Spatial Solitons and Their Applications

PI提出从实验和理论上探索与空间光孤子相关的几个全新的想法。所有提出的研究课题挑战基本的基本问题，其中一些在光学以外的其他领域有直接的影响。其中一些研究课题提供了其他方法无法实现的新应用，其中一个研究目标是研究二维系统中的离散孤子。最近，该小组发现了如何在真实的时间内诱导密集的二维非线性波导阵列。PI建议演示这些系统中的（2+1）D离散孤子，这些孤子之间的碰撞（包括当输入离散孤子携带角动量时），显示与它们的全光开关，并演示与它们的2D衍射管理（负衍射）。一个与此相关的想法是在二维非线性波导中由光折变孤子诱导产生隙（或布拉格）孤子。这种实现Gap孤子的新方法将导致首次观测到Gap孤子之间的相互作用，使这种时空脉冲的速度变慢（到很低的值），并实现Gap孤子的全光开关。另一个研究方向是非相干腔孤子和非线性弱关联波系统中腔斑图的形成。这些想法源于他们对非相干孤子和非相干调制不稳定性的发现。在这里，他们建议建立在这些发现和研究非相干腔孤子的创建和复杂的模式出现在非相干波前腔。第二个相关的想法是在非线性弱关联波系统中的孤子的集群和聚合进行角动量。该研究小组在2001年指出，孤子可以聚集在一起，形成精细尺度结构的聚集体，同时留下空洞的空间。这些图案自然地演变（通过非相干调制不稳定性过程）从均匀但部分非相干的波前发射到非瞬时非线性介质。他们预期，如果输入波阵面带有角动量（拓扑荷），则所产生的孤子簇将形成类似星系的结构。他们的另一个目标是研究一种新型的孤子：全息孤子，它是由两个共生场组成的孤子，并且仅由它们诱导的光栅支撑。最后，他们提出研究由两个反向传播光场组成的空间光孤子及其相互作用碰撞，空间光孤子在相互作用和稳定性方面表现出类似粒子的行为，能量和动量守恒。空间孤子的迷人的结果，在许多非光学系统，可以支持孤子有重大影响。非相干斑图的形成对玻色-爱因斯坦凝聚体中的动力学和孤子、分数量子霍尔效应以及其他几个非线性多粒子系统，包括颗粒材料（沙子）中的条纹形成具有广泛的影响。这些不相干的图案形成效应直接关联到（有序-无序）相变现象，在经典（相位无关，因此不相干）和量子力学类（相位相关，相干）系统。他们建议在不同相干性的系统中研究图案形成过程中的相变效应，探索居里-外斯定律、临界慢化和相变的其他特征的表现。在过去的三十年里，孤子一直是人们深入研究的课题。在90年代，光学空间孤子强烈影响了这个领域，并刺激了非线性科学的大量研究。该计划的教育目标是培养毕业生，为推动光子学和光通信的发展做好充分准备。他们将利用他们的激光设备和对波导和孤子的研究作为新的教育工具来实现这一目标。想象一下，这个提议涉及的每一所大学都有一系列课程。为了增加该项目的多样性，阿肯色州目前正在与位于松树海崖的阿肯色州大学合作，开发一种名为“科学与工程路径”或“路径智慧”的新方法。

The PI proposes to explore, experimentally and theoretically, several completely new ideas related to optical spatial solitons. All of the proposed research topics challenge basic fundamental questions with some having direct implications in other fields beyond optics. Some of the proposed research topics offer exiting new applications that cannot be otherwise realized.One proposed research objective is an investigation of discrete solitons in 2D systems. Recently, the group has found how to induce, in real time, arrays of closely-spaced 2D nonlinear waveguides. The PIs propose to demonstrate (2+1)D discrete solitons in these systems, collisions between such solitons (including when the input discrete solitons carry angular momentum), show all-optical switching with them, and demonstrate 2D diffraction management (negative diffraction) with them. A somewhat related idea has to do with launching Gap (or Bragg) solitons in a periodically-modulated 2D nonlinear waveguide induced by a photorefractive soliton. This new way to realize Gap solitons could lead to the first observation of interactions between Gap solitons, to slowing down (to very low values) of the velocity of such a spatio-temporal pulse, and to all-optical switching of these solitons.Another proposed research direction is on incoherent cavity solitons and cavity pattern formation in nonlinear weakly-correlated wave-systems. The ideas emerged from their discovery of incoherent solitons and of incoherent modulation instability. Here they propose to build on these discoveries and study the creation of incoherent cavity solitons and the emergence of intricate patterns upon incoherent wave-fronts in cavities. A second related idea is on the clustering and aggregation of solitons in nonlinear weakly-correlated wave-systems that carry angular momentum. the group has shown (2001) that solitons can cluster together and form aggregates of fine-scale structures, while leaving behind them voids of empty space. These patterns evolve naturally (through the incoherent modulation instability process) from a uniform but partially-incoherent wavefront launched into a non-instantaneous nonlinear medium. They expect that if the input wavefront carries angular momentum (topological charge), the resultant clusters ofsolitons will form galaxy-like structures. Here too they plan to study these soliton clustering processes in cavities.Another objective is to investigate a new type of a soliton: the holographic soliton, which is a soliton composed of two symbiotic fields and is supported solely by the grating they induce. Finally, they propose to study solitons that are made of two counter-propagating optical fields, and their interaction collisions.Optical spatial solitons exhibit particle-like behavior in their interactions and stability properties, conserving energy and momentum. The fascinating results obtained with spatial solitons have major consequences in many non-optical systems that can support solitons. Incoherent pattern formation has broad implications on dynamics and solitons in Bose-Einstein Condensates, the fractional quantum Hall effect, and on several other nonlinear many-particle systems, including stripe-formation in granular materials (sand). These incoherent pattern formation effects are directly linked to (order-disorder) phase-transition phenomena, in both classical (phase-independent, thus incoherent) and quantum-mechanic-like (phase-dependent, coherent) systems. they propose to study phase-transition effects during pattern formation in systems of varying coherence, explore the manifestation of the Curie-Weiss Law, Critical Slowing Down, and other features of phase transitions. Solitons have been the subject of intense studyover the last three decades. In the 90's, optical spatial solitons have strongly influenced this field and have stimulated considerable research within nonlinear sciences.The educational goal of the program is to produce graduates that are fully prepared to drive the advancement of photonics and optical communications. They will accomplish this goal by utilizing their laser facilities and research on waveguides and solitons as novel tools for education. Imagine a sequence of courses that already exists at each university involved in this proposal. To increase diversity in the program, Arkansas is current working together with the University of Arkansas at Pine Bluff on a newidea called "Path Way In Science and Engineering" or Path WISE.