Fig. 1. Concept of topological membrane meta-devices. (a) Schematic of topological membrane meta-devices and terahertz near-field scanning microscope systems. Two terahertz probes are employed as the emitter and detector to map the in-plane field distributions of the topological meta-devices. The inset shows the schematic view and the electron microscope image of the fabricated unit cell of the VHPCs. (b) Photonic band structure of meta-atoms with (dashed line) and without (solid line) inversion symmetry, Δ=|Ra−Rb| is the radius difference between the two circular holes. The inset shows the mode profiles of meta-atoms in the K valley, and the arrows denote the electric field vectors. (c) Calculated dispersion of topological edge states from a 20×1 supercell, data points in black are projection bands. (d), (e) Schematic of the two studied domain walls (DW1 and DW2). The Δ is of the opposite sign for the two sides of the domain walls, as is also seen as a mirror arrangement of holes across the interface. DW1 and DW2 are denoted as (+Δ,−Δ) and (−Δ,+Δ), respectively. (f), (g) Fourier spectra of DW1 and DW2 at 0.5 THz were obtained from the calculated real space electric field distribution.

Fig. 2. Topological on-chip waveguides. (a) Optical image of the terahertz near-field microscope probes and the fabricated topological waveguide. The white dashed line denotes the position of the topological waveguide as DW1. (b) SEM image of the fabricated straight waveguide with two parity-inverted VHPCs lattices. (c) Calculated (solid line) and measured (dashed line) transmission curves of Ex, Ey, and Hz for the topological waveguide. (d), (e) Calculated in-plane electric field magnitude distribution for the topological waveguide at 0.5 THz. The white star denotes the position of the excitation source. (f) Measured Ey field distributions of the topological waveguide marked by the black rectangle in (e). (g), (h) Calculated (red solid line) and measured (black dashed line) 1D Ey field distributions across and along the waveguide [lines 1 and 2 in (e)], respectively.

Fig. 3. Topological on-chip multiport couplers. (a) Valley-locked surface modes at domain walls. The blue and green arrows denote the surface mode at the K and K′ valley, respectively. (b), (c) Schematic of the four-port directional coupler consisting of DW1 (red) and DW2 (navy). The arrows denote the power flow of two edge states at the K and K′ valley, and the stars indicate the excitation source. (d)–(f) Conceptual illustration of the topological directional coupler with four identical DW1 and six-port coupler consisting of six identical DW1. (g), (h) Calculated in-plane field distribution (Ex and Ey) on the topological four-port coupler at 0.5 THz with the source at port 1. The inset is the SEM image of the junction point. (i), (j) Corresponding calculated in-plane field distribution with the source at port 3. (k) Calculated and measured transmission of four different ports with the excitation from port 1. Each measurement is taken 10 unit cells from the junction so that the measurement at port 1 corresponds to the incident wave. The signal detection positions are shown by colored circles in (h).

Fig. 4. Topological on-chip splitters. (a) Schematic of the topological splitter containing DW1 (red line) and DW2 (navy line) waveguides. The blue and green arrows denote the power flow of the two edge states σ+ and σ−. (b) Calculated in-plane electric field distribution on the topological splitter at 0.5 THz. (c), (f) Calculated and experimentally measured transmission spectra for in-plane components at positions 1 to 4. The signal detection positions are shown in (b). (d), (e) Optical image of the fabricated topological beam splitter placed in the terahertz near-field microscope. The inset shows the SEM image of the junction point.

Fig. 5. Topological on-chip resonators. (a) Mode coupling of a conventional whispering gallery mode resonator. The arrows show the direction of possible power flow, while stars indicate the position of the excitation source. The energy from the ring couples into both the forward and backward propagating modes of the waveguide. (b) Mode conversion of topological resonators with the source located in the waveguide. The arrows denote the supported (√) and forbidden (×) directions of coupling, and red and navy lines denote DW1 and DW2, respectively. Two types of resonances (traveling and standing waves) arise depending on the coupling of the forward propagation. The dashed arrow denotes the critical coupling. (c) Corresponding mode conversion of topological resonators with the source located on the ring. (d) Electric field spectrum in the resonator (measured at the location of the blue point shown in the inset) and the straight waveguide (red point). (e) Ey field distributions of the topological resonators at peaks 1 to 4 (0.5, 0.518, 0.523, and 0.528 THz). The white arrows denote the power flow of the edge modes σ+. (f), (g) Corresponding electric field spectrum and field distributions of four peaks 1 to 4 (0.513, 0.518, 0.523, and 0.528 THz) with the source exciting the ring directly. The white and yellow arrows display the power flow of the edge modes σ+ and σ−, respectively.