中国物理B ›› 2009, Vol. 18 ›› Issue (12): 5313-5325.doi: 10.1088/1674-1056/18/12/033
全小林, 杨湘波
Quan Xiao-Lin(全小林) and Yang Xiang-Bo(杨湘波)†
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.
中图分类号: (Photonic bandgap materials)