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

被引：0
作者：
Zhen Hu
Ya Yan Lu
机构：
[1] Joint Advanced Research Center of University of Science and Technology of China and City University of Hong Kong,Department of Mathematics
[2] University of Science and Technology of China,Department of Mathematics
[3] City University of Hong Kong,undefined
来源：
Optical and Quantum Electronics | 2008年 / 40卷
关键词：
Photonic crystal; Numerical method; Dirichlet-to-Neumann map; Operator marching; Bloch mode expansion;
D O I：
暂无
中图分类号：
学科分类号：
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.
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页码：921 / 932
页数：11
相关论文
共 40 条
  • [1] Felbacq J.D.(1994)Scattering by a random set of parallel cylinders J. Optical Soc. Am. A 11 2526-2538
  • [2] Tayeb C.(2006)Finite-element modeling of nonlinear Mach-Zehnder interferometers based on photonic-crystal waveguides for all-optical signal processing J. Lightwave Technol. 24 617-623
  • [3] Maystre D.(2008)Efficient analysis of photonic crystal devices by Dirichlet-to-Neumann maps Opt. Express 16 17282-17399
  • [4] Fujisawa T.(2006)Scattering from periodic arrays of cylinders by Dirichlet-to-Neumann maps J. Lightwave Technol. 24 3448-3453
  • [5] Koshiba T.(2007)Modeling photonic crystals with complex unit cells by Dirichlet-to-Neumann maps J. Comput. Math. 25 337-349
  • [6] Hu Z.(2007)Analyzing photonic crystal waveguides by Dirichlet-to-Neumann maps J. Optical Soc. Am. B 24 2860-2867
  • [7] Lu Y.Y.(2007)Multipole Dirichlet-to-Neumann map method for photonic crystals with complex unit cells J. Optical Soc. Am. A 24 2438-2442
  • [8] Huang Y.(1999)Calculation of electromagnetic properties of regular and random arrays of metallic and dielectric cylinders Phys. Rev. E 60 7614-7617
  • [9] Lu Y.Y.(2004)Block mode scattering matrix methods for modeling exteded photonic crystal structures Applications Phys. Rev. E 70 056607-1473
  • [10] Huang Y.(2008)Dirichlet-to-Neumann map method for analyzing interpenetrating cylinder arrays in a triangular lattice J. Optical Soc. Am. B 25 1466-2611
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