中国物理B ›› 2009, Vol. 18 ›› Issue (12): 5313-5325.doi: 10.1088/1674-1056/18/12/033

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Band rules for the frequency spectra of three kinds of aperiodic photonic crystals with negative refractive index materials

全小林, 杨湘波   

  1. MOE Key Laboratory of Laser Life Science \& Institute of Laser Life Science, South China Normal University, Guangzhou 510631, China
  • 收稿日期:2009-04-03 修回日期:2009-04-27 出版日期:2009-12-20 发布日期:2009-12-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10974061) and the Program for Innovative Research Team of the Higher Education of Guangdong Province of China (Grant No 06CXTD005).

Band rules for the frequency spectra of three kinds of aperiodic photonic crystals with negative refractive index materials

Quan Xiao-Lin(全小林) and Yang Xiang-Bo(杨湘波)†   

  1. MOE Key Laboratory of Laser Life Science & Institute of Laser Life Science, South China Normal University, Guangzhou 510631, China
  • Received:2009-04-03 Revised:2009-04-27 Online:2009-12-20 Published:2009-12-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10974061) and the Program for Innovative Research Team of the Higher Education of Guangdong Province of China (Grant No 06CXTD005).

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摘要： By means of the theory of electromagnetic wave propagation and transfer matrix method, this paper investigates the band rules for the frequency spectra of three kinds of one-dimensional (1D) aperiodic photonic crystals (PCs), generalized Fibonacci GF(p,1), GF(1,2), and Thue--Morse (TM) PCs, with negative refractive index (NRI) materials. It is found that all of these PCs can open a broad zero-? gap, TM PC possesses the largest zero-? gap, and with the increase of p, the width of the zero-? gap for GF(p,1) PC becomes smaller. This characteristic is caused by the symmetry of the system and the open position of the zero-? gap. It is found that for GF(p,1) PCs, the possible limit zero-? gaps open at lower frequencies with the increase of p, but for GF(1,2) and TM PCs, their limit zero-? gaps open at the same frequency. Additionally, for the three bottom-bands, we find the interesting perfect self-similarities of the evolution structures with the increase of generation, and obtain the corresponding subband-number formulae. Based on 11 types of evolving manners Qi(i=1,2,....,11) one can plot out the detailed evolution structures of the three kinds of aperiodic PCs for any generation.

Abstract: By means of the theory of electromagnetic wave propagation and transfer matrix method, this paper investigates the band rules for the frequency spectra of three kinds of one-dimensional (1D) aperiodic photonic crystals (PCs), generalized Fibonacci GF(p,1), GF(1,2), and Thue--Morse (TM) PCs, with negative refractive index (NRI) materials. It is found that all of these PCs can open a broad zero-$\bar{n}$ gap, TM PC possesses the largest zero-$\bar{n}$ gap, and with the increase of p, the width of the zero-$\bar{n}$ gap for GF(p,1) PC becomes smaller. This characteristic is caused by the symmetry of the system and the open position of the zero-$\bar{n}$ gap. It is found that for GF(p,1) PCs, the possible limit zero-$\bar{n}$ gaps open at lower frequencies with the increase of p, but for GF(1,2) and TM PCs, their limit zero-$\bar{n}$ gaps open at the same frequency. Additionally, for the three bottom-bands, we find the interesting perfect self-similarities of the evolution structures with the increase of generation, and obtain the corresponding subband-number formulae. Based on 11 types of evolving manners $Q_i$ ($i$ = 1, 2, ...., 11) one can plot out the detailed evolution structures of the three kinds of aperiodic PCs for any generation.

Key words: negative refractive index, photonic crystals, generalized Fibonacci photonic crystal, Thue--Morse photonic crystal

中图分类号:  (Photonic bandgap materials)

  • 42.70.Qs
78.20.Ci (Optical constants (including refractive index, complex dielectric constant, absorption, reflection and transmission coefficients, emissivity))