High Order Numerical Methods for Light Propagation in Micro-Photonics

本论文是一个跨学科的研究项目，旨在发展高阶数值方法，以提供光在微光子学中传播的精确建模能力。光在这类器件中的传输问题与延迟线、光缓冲器件的设计密切相关。由于这些器件的尺度较小以及光信号的波动性，数值方法的精度，尤其是数值方法的相位精度，对于获得光信号通过光子器件的速度和相位信息至关重要。 微光子学（如谐振波导）建模算法的发展将导致在非均匀介质中求解线性和非线性麦克斯韦方程的先进能力，用于广泛的工程问题。这项研究的潜在技术应用将提供在单个芯片上集成光学元件，以控制光速，通过将非线性光学材料结合到微球/微柱中来提供微尺度上的路由和切换功能。这些都是现代光子学研究界正在解决的基本问题。主要的挑战将是发展高精度和高效率的数值算法，用于求解层状和非均匀介质中的线性和非线性麦克斯韦方程。将研究以下专题：（a）时间相关非线性麦克斯韦方程组的不连续谱元方法，（B）迎风嵌入边界方法，（c）用耦合谐振器光波导器件的开发算法建模。我们计划找到解决当前耦合谐振器波导设计中瓶颈问题的解决方案，这对发展具有重大影响下一代光学技术。这包括优化微球或微柱之间的纳米间隔，以实现降低的光群速度（光电应用的期望特性）与降低的光传输效率之间的折衷。这也包括理解存在于目前可用的微球和微柱体的集合中的尺寸无序的作用。本计画之结果将直接应用于本实验室耦合微球或微柱之光子元件之制作。此外，将创建公开可用的代码，用于计算所有类型的光谱（透射，反射和散射）和耦合谐振器波导的光子带结构。 一名研究生将进行研究，以获得博士学位。光学或/和应用数学学位，他/她的参与将有助于在夏洛特夏洛特新成立的光电和光通信中心的教育组成部分。 该提案在新物理和数学建模工具领域的研究成果将纳入该中心目前正在开发的光学课程中，将通过该中心与区域光学公司之间的现有合作关系探索该成果向区域光学工业的潜在技术转移。PI还将积极参与该中心与该地区高中的技术培训计划。

ABSTRACT0513179Wei CaiU of NC @ CharlotteThis interdisciplinary proposal is to develop high order numerical methods to provide accurate modeling capabilities of light propagation through microphotonics. The problems of light propagation through such devices are closely related to the design of delay lines, optical buffering devices. Due to small scales of those devices and wave nature of the light signals, the accuracy of the numerical methods, especially the phase accuracy of the numerical methods, is critical in obtaining the speed and phase information of light signals through photonic devices. The development of algorithms for modeling of microphotonics such as resonant waveguides will result in advanced capabilities in solving linear and nonlinear Maxwell equations in inhomogeneous media for a wide range of engineering problems. The potential technology applications of this research will provide integration of optical elements on a single chip, to control velocity of light, to provide routing and switching functionality on a micro-scale by incorporating nonlinear optical material into the microspheres/microcylinders. These are the fundamental questions being addressed in the research communities of modern photonics. The major challenge will be the development of highly accurate and efficient numerical algorithms for the solution of linear and nonlinear Maxwell equations in layered and inhomogeneous media. The following topics will be studied: (a) Discontinuous spectral element methods for time dependent nonlinear Maxwell equations, (b) Upwinding Embedded Boundary Methods, (c) Modeling with the developed algorithms for coupled resonator optical waveguide devices.As a main goal of this proposal, we plan to find solutions to the current bottleneck problems in the designing of coupled resonator waveguides with significant impact on the development of next generation optical technologies. This includes optimization of the nanometric separation between microspheres or microcylinders to achieve a trade-off between reduced group velocity of light (desirable property for optoelectronic applications) and reduced efficiency of optical transport. This also includes understanding of the role of the size disorder existing in the presently available ensembles of microspheres and microcylinders. The results of this proposal will be directly implemented into the manufacturing of photonic devices of coupled microspheres or microcylinders in our laboratory. In addition, publicly available codes will be created for calculating of all types of optical spectra (transmission, reflection and scattering) and photonic band structures of coupled resonator waveguides. One graduate student will conduct research toward a Ph.D. degree in either optics or/and applied mathematics, and his/her participation will contribute to the educational components of the newly established Center of Optoelectronics and Optical Communications at the UNC Charlotte. Research results from this proposal, in the area of new physics and mathematical modeling tools, will be incorporated into the optics curriculum now under development at the Center, potential technology transfer of the results to the area optics industrial will be explored through the existing partnership between the Center and area optics companies. The PIs will also actively participate in the Center's technology training programs with the area high schools.