束诱导非线性空间光怪波的统计研究，得出了怪波激发几率与非线性正相关的结论。然而，输入紧聚焦高斯光的广域空间频率分布的激发条件无法直接体现调制不稳在怪波激发中的作用。

近日，宁波大学楼慈波教授团队针对上述问题，提出使用宽高斯光在铌酸锶钡（SBN）晶体中激发空间怪波并统计研究怪波激发几率与非线性关系的方法，图1为空间光怪波实验光路。研究发现宽光束入射条件下，光怪波激发几率在饱和非线性调制不稳性引发光分丝时出现最大值，还实验观测到了光怪波激发几率随非线性强度的变化现象。

相关研究成果以“Statistical study on rogue waves in Gaussian light field in saturated nonlinear media”为题发表于Chinese Optics Letters2022年20卷第8期，并被选为当期封面。

研究发现，随非线性增强，光束经历高斯-腐蚀状区域-分丝的变化过程，在光束刚分丝时怪波激发几率达到最高，随后怪波激发几率出现波动变化。研究发现，怪波激发几率与闪烁指数有相同的变化趋势（如图2（a）所示），这为人们研究怪波提供了另一个参量视角。此外，对怪波激发几率-外加电压数值模拟很好的支撑了该实验结果（如图2（b）所示）。

研究者通过观察不同电压下SBN晶体出射面的光强和空间频谱进一步验证了高振幅光斑的怪波特性，如图3所示。高阶频谱的出现是出现怪波的一个重要特征，在400 V电压下达到分丝临界时，频谱明显展宽，并伴随离散的高阶频谱出现，这进一步证明了高振幅光斑符合怪波特性。

综上所述，饱和非线性下宽高斯光激发空间怪波的机制比一般认为的要复杂得多，随着非线性增强，高强度光丝分裂和整体光丝数量的增加都会导致怪波激发几率的下降。在后续的研究中，研究者还将研究不同的微扰强度和入射光梯度对怪波激发的影响，并引入扩散效应，探究更高非线性下的怪波激发机制。