Band-edge states of the zeroth-order gap in quasi-periodic photonic superlattices

A. Bruno-Alfonso; E. Reyes-Gómez; S. B. Cavalcanti; L. E. Oliveira

doi:10.1117/12.818014

18 November 2008 Band-edge states of the zero^th-order gap in quasi-periodic photonic superlattices

A. Bruno-Alfonso, E. Reyes-Gómez, S. B. Cavalcanti, L. E. Oliveira

Proceedings Volume 7138, Photonics, Devices, and Systems IV; 71381A (2008) https://doi.org/10.1117/12.818014
Event: Photonics, Devices, and Systems IV, 2008, Prague, Czech Republic

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 zero^th-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.

Citation Download Citation

A. Bruno-Alfonso, E. Reyes-Gómez, S. B. Cavalcanti, and L. E. Oliveira "Band-edge states of the zero^th-order gap in quasi-periodic photonic superlattices", Proc. SPIE 7138, Photonics, Devices, and Systems IV, 71381A (18 November 2008); https://doi.org/10.1117/12.818014

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