Reconfigurable topological states in valley photonic crystals

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Reconfigurable topological states in valley photonic crystals

You Wu, Xiaoyong Hu, and Qihuang Gong

Phys. Rev. Materials 2, 122201(R) – Published 21 December 2018

Abstract

Valley photonic crystals can enable nontrivial topology locked to the valley index. Since time-reversal symmetry is preserved, no external magnetic field has to be applied. Therefore, the valley topological insulators can be easily used to construct photonic devices. Here, a reconfigurable valley photonic crystal is proposed, where the inversion symmetry is broken by constructing the unit cell with two different materials. Also, since one of the materials is electro-optic material barium titanate, by simply changing the applied voltage, not only the band-gap frequency will shift, but the topological phase transition can also happen. This is highly beneficial to the design and optimization of integrated photonic devices because a balance between the flexibility of devices and the robustness of topological properties is realized successfully. Moreover, a two-port optical switch as an example of the possible applications is proposed.

Received 4 August 2018

DOI:https://doi.org/10.1103/PhysRevMaterials.2.122201

Physics Subject Headings (PhySH)

Photonic crystals Photonics Topological effects in photonic systems

Atomic, Molecular & Optical

Authors & Affiliations

You Wu¹, Xiaoyong Hu^1,2,*, and Qihuang Gong^1,2

¹State Key Laboratory for Mesoscopic Physics, Department of Physics, Collaborative Innovation Center of Quantum Matter, Peking University, Beijing 100871, China
²Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China

^*xiaoyonghu@pku.edu.cn

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Issue

Vol. 2, Iss. 12 — December 2018

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Images

Figure 1
(a) Three-dimensional configuration of the reconfigurable valley photonic crystal. The photonic crystal rod slab is embedded in a ${SiO}_{2}$ layer, and covered by two gold films on the top and bottom. (b) A two-dimensional model of the valley photonic crystal composed of ${TiO}_{2}$ (rod 1, gray rods) and ${BaTiO}_{3}$ (rod 2, blue rods). The black hexagon and rhombus are primitive cells including two rods. The lattice constant is $a$ , and the rod's radius $r = 3 \sqrt{3} / 25 a$ . The background material is air ( $n_{0} = 1$ ). (c) The band structure of the TM mode for the two-dimensional photonic crystals when $n_{{TiO}_{2}} = n_{BTO}$ (the gray area is the light cone). There exists a Dirac cone at the $K$ ( $K^{'}$ ) point. The inset is the first Brillouin zone.
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Figure 2
Topological phase transition along with band inversion. (a) A band gap (pink shaded area) emerges as long as $n_{BTO} \neq n_{{TiO}_{2}}$ . The band gap is from $0.3710 \times 2 π c / a$ to $0.3857 \times 2 π c / a$ when $n_{BTO} = 2.26$ , and from $0.3553 \times 2 π c / a$ to $0.3690 \times 2 π c / a$ when $n_{BTO} = 2.5$ . (b) The eigenstates (phase profile of $E_{z}$ component) at $K$ and $K^{'}$ for bands 1 and 2 when $n_{BTO} = 2.26$ and $2.5$ , respectively. The black arrows represent the direction of Poynting vectors. The eigenstates of bands 1 and 2 are inversed in the process when $n_{BTO}$ increases from 2.26 to 2.5, indicating the topological phase transition at the critical point when $n_{BTO} = n_{{TiO}_{2}}$ . The orbital angular momentum of each state is marked in the parentheses on the top left of each panel: left circular polarization (LCP) or right circular polarization (RCP).
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Figure 3
Valley-dependent topological edge states. Panels (a) and (c) are two types of edge, constructed by valley photonic crystals with different topological properties. Panels (b) and (d) are corresponding energy density distribution at the frequency of $0.3756 \times 2 π c / a$ . (e) The blue and red lines are the calculated dispersion curves for edge types 1 and 2, respectively, and the gray lines are bulk states.
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Figure 4
(a) The transmittance curves of a bulk photonic crystal (black solid line), a Z-shape edge (red dashed line), a type 1 straight edge (blue dotted line), and a type 2 straight edge (green dashed-dotted line). The pink area is the band gap. (b) The energy density profile at $0.3756 \times 2 π c / a$ for the Z-shape bending when light is input from the left port (red arrow). (c) The directionality $D (ω)$ under different $n_{BTO}$ . $D (ω)$ is close to either 1 or $- 1$ in the band gap indicated by the two black lines when $n_{BTO} < n_{{TiO}_{2}}$ or $n_{BTO} > n_{{TiO}_{2}}$ , respectively. The insets are the $P_{x}$ component at $0.3678 \times 2 π c / a$ and $0.3755 \times 2 π c / a$ when $n_{BTO} = 2.26$ , and at $0.3624 \times 2 π c / a$ and $0.3678 \times 2 π c / a$ when $n_{BTO} = 2.5$ , respectively.
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Figure 5
A two-port optical switch based on valley photonic crystals. (a) The structure of the optical switch, where an edge is formed by two topologically distinct valley photonic crystals. A circularly polarized dipole $[H = H_{0} (\vec{x} - i \vec{y})$ , marked as a red star] excites the topological edge states, and the edge states will propagate through either the left port or the right port. (b) The dispersion curves of the edge states when $n_{BTO} = 2.26$ or 2.5, respectively. (c) The directionality $D (ω)$ is close to 1 or $- 1$ in the band gap. (d) The ON/OFF ratio of this optical switch for both ports.
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