Visualization of a Unidirectional Electromagnetic Waveguide Using Topological Photonic Crystals Made of Dielectric Materials

Yuting Yang, Yun Fei Xu, Tao Xu, Hai-Xiao Wang, Jian-Hua Jiang, Xiao Hu, and Zhi Hong Hang

Phys. Rev. Lett. 120, 217401 – Published 22 May 2018

Abstract

We demonstrate experimentally that a photonic crystal made of ${Al}_{2} O_{3}$ cylinders exhibits topological time-reversal symmetric electromagnetic propagation, similar to the quantum spin Hall effect in electronic systems. A pseudospin degree of freedom in the electromagnetic system representing different states of orbital angular momentum arises due to a deformation of the photonic crystal from the ideal honeycomb lattice. It serves as the photonic analogue to the electronic Kramers pair. We visualized qualitatively and measured quantitatively that microwaves of a specific pseudospin propagate only in one direction along the interface between a topological photonic crystal and a trivial one. As only a conventional dielectric material is used and only local real-space manipulations are required, our scheme can be extended to visible light to inspire many future applications in the field of photonics and beyond.

Received 13 November 2017

DOI:https://doi.org/10.1103/PhysRevLett.120.217401

Physics Subject Headings (PhySH)

Photonics Topological effects in photonic systems Topological materials Topological phases of matter

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Yuting Yang¹, Yun Fei Xu¹, Tao Xu¹, Hai-Xiao Wang¹, Jian-Hua Jiang¹, Xiao Hu^2,*, and Zhi Hong Hang^1,3,†

¹College of Physics, Optoelectronics and Energy and Collaborative Innovation Center of Suzhou Nano Science and Technology, Soochow University, Suzhou 215006, China
²International Center for Materials Nanoarchitectonics (WPI-MANA), National Institute for Materials Science, Tsukuba 305-0044, Japan
³Key Laboratory of Modern Optical Technologies (Soochow University), Ministry of Education and Key Lab of Advanced Optical Manufacturing Technologies of Jiangsu Province, Suzhou 215006, China

^*Corresponding author. hu.xiao@nims.go.jp
^†Corresponding author. zhhang@suda.edu.cn

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Vol. 120, Iss. 21 — 25 May 2018

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Images

Figure 1
(a) Photo of the experimental setup to realize EM pseudospin states and a unidirectional photonic channel, where two photonic crystals ${PC}_{1}$ and ${PC}_{2}$ are assembled in the regions above and below the interface (dashed line). A square-shaped antenna array (dashed circle near the interface and enlarged in the inset) is used to selectively excite one of the two EM pseudospin states indicated by circular arrows. The sample is located inside a parallel-plate waveguide with the top metallic plate removed in the photo. (b) Schematics of ${PC}_{1}$ in dark gray (red online) and ${PC}_{2}$ in gray (blue online) as characterized by two competing lengths $h_{1}$ and $h_{2}$ . (c) Calculated bulk TM photonic band diagrams of ${PC}_{1}$ (right) and ${PC}_{2}$ (left), with the corresponding 2D representations of eigenmodes at high-symmetry points labeled. (d) Upon increasing the ratio between $h_{1}$ and $h_{2}$ , the frequencies of the doubly degenerate $E_{1} (E_{2})$ modes increase (decrease), and a band inversion occurs when $h_{1} / h_{2} = 1$ .
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Figure 2
(a) Calculated band diagram based on a supercell composed of ${PC}_{1}$ and ${PC}_{2}$ shown in the right panel, where a periodic (absorbing) boundary condition is applied on the $x (y)$ direction, respectively. The folded bulk bands belonging to ${PC}_{1}$ or ${PC}_{2}$ are painted in gray, whereas the two topological interface bands are shown by symbols. (b) Distributions of the out-of-plane electric field (in gray levels, in color online) at the two opposite momenta denoted by the triangles in (a). The corresponding in-plane magnetic field is also displayed by arrows for the highlighted regions where the length of the arrow indicates the field strength. Black circular arrows indicate that the magnetic field rotates either counterclockwise or clockwise at the two opposite momenta.
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Figure 3
(a) Experimentally measured distributions of the out-of-plane electric field at 7.42 GHz [indicated by the star in (b)] where an antenna array with positive OAM (represented by a counterclockwise circular arrow) is used to excite the $| σ_{z} = + ⟩$ state. (b) Measured transmissions to the two ends $S 1$ and $S 2$ of the sample. (c) Profiles of the magnitude of the out-of-plane electric field along the $y$ direction at $x = 100 mm$ away from the source at 7.42 (upper panel) and 7.04 GHz (lower panel) indicated by the star and triangle in (b), respectively. Magnitudes of the electric field are normalized to the incident field. The absorbing materials in experiments are indicated in gray.
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Figure 4
(a) Photo of the experimental setup for the system with a 120° sharp turn in the interface between ${PC}_{1}$ (highlighted in gray, orange online) and ${PC}_{2}$ , where the $| σ_{z} = - ⟩$ state is excited by a four-antenna array as indicated by a clockwise circular arrow. (b) Measured distribution of the out-of-plane electric field at frequency 7.41 GHz. (c) Measured transmissions to $S 1$ and $S 2$ as indicated in (b) by the dashed lines.
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Figure 5
(a) Simulated unidirectional propagation of the $| σ_{z} = - ⟩$ state at 6.69 GHz along the interface with 90° turns shown schematically in the upper panel. (b) Simulated unidirectional propagation with the same setup as (a) except that a photonic-insulating square-latticed ${PC}_{3}$ is included as a part of the interface to ${PC}_{1}$ as shown schematically in the upper panel.
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