Fig. 1. Spin-momentum locking exists at the interface of two metamaterials. (a) The chirality of the source decides the transmission direction. Unidirectional transmission at the interface between: (b) spoof SPPs: air and corrugated structures (εair>0, εeff<0); (c) LWs: dual-impedance surfaces (ZTM>0, ZTE<0); and (d) PTIs: Berry phase flips.

Fig. 2. Two chiral sources carrying (a) SAM and (b) OAM. (c) Spin-momentum locking phenomenon. (d) SAM-OAM conversion. (e) Five-ports-feeding network and measured performance: (f) balanced amplitude and (g) π/2-phase step.

Fig. 3. (a) Spoof SPPs under study. (b) Enlarged absorptive terminal design. (c) Electric field vector of spoof SPPs with spin-momentum locking. (d) Dispersion curves of two spoof SPPs (SSPPs).

Fig. 4. Visualization of unidirectional spoof SPPs. (a) The near-field scanning setup. (b) Transmission at two opposite terminals excited by an RHCP source. (c) Measured distribution of the out-of-plane electric field (Ez) at 10 GHz along the transmission route. (d) Field distributions on the 2D surface. (e) The planar structure is wrapped on the surface of a cylinder. (f) Unidirectional coupling on the surface of the cylinder [unidirectional planar spoof SPPs (Video 1, MP4, 2.26 MB [URL: https://doi.org/10.1117/1.AP.4.4.046004.1]) and unidirectional conformal spoof SPPs (Video 2, MP4, 1.59 MB [URL: https://doi.org/10.1117/1.AP.4.4.046004.2)].

Fig. 5. (a) Structure of the LWs waveguide under study. (b) Electric field distribution at the x-z cross section. (c) Dispersion curves of surface modes and LWs, and equivalent surface reactance can be calculated. Black solid line: dispersion curves of surface waves and LWs. Gray dashed line: light cone. Colored dashed line: extracted surface impedance.

Fig. 6. Visualization of unidirectional LWs. (a) The near-field scanning setup. (b) Simulated electric field (Ez) distribution on the surface of the planar structure where we set up uniform equivalent impedance surfaces as a simplified simulation model. (c) Measured electric field (Ez) distribution [unidirectional LWs (Video 3, MP4, 2.99 MB [URL: https://doi.org/10.1117/1.AP.4.4.046004.3])].

Fig. 7. (a) The valley waveguide. (b) Unit cell analysis: topological bandgap, intrinsic OAM (l=±1), and flipping Berry curvature. (c) Superlattice analysis: dispersion and field distributions of valley PTIs at two different interfaces. Unidirectional OAM coupling with (d) different vortex charges l and (e) different phase step Δφ. The transmission is defined by the proportion of received energy at terminals (left/right) and the total energy of the source: T=Pleft/right/Psource. The maximum transmission (T=1) represents an ideal unidirectional coupling.

Fig. 8. Visualization of unidirectional valley PTIs. (a) Near-field scanning setup. (b) Simulated electric field distributions of two waveguides with horn-type and straight-line-type terminals. (c) Measured electric field distribution at opposite terminals. (d) Measured unidirectional transmission [unidirectional valley PTIs with the horn-type terminal (Video 4, MP4, 1.32 MB [URL: https://doi.org/10.1117/1.AP.4.4.046004.4]) and unidirectional valley PTIs with the straight-line-type terminal (Video 5, MP4, 1.26 MB [URL: https://doi.org/10.1117/1.AP.4.4.046004.5])].

Fig. 9. Digital coding metamaterial waveguides with spin-momentum locking. (a) Spoof SPPs: manipulating the wavevector and bi-directional chiral sorting. (b) LWs: manipulating impedance to tailor the arbitrary transmission and control the scattering performance of metasurfaces at the same time. (c) PTIs: manipulating the topological invariant to realize dynamic chiral sorting multiplexers.