Controllable discrete Talbot self-imaging effect in Hermitian and non-Hermitian Floquet superlattices

Kaiyun Zhan; Lichao Dou; Xinyue Kang; Bing Liu

doi:10.1364/oe.464562

journal article Sep 13, 2022

Controllable discrete Talbot self-imaging effect in Hermitian and non-Hermitian Floquet superlattices

Kaiyun Zhan

Lichao Dou Xinyue Kang Bing Liu

Optics Express Vol. 30 No. 20 pp. 35256 · Optica Publishing Group

View at Publisher Save 10.1364/oe.464562

Abstract

We investigate the discrete Talbot self-imaging effect in Floquet superlattices based on a mesh of directional couplers with periodically varying separation between waveguides, both theoretically and numerically. The modulated discreteness of the lattices sets strong constraints to ensure the Talbot effect generation. We show that discrete Talbot effect occurs only if the incident periods are N = 1, 2, and 4 in dispersive regimes of the Hermitian superlattices. In both dynamic localized and rectification regimes, self-imaging effect can occur for arbitrary input period N. For the rectification case, Talbot distance equals the input period. In the regime of dynamical localization, the Talbot distance remains unchanged irrespective of the pattern period. For non-Hermitian Floquet superlattices, due to the non-zero imaginary part of quasi-energy spectrum arising at the center of the Brillouin zone, where the mode degeneracy occurs, Talbot revival is not preserved when the input period is an even number, and exists only as N = 1 in the dispersive regime. The theoretical calculations and numerical simulations verify each other completely.

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References

33

[1]

Christodoulides Nature (2003) 10.1038/nature01936

[2]

Garanovich Phys. Rep. (2012) 10.1016/j.physrep.2012.03.005

[3]

Longhi Opt. Commun. (2008) 10.1016/j.optcom.2008.05.014

[4]

Kartashov Opt. Lett. (2010) 10.1364/ol.35.000205

[5]

Lobanov Phys. Rev. A (2010) 10.1103/physreva.81.023803

[6]

Qin Opt. Express (2018) 10.1364/oe.26.025721

[7]

Regensburger Nature (2012) 10.1038/nature11298

[8]

Lindner Nat. Phys. (2011) 10.1038/nphys1926

[9]

Periodically Driven Quantum Systems: Effective Hamiltonians and Engineered Gauge Fields

N. Goldman, J. Dalibard

Physical Review X 2014 10.1103/physrevx.4.031027

[10]

Rudner Phys. Rev. X (2013) 10.1103/physrevx.3.031005

[11]

Eisenberg Phys. Rev. Lett. (2000) 10.1103/physrevlett.85.1863

[12]

Longhi Phys. Rev. Lett. (2006) 10.1103/physrevlett.96.243901

[13]

Szameit Phys. Rev. Lett. (2009) 10.1103/physrevlett.102.153901

[14]

Lenz Phys. Rev. Lett. (1999) 10.1103/physrevlett.83.963

[15]

Zhang Phys. Rev. A (2018) 10.1103/physreva.97.063845

[16]

Kartashov Phys. Rev. Lett. (2007) 10.1103/physrevlett.99.233903

[17]

Zhan Opt. Lett. (2021) 10.1364/ol.415326

[18]

Rechtsman Nature (2013) 10.1038/nature12066

[19]

Longhi Opt. Lett. (2009) 10.1364/ol.34.000458

[20]

Dreisow Europhys. Lett. (2013) 10.1209/0295-5075/101/44002

[21]

Kartashov Phys. Rev. A (2016) 10.1103/physreva.93.013841

[22]

Zhang ACS Photonics (2017) 10.1021/acsphotonics.7b00448

[23]

Discrete Talbot Effect in Waveguide Arrays

Robert Iwanow, Daniel A. May-Arrioja, Demetrios N. Christodoulides et al.

Physical Review Letters 2005 10.1103/physrevlett.95.053902

[24]

Chen Opt. Express (2015) 10.1364/oe.23.014724

[25]

Talbot Philos. Mag. (1836)

[26]

XXV. On copying diffraction-gratings, and on some phenomena connected therewith

Lord Rayleigh

The London, Edinburgh, and Dublin Philosophical Ma... 1881 10.1080/14786448108626995

[27]

PT-Symmetric Talbot Effects

Hamidreza Ramezani, D. N. Christodoulides, V. Kovanis et al.

Physical Review Letters 2012 10.1103/physrevlett.109.033902

[28]

Wang Opt. Express (2018) 10.1364/oe.26.019235

[29]

Wang Phys. Rev. A (2018) 10.1103/physreva.98.043832

[30]

Solitons in Polyacetylene

W. P. Su, J. R. SCHRIEFFER, A. J. Heeger

Physical Review Letters 1979 10.1103/physrevlett.42.1698

[31]

Wu Phys. Rev. Res. (2021) 10.1103/physrevresearch.3.023211

[32]

Photonic zero mode in a non-Hermitian photonic lattice

Mingsen Pan, Han Zhao, Pei Miao et al.

Nature Communications 2018 10.1038/s41467-018-03822-8

[33]

Zhang Opt. Lett. (2015) 10.1364/ol.40.005742

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Citations

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References

Details

Published: Sep 13, 2022
Vol/Issue: 30(20)
Pages: 35256
License: View

Authors

Funding

National Natural Science Foundation of China Award: 61605251

Fundamental Research Funds for the Central Universities Award: 22CX03028A

Natural Science Foundation of Shandong Province Award: ZR2021MA030

Cite This Article

Kaiyun Zhan, Lichao Dou, Xinyue Kang, et al. (2022). Controllable discrete Talbot self-imaging effect in Hermitian and non-Hermitian Floquet superlattices. Optics Express, 30(20), 35256. https://doi.org/10.1364/oe.464562

Controllable discrete Talbot self-imaging effect in Hermitian and non-Hermitian Floquet superlattices

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