Emulation of the Graphene structure using photonics

在本提案中，我们将使用蜂窝状排列的光波导阵列来模拟石墨烯的物理特性。由于旁轴波方程（描述光通过波导阵列的传播）在数学上等同于Schrödinger方程（描述石墨烯中电子的时间演化），因此在周期性折射率调制（波导阵列）中传播光波的动力学将类似于固体晶体电位中电子波函数的演化。在这种情况下，在以蜂窝几何形状排列的波导阵列中，可以使用经典光波直接观察石墨烯的波动动力学。使用这种光子石墨烯的特殊好处是：(1)电子石墨烯的边缘往往是非常不规则的，并且被吸附物污染，而使用光学结构来探测这些边缘提供了一个天然的优势；(2)在制造过程中，即使最强的均匀和非均匀应变也可以施加到光子石墨烯上，而不会破坏单晶格元素之间的键；(3)可以独立分析复合无序（由周期晶格中的杂质引起）和结构无序（由于晶格位置的随机横向移动），而不存在任何相关性，这与传统石墨烯不同，在传统石墨烯中，两种无序类型同时出现并以相关的方式出现。通过利用石墨烯中电子的演化与蜂窝光子结构中光子的传播之间的类比，我们将制造具有前所未有性能的新型光子器件，为其描述和理解奠定理论基础，并尽可能将结果转移到石墨烯中。利用光学石墨烯器件易于制造的优势，我们将不会局限于完美的蜂窝晶格，但我们将使用实验技术以可控的方式诱导应变，压缩和无序，以诱导器件的新功能。我们将利用应变和无序对石墨烯结构的影响，我们将探索传统石墨烯无法达到的新状态，我们将控制这些状态在制造结构中的存在。在固态物理和材料科学领域，我们将能够探索蜂窝光子结构中比石墨烯本身更容易演示和研究的现象。然而，这些发现将与两类材料共享的蜂窝结构和狄拉克色散关系联系起来。在这方面，充分理解石墨烯独特几何结构的含义将有助于改进基于石墨烯的现有器件，并为各种领域的应用开发新的想法和概念。

In this proposal, we will emulate the physics of graphene using optical waveguide arrays that are arranged in honeycomb geometry. Since the paraxial wave equation (which describes the propagation of light through the waveguide array) is mathematically equivalent to the Schrödinger equation (describing the time-evolution of electrons in graphene), the dynamics of a propagating light wave in a periodic refractive index modulation (a waveguide array) will be similar to the evolution of an electronic wave function in the crystalline potential of a solid. In this vein, in an array of waveguides that are arranged in honeycomb geometry, it is possible to directly observe graphene wave dynamics using classical light waves. Particular benefits of using such photonic graphene are: (1) that the edges of electronic graphene tend to be very irregular and contaminated with adsorbates, whereas the use of optical structures to probe these edges provides a natural advantage; (2) that even strongest homogeneous and inhomogeneous strain can be applied to photonic graphene during the fabrication process without damaging the bonds between the single lattice elements; and (3) the possibility to analyze composite disorder (caused by impurities in the periodic lattice) and structural disorder (due to random lateral shifts of the lattice sites) independently of each other and without any correlations, in contrast to conventional graphene, where both disorder types appear simultaneously and in a correlated fashion.By exploiting the analogy between the evolution of electrons in graphene and the propagation of photons in honeycomb photonic structures, we will fabricate novel photonic devices with unprecedented properties, lay the theoretical foundation for their description and understanding, and transfer the results to graphene, where possible. Taking advantage of the ease of fabrication of optical graphene devices, we will not be limited to perfect honeycomb lattices, but we will use experimental techniques to induce strain, compression, and disorder in a controllable fashion, in order to induce new functionalities to the devices. We will exploit the impact of strain and disorder on the graphene structure, we will probe new states inaccessible to conventional graphene, and we will control the existence of these states in the fabricated structures. In the field of solid state physics and materials science, we will be able to explore phenomena which are much easier to demonstrate and study in honeycomb photonic structures than in graphene itself. However, these findings will be associated with the honeycomb structure and Dirac dispersion relation that the two class of materials share. In this vein, a full understanding of the implications of the unique geometry of graphene will facilitate the refinement of existing devices based on graphene as well as the development of new ideas and concepts for applications in various fields.