%A Quan Xiao-Lin, Yang Xiang-Bo
%T Band rules for the frequency spectra of three kinds of aperiodic photonic crystals with negative refractive index materials
%0 Journal Article
%D 2009
%J Chin. Phys. B
%R 10.1088/1674-1056/18/12/033
%P 5313-5325
%V 18
%N 12
%U {http://cpb.iphy.ac.cn/CN/abstract/article_23673.shtml}
%8 2009-12-20
%X 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 Q_{i}(i=1,2,....,11) one can plot out the
detailed evolution structures of the three kinds of aperiodic PCs
for any generation.