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Proceedings Paper

Band-edge states of the zeroth-order gap in quasi-periodic photonic superlattices
Author(s): A. Bruno-Alfonso; E. Reyes-Gómez; S. B. Cavalcanti; L. E. Oliveira
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Paper Abstract

The photonic modes of Thue-Morse and Fibonacci lattices with generating layers A and B, of positive and negative indices of refraction, are calculated by the transfer-matrix technique. For Thue-Morse lattices, as well for periodic lattices with AB unit cell, the constructive interference of reflected waves, corresponding to the zeroth-order gap, takes place when the optical paths in single layers A and B are commensurate. In contrast, for Fibonacci lattices of high order, the same phenomenon occurs when the ratio of those optical paths is close to the golden ratio. In the long wavelength limit, analytical expressions defining the edge frequencies of the zeroth order gap are obtained for both quasi-periodic lattices. Furthermore, analytical expressions that define the gap edges around the zeroth order gap are shown to correspond to the < ε > =0 and <μ> = 0 conditions.

Paper Details

Date Published: 18 November 2008
PDF: 5 pages
Proc. SPIE 7138, Photonics, Devices, and Systems IV, 71381A (18 November 2008); doi: 10.1117/12.818014
Show Author Affiliations
A. Bruno-Alfonso, Univ. Estadual Paulista (Brazil)
E. Reyes-Gómez, Univ. de Antioquia (Colombia)
S. B. Cavalcanti, Univ. Federal de Alagoas (Brazil)
Inmetro (Brazil)
L. E. Oliveira, Inmetro (Brazil)
Univ. Estadual de Campinas (Brazil)

Published in SPIE Proceedings Vol. 7138:
Photonics, Devices, and Systems IV
Pavel Tománek; Dagmar Senderáková; Miroslav Hrabovský, Editor(s)

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