Pulse propagation and soliton formation in nonlinear Photonic Band Gap materials

周期性微结构介电材料的线性特性是通过光子能带结构来表征的，对于相关参数的适当选择，可能会表现出光子带隙(PBG)，这是一个普通(线性)传播不被允许的频率范围。然而，在存在光学非线性的情况下，对于足够强的间隙孤子形式的脉冲，可以实现PBG内部频率的波传播。微细加工技术的最新进展使人们能够制造出成分表现出相当大的非线性的光子带隙材料，从而使非线性光子带隙材料在非线性效应的基础研究以及在全光信息处理和逻辑门的高级应用中变得越来越重要。在这个项目中，我们将研究脉冲在非线性光子带隙材料中的传输以及它们与缺陷以及相互之间的相互作用。通过数值模拟和变分技术的结合，我们将研究非线性脉冲到禁带孤子的演化，其中由于光子带隙附近的强多次散射，我们预计将发生强烈的非马尔科夫辐射动力学。我们将对PBG材料中线性和非线性缺陷处的孤子陷阱以及如何通过与传播的禁带孤子相互作用来控制孤子进行类似的研究。这些研究将对实现实用的全光技术具有重要意义，并为基本的非线性现象提供新的见解，由于非线性过程的普遍性质，这些现象可能会对其他非线性系统产生影响，例如光学晶格中玻色-爱因斯坦凝聚体中的孤子。

Periodically microstructured dielectric materials whose linear properties are characterized through a photonic bandstructure that - for appropriate choices of the relevant parameters - may exhibit a photonic band gap (PBG), a frequency range where ordinary (linear) propagation is disallowed. However, in the presence of optical nonlinearities, wave propagation for frequencies inside the PBG may be realized for sufficiently intense pulses in the form of gap-solitons. Recent progress in mircofabrication technology allows one to manufacture Photonic Band Gap materials whose constituents exhibit sizeable nonlinearities so that nonlinear PBG materials will become increasingly important both in fundamental studies of nonlinear effects and advanced applications in all-optical information processing and logic gates. Within this project, we will investigate the propagation of pulses in nonlinear PBG materials and their interaction with defects as well as with each other. Through a combination of numerical simulations and variational techniques, we will study the evolution of nonlinear pulses into gap-solitons where - due to the strong multiple scattering near the PBG - we expect strongly non-Markovian radiation dynamics to occur. We will carry out similar investigations for the trapping of soliton at linear and nonlinear defects within the PBG material and how to control trapped solitons through interactions with propagating gap-solitons. These investigations will be of significance for the realization of practical all-optical technologies as well as provide novel insights into basic nonlinear phenomena which -owing to the universal nature of nonlinear processes - may have implications to other nonlinear systems such as solitons in Bose-Einstein condensates in optical lattices.