Two-dimensional non-Hermitian Skin Effect in a Synthetic Photonic Lattice

Yiling Song, Weiwei Liu, Lingzhi Zheng, Yicong Zhang, Bing Wang, and Peixiang Lu

Phys. Rev. Applied 14, 064076 – Published 30 December 2020

Abstract

Non-Hermitian skin effect (NHSE) has led to interesting physics and sophisticated applications beyond the conventional framework. However, NHSE studies have been limited to an individual dimension due to the difficulty of constructing nonreciprocal coupling in higher-dimensional systems. With the concept of synthetic dimension, we realize two-dimensional (2D) NHSE in a synthetic photonic lattice. The synthetic photonic lattice is composed of a spatial dimension and a synthetic frequency dimension, which is constructed by introducing gain and loss and dynamically modulating the complex refractive index in a one-dimensional ring-resonator array. In the synthetic 2D NHSE system, we can manipulate the spatial position and frequency mode of the light in real time, thus enabling programmable light propagation and frequency conversion. Specifically, the incident light can be localized in the spatial dimension and the frequency dimension simultaneously, leading to second-order corner modes in the synthetic 2D NHSE lattice. Besides, the 2D NHSE system exhibits an excellent robustness for the disorder and point defect in the lattice. This work generalizes the non-Hermitian skin effect in synthetic dimension to control the light in different dimensions, which shows great promise for potential applications in on-chip light manipulation, frequency synthesis, and information processing.

Received 13 October 2020
Revised 30 November 2020
Accepted 8 December 2020

DOI:https://doi.org/10.1103/PhysRevApplied.14.064076

Physics Subject Headings (PhySH)

Interference & diffraction of light Lasers Photonics Synthetic gauge fields

Nonlinear DynamicsAtomic, Molecular & Optical

Authors & Affiliations

Yiling Song¹, Weiwei Liu^1,*, Lingzhi Zheng¹, Yicong Zhang¹, Bing Wang ^1,†, and Peixiang Lu^1,2

¹Wuhan National Laboratory for Optoelectronics and School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
²Hubei Key Laboratory of Optical Information and Pattern Recognition, Wuhan Institute of Technology, Wuhan, 430205, China

^*lwhust@hust.edu.cn
^†wangbing@hust.edu.cn

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Vol. 14, Iss. 6 — December 2020

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Images

Figure 1
1D non-Hermitian skin effect in spatial dimension. (a) Scheme of the structure for the 1D NHSE model. The red part and green part represent gain and loss mediums, respectively. (b) Schematic diagram for the 1D NHSE model. (c) Calculated eigenenergy for the OBC (black spots) and PBC (red line), respectively. (d) A 1D lattice composed of isotropically coupled ring resonators (120 sites), and the calculated eigenmodes. (e) A 1D lattice composed of anisotropically coupled ring resonators (120 sites), and the calculated eigenmodes.
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Figure 2
1D NHSE in synthetic frequency dimension. (a) Schematic for constructing the synthetic frequency dimension. (b) Real part (bottom) and imaginary part (top) of the band structure, respectively. Calculated spectrum evolution for different phase differences (c) φ_r−φ_i = 0, (d) φ_r−φ_i = −π/2, (e) φ_r−φ_i = π/2, when excited by a single-frequency light. The results in (c)−(e) are calculated by finite-difference approaches.
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Figure 3
Constructing a 2D NHSE lattice by combining the spatial dimension and the synthetic frequency dimension. (a) Schematic diagram of a lattice with isotropic coupling in space. The complex refractive index of the on-site ring at the center of the array is modulated dynamically. (b) The corresponding schematic diagram for the 2D lattice synthesized with the model in (a). (c) Schematic diagram of a lattice composed of two lattices with opposite anisotropic coupling. The complex refractive index of the on-site ring at the center of the array is modulated dynamically. (d) The corresponding schematic diagram for the 2D lattice synthesized with the model in (c).
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Figure 4
Calculated light evolutions and distributions in the synthetic 2D photonic lattices (61×41 sites). (a)–(c) The calculated results for the 2D lattice with isotropic coupling in space [Fig. 3]. When a single-frequency light is incident from the leftmost on-site ring, the light flows back and forth in the lattice and has a wide distribution in space. The center frequency of the light experiences (a) an up-conversion for φ_r−φ_i = −π/2, (b) a symmetric conversion for φ_r−φ_i = 0, and (c) a down-conversion for φ_r−φ_i = π/2, respectively. (d)–(f) The calculated results for the 2D lattice with anisotropic coupling in space [Fig. 3]. When a single-frequency light is incident from the leftmost on-site ring, the light flows to the interface unidirectionally. The center frequency of the light experiences (d) an up-conversion for φ_r−φ_i = −π/2, (e) a symmetric conversion for φ_r−φ_i = 0, and (f) a down-conversion for φ_r−φ_i = π/2, respectively.
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Figure 5
Robustness for the synthetic 2D NHSE lattice. (a)–(c) Robustness of the 2D NHSE lattice in the spatial dimension. Calculated light distribution with (a) a gain-loss disorder, (b) a point defect with greatly weakened coupling (δ = −0.9 κ), and (c) a point defect with blocked coupling, respectively. (d)–(e) Robustness of the synthetic 2D NHSE lattice in the frequency dimension. The disorder is created by introducing a uniformly distributed phase differences between the real part and imaginary part of the complex refractive index of the ring resonator, φ_r−φ_i = −π/2 + Δφ, Δφ ∈ [−Q, Q]. Calculated light distribution for (d) Q = π/2, (e) Q = π, and (f) Q = 2π, respectively.
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