Fig. 1. Topological metasurface evolved from passive toward active and beyond.

Fig. 2. Analog quantum Hall topological metasurface. (a) Bulk dispersion of a gyromagnetic photonic crystal under zero external magnetic field [22]. (b) Experimental setup for measuring the one-way chiral edge state in a gyromagnetic topological metasurface [23]. (c) Gyromagnetic topological metasurface supporting self-guiding unidirectional electromagnetic edge states [24]. (d) Topological bandgap map as a function of magnetic field strength and frequency [25]. (e) Magnetic topological metasurface composed of ferromagnetic rods arranged in a honeycomb lattice [26]. (f) Band structure of magnetic topological metasurface with an unpaired Dirac point [27]. (g) Spectrum and field profiles of the dislocation-induced topological metasurface [28]. (h) Topological phase transition diagram and simulated mode profile of quadrupole topological corner state [29]. (i) Experimental setup for measuring the antichiral edge state [30]. (j) Nonreciprocal large-area topological metasurface [31]. (k) Anomalous nonreciprocal topological metasurface made of ferrite circulators connected with microstrip lines [33].

Fig. 3. Photonic analogs of the quantum spin Hall effect. (a) Band structure of a metacrystal with a hexagonal lattice [37]. (b) Experimental realization of QSHE by metacrystal waveguides [38]. (c), (d) Theoretical proposal [39] and experimental realization [40] of QSHE by bi-anisotropic metawaveguides. (e) Schematic of a triangular all-dielectric photonic crystal as a photonic analog of QSHE [42]. (f)–(j) Experimental realization of QSHE by crystalline metamaterials in the microwave range (f) [43], (g) [44], visible spectral range (h) [45], near-infrared region (i) [46], and terahertz range (j) [47].

Fig. 4. Valley-Hall PTI and its metasurface realizations. (a) Illustration of Dirac cones with different mass terms located at the corners of the Brillouin zone. (b) Schematic diagram of domain wall consisting of two valley-Hall PTIs. (c) Dispersions of the supercell shown in (b) (dashed rectangle). (d) Typical unit cells of topological valley-Hall metasurfaces. (e) Statistics of existing literature on topological valley photonics by June 2022. Each bubble denotes a theoretical/experimental (hollow/solid) literature on active/passive (red/blue) devices. The size denotes the number of citations.

Fig. 5. Passive photonic devices based on topological valley-Hall metasurfaces. (a) Silicon topological valley-Hall metasurface for on-chip THz communication [86]. (b) Simulated field distribution for structure in (a) [86]. (c) Measured bit error rate as a function of data rate at 0.335 THz [86]. (d) Momentum-space analysis on the outcoupling of (e) simulated (left) and measured (right) field patterns for the outcoupling of TE-mode valley kink state to vacuum space [54]. (f) Measured reflectance for zigzag (gray) and armchair (purple) terminations [54]. (g) Schematic diagram of photonic routing based on the valley kink states [67]. (h) Scanning-electron-microscope (SEM) view of the experimental sample [67]. (i), (j) Measurement of photonic routing profiles at λ=1400  nm for light injected from the WVG1/WVG2 port [67].

Fig. 6. (a) Dynamically modulated photonic resonator lattice exhibiting an effective magnetic field for photons [96]. (b) Kagomé lattice with three sites in the primitive cell, and the corresponding Brillouin zone [97]. (c) The FTI consists of a static PhC and permittivity modulations by three Bloch waves [98]. (d) Non-Hermitian Floquet kagomé lattice [100].

Fig. 7. (a) Schematic of a unit cell in a 2D lattice of photonic ring resonators (upper) and the equivalent periodic network (lower) [103]. (b) Photo of metallic rods on a flat metallic surface (left), and schematic of a 5×5 lattice in experiment (right) [104]. (c) Photo of CSP ring resonators printed on a flexible paper-like dielectric film (left) and schematic of the folded flexible photonic TI (right) [105]. (d) Schematic of a unit cell of a Floquet lattice of identical, evanescently coupled octagon resonators, with octagon D rotated by 45° with respect to the other three resonators [106].

Fig. 8. Second-order photonic corner states. (a) Second-order photonic corner states in a photonic crystal with dielectric rods [114]. (b) Second-order photonic corner states in a kagomé metasurface [119]. (c) Photonic crystal nanocavity based on a topological corner state [120]. (d) Enhanced photoluminescence mediated by a topological metasurface [122]. (e) Quadrupole topological phase in a twisted photonic crystal [129].

Fig. 9. (a) Far-field polarizations form vortices with BICs as polarization singularities [144]. (b) Multiple BICs are tuned together as a merging BIC. The Q factors of nearby resonances have been significantly enhanced at the merging BIC compared to isolated BICs [147]. (c) The accidental BIC and the FW-BIC are tuned to merge at an off-Γ point by varying structural parameters [148]. (d) Circularly polarized states are spawned from BICs under C2 symmetry breaking. Adapted with permission [150]. (e) The higher-charged BIC is split into two off-Γ BICs by reducing symmetry [151]. (f) UGRs are created by eliminating radiation loss using polarization singularity at only one single side [152].

Fig. 10. (a) Zero-index materials with light confined by BICs in out-of-plane [156]. (b) Diffraction-free beams are guided by BICs beyond the light cone [159]. (c) Ultrasensitive hyperspectral imaging by detecting BIC-inspired resonance shifts [162]. (d) Angular-scanning sensors using BIC-inspired narrow spectra [163]. (e) Optical vortices generated from the polarization vortex around BICs [166].

Fig. 11. (a) Bloch-type skyrmion and (b) Néel-type skyrmion with p=1 and m=1. (c) Illustration shows the relation between a skyrmion and a meron (antimeron).

Fig. 12. Second-harmonic generation (SHG) in active topological metasurface. (a) SHG mediated by two corner modes that reside within two different topological bandgaps and could be frequency matched to greatly boost harmonic conversion efficiency by the mechanism of double resonance [208]. (b) Spatial mapping of SHG in a fabricated slotted nanocube array [214]. (c) Band diagram and simulated field intensities of fundamental (E1) and second-harmonic (E2) waves in a dielectric metasurface [210].

Fig. 13. Third-harmonic generation (THG) in active topological metasurfaces. (a) THG in a QSH topological metasurface consisting of silicon pillars arranged into hexagon clusters [215]. (b) THG in a nonlinear and asymmetric metasurface governed by BIC [216]. (c) THG enhanced by a topologically protected edge mode in high-order topological metasurfaces [218].

Fig. 14. Four-wave mixing (FWM) in active topological metasurfaces. (a) FWM of topologically protected one-way edge plasmons in a graphene QH topological metasurface [221]. (b) Generation of indistinguishable photon pairs via spontaneous FWM in an anomalous QH topological metasurface [219]. (c) Entangled photons emerge and flow at a pair of edge modes in a silicon anomalous Floquet topological metasurface [107].

Fig. 15. High-harmonic generation (HHG) and Kerr effects in active topological metasurfaces. (a) High-harmonic optical vortex generation in a symmetric BIC topological metasurface [225]; (b) 3rd to 11th optical harmonics generated in a nonlinear and asymmetric BIC topological metasurface [224]. (c) Power-dependent corner states and solitons in high-order topological metasurfaces [229].

Fig. 16. Topological laser based on active topological metasurface. (a) Topological laser in a QH topological metasurface consisting of honeycomb lattice of coupled ring resonators [253]. (b) Electrically pumped topological laser in a QSH topological metasurface comprising a square lattice of ring cavities and link resonators [242]. (c) Topological bulk laser in a QSH topological metasurface based on band-inversion-induced reflection [241]. (d) Electrically pumped topological laser based on QVH effect operating at terahertz frequencies [237]. (e) Low-threshold topological laser in a second-order topological metasurface [238]. (f) Lasing improved by BICs [232].

Fig. 17. Electrically controlled reconfiguration in topological metasurfaces. (a) Ultrafast reprogrammable plasmonic topological metasurface based on QVH effect [269]. (b) Chip-scale Floquet topological metasurface based on switched-capacitor networks [273]. (c) Reconfigurable QSH topological metasurface based on liquid crystal [266]. (d) HOTI topological metasurface supporting edge-corner state switching [271].

Fig. 18. Optically controlled reconfiguration in topological metasurfaces. (a) All-optical control of topological states in a Floquet topological metasurface [274]. (b) Transmission modulation in a QVH topological metasurface by optically tuning the refractive index of silicon [275]. (c) Optically reconfigured topological edge states by breaking local non-Hermitian symmetry [276]. (d) Ultrafast all-optical switching between the vortex beam lasing and linearly polarized beam lasing [240].

Fig. 19. Mechanically controlled reconfiguration in topological metasurfaces. (a) Robust reconfigurable microwave propagation routes in a QSH topological metasurface [40]. (b) Tunable edge states in a split-ring topological metasurface [278]. (c) Reconfigurable topological metasurface based on honeycomb lattice of rotating dielectric cuboids [279].

Fig. 20. Thermally controlled reconfiguration in topological metasurfaces. (a) Dynamically reconfigurable topological edge state in a thermally controlled topological metasurface [280]. (b) Thermally controlled topological metasurface based on silicon-on-insulator technology [281]. (c) Thermally controlled edge and corner states in HOTI topological metasurfaces [282].

Fig. 21. Quantum information applications of topological photonics. (a) Topological source of quantum light in a coupled array of ring resonators [220]. (b) On-chip Hong–Ou–Mandel interference in a topologically protected valley-dependent quantum circuit [288]. (c) Topological protection of biphoton states in a nanophotonic platform [289]. (d) Topologically protected entangled photonic states in a nanophotonic platform with two topological defects [290]. (e) Topologically protected energy–time entangled biphoton states in spin-Hall topological photonic crystals [291]. (f) Topologically protected polarization quantum entanglement on a photonic chip [292].

Fig. 22. Coupling of a single quantum emitter to topological photonic systems. (a) Chiral coupling between the helical topological edge modes of spin-Hall topological photonic crystals and a quantum emitter [46]. (b) Chiral topological photonics with an embedded quantum emitter in a valley-Hall topological photonic crystal waveguide [301]. (c) Coupling between a quantum emitter and second-order topological corner state for cavity quantum electrodynamics [302].

Fig. 23. Multiple quantum emitters in structured photonic environments for engineering of topological quantum metamaterials. (a) Topologically protected quantum entanglement emitters in a coupled array of ring resonators [107]. (b) 1D array of quantum emitters coupled to the chiral edge state of a topological photonic crystal [307]. (c) Topological quantum optics using 2D array of quantum emitters coupled to a photonic crystal slab [310]. (d) 2D array of quantum emitters embedded in a photonic cavity [311].

Table 1. Typical Nonlinear Effects in Active Topological Metasurface^a

Table 2. Typical Reconfigurable Manners in Active Topological Metasurface^a