OP: Collaborative Research: Landau levels and Dirac points in Continuous Photonic Systems

描述光与物质之间相互作用的科学已经产生了各种各样的技术上的重要应用，我们的社会已经开始依赖（例如，构成互联网骨干的光纤，从电信到制造业等行业使用的激光，用于可持续能源的太阳能电池，等等）。几十年来，研究人员一直试图通过工程设计人工介电结构（如硅或玻璃）与入射光共振来增加光与物质之间的耦合强度。几乎所有这样的结构都是在空间中周期性重复的模式：一种微观的脚手架。该项目的主要目标之一是证明某些没有重复单元的非周期结构比周期设计更能促进光-物质耦合。这可能会为光与物质的相互作用开辟一个新的设计原则，并导致更高效的照明、太阳能电池，甚至光学量子计算机组件等应用。主要研究人员将设计光子结构（硅中的波导阵列和硅中的光子晶体），使其能带结构具有狄拉克点。这些结构将被“拉伸”（要么赋予物理张力，要么通过制造人工拉伸的结构），从而使它们变得非周期性，并经历一个“伪磁场”。这个伪磁场使特征值谱变得高度简并，导致大的态密度，这反过来又导致更强的光-物质耦合（Purcell增强）。这个项目是一个跨学科的努力，一个工程师，他的贡献是通过光学介质的制造和表征（Kevin Chen，匹兹堡大学），一个物理学家（Mikael Rechtsman，宾夕法尼亚州立大学），他将进行光学实验和建模，一个应用数学家（Michael Weinstein，哥伦比亚大学），他将共同开发数学PDE /离散模型并与Rechtsman和Chen合作分析这些模型。他们每个人的专业知识都对项目的成功至关重要。

The science describing the interaction between light and matter has produced a wide variety of technologically important applications that our society has come to rely on (for example, fiber optics that form the backbone of the internet, lasers used in industries ranging from telecommunications to manufacturing, solar cells used for sustainable energy, and many others). For decades, researchers have been trying to increase the strength of coupling between light and matter by engineering artificial dielectric structures (like silicon or glass) to be in resonance with incoming light. Nearly all such structures have been patterns that are periodically repeating in space: a kind of microscopic scaffolding. One of the principal goals of this project is to show that certain non-periodic structures with no repeating units can facilitate stronger light-matter coupling than periodic designs. This could open a new design principle for light-matter interaction and lead to applications like more efficient lighting, solar cells, or even components for optical quantum computers. The principal investigators will engineer photonic structures (both waveguide arrays in silica and photonic crystals in silicon) to have Dirac points in their band structure. These structures will be "strained" (either imparting physical strain or by fabricating artificially-strained structures) in such a way that they become aperiodic and experience a "pseudomagnetic field." This pseudomagnetic field causes the eigenvalue spectrum to become highly degenerate, leading to a large density-of-states, which in turn causes stronger light-matter coupling (Purcell enhancement). This project is a cross-disciplinary endeavor of an engineer, whose contribution is through fabrication and characterization of optical media (Kevin Chen, University of Pittsburgh), a physicist (Mikael Rechtsman, Penn State), who will perform optical experiments and modeling and an applied mathematician (Michael Weinstein, Columbia), who will co-develop mathematical PDE / discrete models and analyze these in collaboration with Rechtsman and Chen. Each of their expertise will be essential for the project's success.