光诱导光子石墨烯中离散衍射与带隙孤子的研究

In recent years, light propagating behavior in optical periodic structures, especially discrete diffraction in linear arrays and gap solitons in nonlinear waveguides, become one of the hot research subjects in optical field. But most of the works are done in one-dimensional(1D) and 2D rectangular or triangular(hexagonal) photonic lattices. While the light propagating behavior in the photonic graphene possessing a unique band structure is studied only by theory. So, in this project we propose, with the nonlinear schrodinger equation and band gap theory as a foundation, using optically induced photonic graphene as the platform, to study the optical discrete diffraction, gap solitons, Brillouin zone spectrum distribution and Bloch oscillations etc.by experimantal method mainly and by computer simulations subsequently. This research results will deepen our understanding of the wave dynamics in different photonics mesoscopic structure, and perfect our cognition to the method and means of manipulating light waves in mesoscopic size, meanwhile, they lay the foundation for realization of novel photonic devices.In addition, they can provide reference to the electron wave dynamics in graphene(single graphene sheets of carbon atoms ).

近年来，光在周期结构中的传输行为，特别是线性波导中的离散衍射和非线性波导中的带隙孤子成为光学领域的热门课题之一。但是绝大部分工作是一维或二维四方、三角（六角）光子晶格中进行的。而光在具有特殊结构的光子石墨烯（蜂窝状光子晶格）中传输行为的研究却仅限于理论。所以，本项目拟以非线性薛定谔方程和带隙理论为基础，用光诱导法实时制作的光子石墨烯作为平台，以实验为主计算模拟为辅研究离散衍射，带隙孤子，布里渊区谱和布洛赫振荡等。其研究结果将加深人们对不同周期介质中波动力学理解，完善在介观系统中人们操控光波方法和手段的认识，并为实现新型光子学器件打下基础。另外，该研究为石墨烯（由碳原子构成的单层石墨）中电子波动力学的研究提供参考。

1.利用掩模法和空间光调制器法两种方法在光折变晶体中成功制作了光子石墨烯以及相关的一些光子晶格。数学上用傅立叶变换法求解了掩模法制作的光子晶格准确数学表达式，用麦克斯韦方程组求解多光束干涉产生的光子晶格的准确数学表达式。2.实验研究了光子石墨烯及相关光子晶格中的远场衍射图样，布里渊区谱，离散衍射及带隙孤子。3.用空间光调制器制作了复杂涡旋光子晶格光场。4.发现把两个相同的光子晶格光场以特定的角度θ叠加，能产生复杂的无衍射周期光子晶格光场。作为特例，我们计算了两个相同的四方格子“4+4”和两个相同的六方格子“6+6”，并得倒了一系列的周期无衍射光场。