Zener tunnelling in periodic two-dimensional photonic lattices with three-fold symmetry

A. S. Desyatnikov; Yu S. Kivshar; V. S. Shchesnovich; S. B. Cavalcanti; J. M. Hickmann

doi:10.1109/ICTON.2007.4296145

Zener tunnelling in periodic two-dimensional photonic lattices with three-fold symmetry

A. S. Desyatnikov, Yu S. Kivshar, V. S. Shchesnovich, S. B. Cavalcanti, J. M. Hickmann

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

We study the interband wave tunnelling (Zener transitions) in two-dimensional hexagonal lattices with superimposed index gradient and derive simple analytical models capturing the essence of the tunnelling phenomenon. We find that the two-dimensional tunnelling in hexagonal lattices occurs at the high-symmetry points (e.g., the M and Γ points), and it involves either three or six Bloch bands being described by the corresponding multi-level Landau-Zener-Majorana (LZM) system. We derive several types of the generalized LZM systems and verify analytical predictions by direct numerical simulations of the full linear Schrödinger equation with tilted periodic potential.

Original language	English
Title of host publication	Proceedings of 2007 9th International Conference on Transparent Optical Networks, ICTON 2007
Pages	66-69
Number of pages	4
DOIs	https://doi.org/10.1109/ICTON.2007.4296145
Publication status	Published - Dec 1 2007
Externally published	Yes
Event	2007 9th International Conference on Transparent Optical Networks, ICTON 2007 - Rome, Italy Duration: Jul 1 2007 → Jul 5 2007

Publication series

Name	Proceedings of 2007 9th International Conference on Transparent Optical Networks, ICTON 2007
Volume	2

Other

Other	2007 9th International Conference on Transparent Optical Networks, ICTON 2007
Country	Italy
City	Rome
Period	7/1/07 → 7/5/07

ASJC Scopus subject areas

Computer Networks and Communications
Electrical and Electronic Engineering
Communication

Access to Document

10.1109/ICTON.2007.4296145

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Desyatnikov, A. S., Kivshar, Y. S., Shchesnovich, V. S., Cavalcanti, S. B., & Hickmann, J. M. (2007). Zener tunnelling in periodic two-dimensional photonic lattices with three-fold symmetry. In Proceedings of 2007 9th International Conference on Transparent Optical Networks, ICTON 2007 (pp. 66-69). [4296145] (Proceedings of 2007 9th International Conference on Transparent Optical Networks, ICTON 2007; Vol. 2). https://doi.org/10.1109/ICTON.2007.4296145

Zener tunnelling in periodic two-dimensional photonic lattices with three-fold symmetry. / Desyatnikov, A. S.; Kivshar, Yu S.; Shchesnovich, V. S.; Cavalcanti, S. B.; Hickmann, J. M.

Proceedings of 2007 9th International Conference on Transparent Optical Networks, ICTON 2007. 2007. p. 66-69 4296145 (Proceedings of 2007 9th International Conference on Transparent Optical Networks, ICTON 2007; Vol. 2).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Desyatnikov, AS, Kivshar, YS, Shchesnovich, VS, Cavalcanti, SB & Hickmann, JM 2007, Zener tunnelling in periodic two-dimensional photonic lattices with three-fold symmetry. in Proceedings of 2007 9th International Conference on Transparent Optical Networks, ICTON 2007., 4296145, Proceedings of 2007 9th International Conference on Transparent Optical Networks, ICTON 2007, vol. 2, pp. 66-69, 2007 9th International Conference on Transparent Optical Networks, ICTON 2007, Rome, Italy, 7/1/07. https://doi.org/10.1109/ICTON.2007.4296145

Desyatnikov AS, Kivshar YS, Shchesnovich VS, Cavalcanti SB, Hickmann JM. Zener tunnelling in periodic two-dimensional photonic lattices with three-fold symmetry. In Proceedings of 2007 9th International Conference on Transparent Optical Networks, ICTON 2007. 2007. p. 66-69. 4296145. (Proceedings of 2007 9th International Conference on Transparent Optical Networks, ICTON 2007). https://doi.org/10.1109/ICTON.2007.4296145

Desyatnikov, A. S. ; Kivshar, Yu S. ; Shchesnovich, V. S. ; Cavalcanti, S. B. ; Hickmann, J. M. / Zener tunnelling in periodic two-dimensional photonic lattices with three-fold symmetry. Proceedings of 2007 9th International Conference on Transparent Optical Networks, ICTON 2007. 2007. pp. 66-69 (Proceedings of 2007 9th International Conference on Transparent Optical Networks, ICTON 2007).

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abstract = "We study the interband wave tunnelling (Zener transitions) in two-dimensional hexagonal lattices with superimposed index gradient and derive simple analytical models capturing the essence of the tunnelling phenomenon. We find that the two-dimensional tunnelling in hexagonal lattices occurs at the high-symmetry points (e.g., the M and Γ points), and it involves either three or six Bloch bands being described by the corresponding multi-level Landau-Zener-Majorana (LZM) system. We derive several types of the generalized LZM systems and verify analytical predictions by direct numerical simulations of the full linear Schr{\"o}dinger equation with tilted periodic potential.",

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