三波谐振介质中光学异常波的共存及其实验观测

项目名称： 三波谐振介质中光学异常波的共存及其实验观测

项目编号： No.11474051

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 陈世华

作者单位： 东南大学

项目金额： 96万元

中文摘要： 由于其神秘莫测和潜在破坏性，海洋异常波(rogue waves)一直是过去十多年来的研究焦点。最近，异常波研究已延伸至物理学的其他学科，如流体动力学、非线性光学、等离子体物理、波色爱因斯坦凝聚等。特别在非线性光学领域，光学异常波已成为当前最为前沿的研究话题之一，并相继在光纤、锁模激光器、和飞秒成丝中得到实验证实。尽管如此，但科学界对异常波根源的理解还在争论中，一些新颖的动力学如暗异常波、异常波共存等还未得到实验验证。本项目将致力于理论和实验研究三波谐振光学介质中不同异常波态的形成与共存现象，其内容包括：寻求三波谐振方程（3C LWSW/TWRI方程）的精确异常波解，讨论异常波的产生机制与复杂动力学；数值模拟异常波的典型动力学及其坚固性；建立与模型方程自洽的三波谐振光学系统，实验观测暗异常波产生及异常波的共存现象。我们预期这些研究将有助于澄清异常波现有的学术争议，加深人们对其本质特征的理解。

中文关键词： 异常波；光孤子；三波谐振相互作用；Hirota双线性方法；达布变换

英文摘要： Because of their mysterious and potentially devastating manifestations, oceanic rogue waves have been the focus of intense research for more than a decade. The rogue wave terminology itself refers to the adverse surprise that is experienced when a transient giant wave of extreme amplitude or steepness is suddenly formed in the vicinity of a cruising ship. Recently, rogue wave research was also spreading widely to other physical disciplines that share general features of nonlinearity and complexity. These new avenues for rogue wave research include fluid dynamics, nonlinear optics, plasma physics, and Bose-Einstein condensation. Particularly, in nonlinear optics, optical rogue waves have become one of the most active topics on the cutting edge of fundamental soliton research, and have been confirmed experimentally in optical fibers, mode-locked lasers, and femtosecond filamentation. Despite all this, however, the possibility to accede to a general understanding of the origin of rogue waves is still an open question, and some novel rogue wave dynamics such as dark rogue waves and coexisting rogue waves is still not observed yet. In this project, we commit ourselves to explore the coexistence of optical rogue waves in three-wave resonant media both theoretically and experimentally. Specifically, we first derive the exact rogue wave solutions of the three-wave resonant equations, including the 3-component long wave-short wave (3C LWSW) equations and the three-wave resonant interaction (TWRI) equations, based on either the Darboux transformation or the Hirota bilinear method, and discuss their complex dynamics as well as the underlying physics. Then, we perform extensive numerical simulations to confirm the robustness of the involved dynamics, using the multiphysics simulation software or the split-step Fourier method. Lastly, we set up a self-consistent three-wave resonant optical system and use it to observe the formation of a dark rogue wave and the coexistence of different rogue waves. We expect that these studies may help to clarify some disputable issues in current rogue wave research and thus enrich our understanding on the nature of rogue waves.

英文关键词： Rogue Wave;Optical Soliton;Three-Wave Resonance Interaction;Hirota Bilinear Method;Darboux Transformation