Observation of Weyl Interface States in Non-Hermitian Synthetic Photonic Systems

Wange Song, Shengjie Wu, Chen Chen, Yuxin Chen, Chunyu Huang, Luqi Yuan, Shining Zhu, and Tao Li

Phys. Rev. Lett. 130, 043803 – Published 25 January 2023

Abstract

Weyl medium has triggered remarkable interest owing to its nontrivial topological edge states in 3D photonic band structures that were mainly revealed as surface modes yet. It is undoubted that the connection of two different Weyl media will give rise to more fruitful physics at their interface, while they face extreme difficulty in high-dimensional lattice matching. Here, we successfully demonstrate the non-Hermitian Weyl interface physics in complex synthetic parameter space, which is implemented in a loss-controlled silicon waveguide array. By establishing non-Hermitian Hamiltonian in the parameter space, new Weyl interfaces with distinct topological origins are predicted and experimentally observed in silicon waveguides. Significantly, our Letter exploits the non-Hermitian parameter to create the synthetic dimension by manipulating the non-Hermitian order, which successfully circumvents the difficulty in lattice matching for high-dimensional interfaces. The revealed rich topological Weyl interface states and their phase transitions in silicon waveguide platform further imply potentials in chip-scale photonics integrations.

Received 13 October 2022
Accepted 5 January 2023

DOI:https://doi.org/10.1103/PhysRevLett.130.043803

Physics Subject Headings (PhySH)

Edge states Integrated optics Topological effects in photonic systems

Waveguide arrays

Atomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Wange Song ¹, Shengjie Wu¹, Chen Chen¹, Yuxin Chen¹, Chunyu Huang¹, Luqi Yuan ^2,*, Shining Zhu¹, and Tao Li ^1,†

¹National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Integration, Jiangsu Key Laboratory of Artificial Functional Materials, College of Engineering and Applied Sciences, Nanjing University, Nanjing 210093, China
²State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China

^*Corresponding author. yuanluqi@sjtu.edu.cn
^†Corresponding author. taoli@nju.edu.cn

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Issue

Vol. 130, Iss. 4 — 27 January 2023

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Images

Figure 1
(a) Schematics of the Cr-deposited curved silicon waveguides and the cross section of the unit cell. (b) Band structures in the $δ l - δ n$ synthetic space with $δ k = 0$ for the Hermitian case. The WP is marked by the red dot. (c) Real part of the spectrum on $δ k - δ n$ space at $δ l = 0$ in the non-Hermitian system. A WER is identified and marked by the red circle. The inset shows the corresponding imaginary part. (d) The same system viewed on $δ l - δ n$ space with $δ k = 0$ . The two EPs are marked by the pentagrams.
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Figure 2
(a) Rotational sphere in $δ l - δ m - δ n$ parameter spaces. (b) Real part of the band structures in $δ l - δ m$ space. The EPs with opposite chirality are marked by the red and blue pentagrams. A projective rotational loop is introduced, where $ϕ_{I}$ and $ϕ_{II}$ are rotational angles that define the two synthetic Weyl media (I and II). Bottom: the positions of the two Weyl media at $δ l - δ m$ space for $ϕ_{I} = π / 2$ and $ϕ_{II} = ϕ_{I} + π$ . (c) Real part of the eigenvalue spectra as a function of $ϕ_{I}$ for loops in (b), with $ϕ_{II} = ϕ_{I} + π$ (top) and $ϕ_{II} = ϕ_{I}$ (bottom). The red and blue curves are the interface modes and gray bands represent the bulk. (d) Schematics of the waveguide structure and field distributions (real part of the complex amplitude) of the interface states [marked by red and blue triangles in (c)]. The black dashed line indicates the interface and four central waveguides are enlarged.
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Figure 3
(a) Two rotational loops of different sizes are introduced in $δ l - δ m$ spaces, where $ϕ_{I}$ and $ϕ_{II}$ are azimuthal angles that define the two synthetic Weyl media (I and II). Weyl medium I and II (blue and red dots) are outside and inside the WER (red circle). The real (b) and imaginary (d) part of the eigenvalue spectra for loops in (a) with $ϕ_{II} = ϕ_{I}$ . The red curve represents the interface mode. (c) Schematics of the waveguide structure and field distributions of the interface states at $ϕ_{I} = π / 2$ . Here, $a_{I} = 0.0 0576 μ m^{- 1}$ , $a_{II} = 0.0 2247 μ m^{- 1}$ , $δ l_{0} = 0.0 01$ , and $δ n_{0} = - 0.0 5$ .
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Figure 4
(a) SEM top view of a sample. (b) and (c) Enlarged regions. (d)–(f) Simulated light propagations (d), experimentally detected output intensities (e), and normalized intensity (NI) profiles (f) of simulation (green bars) and experimental results (orange bars) for the imaginary mass transition case. Corresponding results for crossing the WER case (g)–(i) and Hermitian trivial case (j)–(l).
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