中国物理B ›› 2003, Vol. 12 ›› Issue (6): 642-648.doi: 10.1088/1009-1963/12/6/313

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Obtaining the band structure of a complicated photonic crystal by linear operations

吴良1, 叶卓1, 何赛灵2   

  1. (1)State Key Laboratory for Modern Optical Instrumentation, Centre for Optical and Electromagnetic Research, Zhejiang University, Hangzhou 310027, China; (2)State Key Laboratory for Modern Optical Instrumentation, Centre for Optical and Electromagnetic Research, Zhejiang University, Hangzhou 310027, China; Department of Electromagnetic Theory, Royal Institute of Technology, S-100, 44 Stockholm, Sweden
  • 收稿日期:2002-05-12 修回日期:2003-02-23 出版日期:2003-06-16 发布日期:2005-03-16
  • 基金资助:
    Project supported in part by the National Natural Science Foundation of China (Grant No 90101024).

Obtaining the band structure of a complicated photonic crystal by linear operations

Wu Liang (吴良)a, Ye Zhuo (叶卓)a, He Sai-Ling (何赛灵)ab   

  1. a State Key Laboratory for Modern Optical Instrumentation, Centre for Optical and Electromagnetic Research, Zhejiang University, Hangzhou 310027, China; b Department of Electromagnetic Theory, Royal Institute of Technology, S-100, 44 Stockholm, Sweden
  • Received:2002-05-12 Revised:2003-02-23 Online:2003-06-16 Published:2005-03-16
  • Supported by:
    Project supported in part by the National Natural Science Foundation of China (Grant No 90101024).

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摘要： Absolute band gaps can be created by lifting the degeneracy in the bands of a photonic crystal. To calculate the band structure of a complicated photonic crystal generated by e.g. symmetry breaking, general forms of all possible linear operations are presented in terms of matrices and a procedure to combine these operations is given. Other forms of linear operations (such as the addition, subtraction, and translation transforms) are also presented to obtain an explicit expression for the Fourier coefficient of the dielectric function in the plane-wave expansion method. With the present method, band structures for various complicated photonic crystals (related through these linear operations) can be obtained easily and quickly. As a numerical example, a large absolute band gap for a complicated photonic crystal structure of GaAs is found in the high region of normalized frequency.

Abstract: Absolute band gaps can be created by lifting the degeneracy in the bands of a photonic crystal. To calculate the band structure of a complicated photonic crystal generated by e.g. symmetry breaking, general forms of all possible linear operations are presented in terms of matrices and a procedure to combine these operations is given. Other forms of linear operations (such as the addition, subtraction, and translation transforms) are also presented to obtain an explicit expression for the Fourier coefficient of the dielectric function in the plane-wave expansion method. With the present method, band structures for various complicated photonic crystals (related through these linear operations) can be obtained easily and quickly. As a numerical example, a large absolute band gap for a complicated photonic crystal structure of GaAs is found in the high region of normalized frequency.

Key words: photonic crystal, plane-wave expansion method, linear operation, Fourier coefficients

中图分类号:  (Semiconductor compounds)

  • 71.20.Nr
42.70.Qs (Photonic bandgap materials)