Talbot effect in anti-PT symmetric synthetic photonic lattices

Zhaofeng Liu; Siwei Tang; Zengrun Wen; Yuanmei Gao; Yangjian Cai; Liren Zheng

doi:10.3788/COL202422.031901

Journals >Chinese Optics Letters >Volume 22 >Issue 3 >Page 031901 > Article

Chinese Optics Letters
Vol. 22, Issue 3, 031901 (2024)

Talbot effect in anti-PT symmetric synthetic photonic lattices

Zhaofeng Liu¹, Siwei Tang¹, Zengrun Wen^1、*, Yuanmei Gao¹, Yangjian Cai^1、2、**, and Liren Zheng^1、***

Author Affiliations

¹Shandong Provincial Engineering and Technical Center of Light Manipulations & Shandong Provincial Key Laboratory of Optics and Photonic Device, School of Physics and Electronics, Shandong Normal University, Jinan 250358, China

²School of Physical Science and Technology, Soochow University, Suzhou 215006, China

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DOI: 10.3788/COL202422.031901 Cite this Article Set citation alerts

Zhaofeng Liu, Siwei Tang, Zengrun Wen, Yuanmei Gao, Yangjian Cai, Liren Zheng. Talbot effect in anti-PT symmetric synthetic photonic lattices[J]. Chinese Optics Letters, 2024, 22(3): 031901 Copy Citation Text

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Abstract

We investigated the Talbot effect in an anti-parity-time (PT) symmetric synthetic photonic lattice composed of two coupled fiber loops. We calculated the band structures and found that with an increase in the gain-loss parameter, the band transitions from a real spectrum to a complex spectrum. We study the influence of phase in the Hermitian operator on the Talbot effect, and the Talbot effect disappears when the period of the input field is N > 8. Further study shows that the variation of Talbot distance can also be modulated by non-Hermitian coefficients of gain and loss. This work may find significant applications in pulse repetition-rate multiplication, temporal invisibility, and tunable intensity amplifiers.

Keywords

anti-PT symmetry photonic lattices synthetic dimensions Talbot effect

φ_{n} = {\begin{cases} - φ, & n = 2 k \\ + φ, & n = 2 k + 1 \end{cases},

(1)

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{\begin{matrix} γ_{p} = γ, γ_{q} = G, & for & mod (n + 3; 4) = 0 \\ γ_{p} = γ, γ_{q} = γ, & for & mod (n + 3; 4) = 1 \\ γ_{p} = G, γ_{q} = γ, & for & mod (n + 3; 4) = 2 \\ γ_{p} = G, γ_{q} = G . & otherwise \end{matrix} .

(2)

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{\begin{cases} U_{n}^{m + 1} = \frac{1}{\sqrt{2}} e^{γ_{p}} (U_{n + 1}^{m} + i D_{n + 1}^{m}) e^{- i φ_{n}} \\ D_{n}^{m + 1} = \frac{1}{\sqrt{2}} e^{γ_{q}} (D_{n - 1}^{m} + i U_{n - 1}^{m}) \end{cases} .

(3)

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\cos (4 k) = 2 + 4 \cos (4 β) + \cos (2 φ) + 8 \cos (2 β) \cos φ \cosh (2 G) + 2 \cosh (4 G) .

(4)

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(\begin{matrix} U_{n}^{m} \\ D_{n}^{m} \end{matrix}) = \sum_{j = 1}^{8} \sum_{l = 0}^{M - 1} c_{j, l} (\begin{matrix} U_{j, l} \\ D_{j, l} \end{matrix}) \exp (i k_{l} n) \exp (i β_{j, l} m) .

(5)

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β_{4, 0} = \frac{1}{4} \arccos (- \frac{1}{2} \cosh (4 G)), β_{4, 1} = \frac{1}{4} \arccos (- \frac{1}{2} \cosh (4 G)) .

(6)

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Zhaofeng Liu, Siwei Tang, Zengrun Wen, Yuanmei Gao, Yangjian Cai, Liren Zheng. Talbot effect in anti-PT symmetric synthetic photonic lattices[J]. Chinese Optics Letters, 2024, 22(3): 031901

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