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
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
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.
Received: 12 May 2002
Revised: 23 February 2003
Accepted manuscript online:
Fund: Project supported in part by the National Natural Science Foundation of China (Grant No 90101024).
Cite this article:
Wu Liang (吴良), Ye Zhuo (叶卓), He Sai-Ling (何赛灵) Obtaining the band structure of a complicated photonic crystal by linear operations 2003 Chinese Physics 12 642
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