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

Fig. 1 Optical path of space light strange wave experiment

Fig. 2 (a) The flicker index-applied voltage numerical simulation, (b) the rogue wave excitation probability-applied voltage numerical simulation. Inset: light intensity distribution at 700V

Fig.3 (a)-(c) The light intensity distribution of the SBN crystal at different voltages; (d)-(f) The spatial spectrum of the exiting surface at different voltages

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.