In this paper, we investigate transmission of electromagnetic wave through aperiodic dielectric multilayers. A generic feature shown is that the mirror symmetry in the system can induce the resonant transmission, which originates from the positional correlations ͑for example, presence of dimers͒ in the system. Furthermore, the resonant transmission can be manipulated at a specific wavelength by tuning aperiodic structures with internal symmetry. The theoretical results are experimentally proved in the optical observation of aperiodic SiO 2 /TiO 2 multilayers with internal symmetry. We expect that this feature may have potential applications in optoelectric devices such as the wavelength division multiplexing system.
We obtain analytically a universal expression of the resonant energies for any onedimensional (1D) models with the defects having symmetric internal structures. In a 1D periodic system with the on-site energy ε 0 = 0 and a nearest-neighbor matrix element t 0 = 1.0, two classes of the most interesting and simplest wavefunction behaviors are numerically obtained for the resonant energies around (a) 0, ±1, (b) ±( √ 5−1)/2, √ 2, ± √ 3, respectively. We show that similar wavefunction behaviors can be found widely in many quasiperiodic and random systems where the delocalization phenomena are predicted. We suggest that the envelope of these wavefunctions can be generally used as a criterion of delocalization of electronic states in 1D random and quasiperiodic lattices.
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