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Frontiers of Optoelectronics

Front. Optoelectron.    2020, Vol. 13 Issue (1) : 50-72     https://doi.org/10.1007/s12200-019-0949-7
REVIEW ARTICLE
Topological photonic crystals: a review
Hongfei WANG1, Samit Kumar GUPTA1, Biye XIE1, Minghui LU1,2,3()
1. National Laboratory of Solid State Microstructures and Department of Materials Science and Engineering, Nanjing University, Nanjing 210093, China
2. Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
3. Jiangsu Key Laboratory of Artificial Functional Materials, Nanjing University, Nanjing 210093, China
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Abstract

The field of topological photonic crystals has attracted growing interest since the inception of optical analog of quantum Hall effect proposed in 2008. Photonic band structures embraced topological phases of matter, have spawned a novel platform for studying topological phase transitions and designing topological optical devices. Here, we present a brief review of topological photonic crystals based on different material platforms, including all-dielectric systems, metallic materials, optical resonators, coupled waveguide systems, and other platforms. Furthermore, this review summarizes recent progress on topological photonic crystals, such as higher-order topological photonic crystals, non-Hermitian photonic crystals, and nonlinear photonic crystals. These studies indicate that topological photonic crystals as versatile platforms have enormous potential applications in maneuvering the flow of light.

Keywords topological photonic crystals      topological phase transitions      non-Hermitian photonics      higher-order topological photonic crystals     
Corresponding Authors: Minghui LU   
Just Accepted Date: 22 October 2019   Online First Date: 13 January 2020    Issue Date: 03 April 2020
 Cite this article:   
Hongfei WANG,Samit Kumar GUPTA,Biye XIE, et al. Topological photonic crystals: a review[J]. Front. Optoelectron., 2020, 13(1): 50-72.
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http://journal.hep.com.cn/foe/EN/10.1007/s12200-019-0949-7
http://journal.hep.com.cn/foe/EN/Y2020/V13/I1/50
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Hongfei WANG
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Fig.1  Direct analogy between electrons (fermionic) and photons (bosonic) systems
Fig.2  (a) Gyromagnetic photonic crystal used in experiments. The blue rods indicate the gyromagnetic material and 0.2T magnetic field is applied along the z direction; (b) top view of actual waveguides; (c), (e) unidirectional and non-reciprocal propagation; (d) robust propagation against backscattering; (f) reciprocal transmission measured using the bulk photonic crystal and the projected dispersion including bulk and edge states; (g) non-reciprocal transmission via chiral edge states. Reproduced from Ref. [16]
Fig.3  (a) Schematic diagram of triangular photonic crystals; (b) projected dispersion of 2D topological photonic crystals; (c) electromagnetic field distributions ( Ez) in different pseudospins; (d) schematics of the vertical domain composed of bianisotropic metacrystal; (e) band structures of two kinds of unit cells in (d); (f) dispersion relation of surface states with k|| and k directions. Reproduced from Refs. [21,37]
Fig.4  (a) BCC unit cell of gyroid photonic crystals and corresponding Brillouin zone; (b) band structures of nodal lines with two air spheres on two gyroids; (c) schematic of metallic inclusion which includes the saddle shape, and helicoid surface states; (d) Brillouin zone of metallic inclusions and the band structures with Weyl points (rad/blue points). Reproduced from Refs. [130,131]
Fig.5  (a) Arrangement of metallic rods and put into the parallel plate waveguide with different topology characteristics, and the corresponding band structures; (b) schematic plot of the topological switch and the transmission performance with switch operation; (c) schematic of metacrystals with copper cut-wire and their band structures; (d) band structures at kz=0?(2π /a) and kz=0.1 ?(2π /a) planes, and the measured result with the Fourier transform. Reproduced from Refs. [22,143]
Fig.6  (a) Two coupled resonators descripted by Hamiltonian with spin freedom and the 2D array of resonators; (b) edge states in different spins and the transmission in the presence of disorder perturbation; (c) experimental set-up for the measurement; (d) unit coupled resonators including four link and four site resonators, and the scanning electron microscope image (SEM) of the resonant array; (e) topological edge states that propagating around the defect in the experiment and simulation. Reproduced from Refs. [17,146]
Fig.7  (a) Schematics of the helical waveguides comprising the honeycomb lattice; (b) projected dispersion of straight waveguides (R =0? μm) and helical waveguides (R =8? ?μm); (c) microscope image of the photonic waveguide array; (d) light propagation at different distance, z means the length of distances; (e) four different bonds existed in the lattice with coupling constants J1,2, 3,4 and the sketch to achieve it; (f) experiment measured with chiral edge states along different paths. Reproduced from Refs. [27,31]
Fig.8  (a) 2D square lattices made of DBR cavities and connected by phase elements; (b) transmission spectrum (blue line) of two cavities in (a) and the phase in two cavities (red dashed line); (c) schematic of a graphene layer combined with photonic crystals, and their absorption; (d) photonic crystals integrated with graphene. Their optical image of microscope and SEM image; (e) fundamental resonant mode of three-hole defect cavities. Reproduced from Refs. [18,153,154]
Fig.9  (a) 2D lattice of photonic crystal, where d1 and d2 corresponding to the coupling expressed in distance; (b) band structures of trivial, gapless, and nontrivial situations; (c) diagram of 3D structure; (d) photograph of higher-order topological insulator surrounded by ordinary insulators; (e) eigenfrequencies of bulk, edge and corner states; (f) simulation of corner states; (g) experimental measurement of the corner states. Reproduced from Ref. [95]
Fig.10  (a) Nonlinear SSH model, two resonators in every unit cell; (b) band structures of trivial case when the mode intensity I =0; (c) width of band gap changed by intensity; (d) winding number tuned by intensity; (e) time evolution of excitation probability for single-photon state in three qubits Q1,2, 3; (f) probability for a two-photon case. Reproduced from Refs. [54,56]
Fig.11  (a) Dispersion of non-Hermitian system near the exceptional points; (b) array of passive waveguides and realized structure of fused silica glass; (c) SEM image of photonic crystal slabs and their band structure measured by experiment. Reproduced from Refs. [67,72,79]
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