Improved Dirichlet-to-Neumann map method for modeling extended photonic crystal devices

Zhen Hu; Ya Yan Lu

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Improved Dirichlet-to-Neumann map method for modeling extended photonic crystal devices

机译：用于扩展光子晶体器件建模的改进的Dirichlet-to-Neumann映射方法

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摘要

A typical photonic crystal (PhC) device has only a small number of distinct unit cells. The Dirichlet-to-Neumann (DtN) map of a unit cell is an operator that maps the wave field to its normal derivative on the boundary of the cell. Based on the DtN maps of the unit cells, a PhC device can be efficiently analyzed by solving the wave field only on edges of the unit cells. In this paper, the DtN map method is further improved by an operator marching method assuming that a main propagation direction can be identified in at least part of the device. A Bloch mode expansion method is also developed for structures exhibiting partial periodicity. Both methods are formulated on a set of curves for maximum flexibility. Numerical examples are used to illustrate the efficiency of the improved DtN map method.

机译：典型的光子晶体（PhC）器件只有少量不同的晶胞。单位晶格的Dirichlet-Neumann（DtN）映射是将波场映射到其在晶胞边界上的正态导数的算子。基于晶胞的DtN映射，可以通过仅求解晶胞边缘上的波场来有效地分析PhC设备。在本文中，通过假设可以在设备的至少一部分中识别出主传播方向的操作者行进方法，进一步改进了DtN映射方法。还针对具有部分周期性的结构开发了Bloch模式展开方法。两种方法都在一组曲线上制定，以实现最大的灵活性。数值例子说明了改进的DtN图方法的效率。

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来源
《Optical and quantum electronics》 |2008年第12期|921-932|共12页
作者
Zhen Hu; Ya Yan Lu;
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作者单位

Joint Advanced Research Center of University of Science and Technology of China and City University of Hong Kong, Suzhou, Jiangsu, China Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, China Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong;

Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
photonic crystal; numerical method; dirichlet-to-neumann map; operator marching; bloch mode expansion;

机译：光子晶体数值方法狄利克雷到诺伊曼地图操作员行进;bloch模式扩展;

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1. Modeling two-dimensional anisotropic photonic crystals by Dirichlet-to-Neumann maps [J] . Huan Xie, Ya Yan Lu Journal of the Optical Society of America, A. Optics, image science, and vision . 2009,第7期

机译：通过Dirichlet-to-Neumann映射对二维各向异性光子晶体进行建模
2. Modeling photonic crystals by boundary integral equations and Dirichlet-to-Neumann maps [J] . Yuan JH, Lu YY, Antoine X Journal of Computational Physics . 2008,第9期

机译：通过边界积分方程和Dirichlet-to-Neumann映射对光子晶体进行建模
3. MODELING PHOTONIC CRYSTALS WITH COMPLEX UNIT CELLS BY DIRICHLET-TO-NEUMANN MAPS [J] . Yuexia Huang, Ya Yan Lu Journal of Computational Mathematics . 2007,第3期

机译：Dirichlet-to-Neumann Maps对具有复杂单位细胞的光子晶体进行建模
4. Analyzing photonic crystal heterostructure mode-gap cavities by Dirichlet-to-Neumann maps [C] . Zhen Hu IEEE International Conference on Computational Electromagnetics . 2015

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5. Systematic design, optimization, and sensitivity analysis methods for photonic crystal devices. [D] . Jiao, Yang. 2005

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7. Dirichlet-to-Neumann Map Method with Boundary Cells for Photonic Crystals Devices [O] . Jianhua Yuan, Ya Yan Lu 2013

机译：具有光子晶体器件边界单元的Dirichlet到Neumann映射方法

Improved Dirichlet-to-Neumann map method for modeling extended photonic crystal devices

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