Fig. 1. (a) Schematic diagram of the topologically protected photonic waveguide (TPPW). The TPPW consists of three domains, A|Bx|C, where the unit cells of PhCs in A and C domains have broken-inversion symmetry and that in B domain has inversion symmetry. The structure parameters are L1=196  nm and L2=84  nm for A domain (L1=L2=151.2  nm for B domain, L1=84  nm and L2=196  nm for C domain), lattice constant a=280  nm, and thickness of the structure d=150  nm. (b) Band diagrams of PhC in B domain (L1=L2) with Dirac points, and band diagrams of PhC in A or C domain (L1≠L2) with a bandgap. (c)–(f) Hz phase profiles of PhC in A domain and PhC in C domain at K point in the upper (321.11 THz) and lower (293.14 THz) bands.

Fig. 2. (a) Band diagram of A|B5|C waveguide. The red dotted lines show the topological edge state. The zeroth and first bands, marked with black lines, are other gapped waveguide states. The light gray area in the bulk gap of A or C domain is referred to as the topological frequency window. (b) Width of the topological frequency window as a function of the number of layers x in B domain. (c) Frequency gap of the topological frequency window of valley-locked waveguide consisting of honeycomb lattices with two sizes of triangular and circular airholes as a function of the number of layers x in B domain. Inset: band diagrams with different shapes. (d) Hz field distributions of three straight TPPWs with x=1, 5, and 9.

Fig. 3. (a)–(d) Simulated photonic Hz field distributions at 302.08 THz in waveguides with four different defects: bulging, indentation, bending, and disorder. (e) Field intensities measured at the points represented by blue dots near the exits of the four waveguides with defects in (a)–(d). The black line is the field intensity of a waveguide without defects. The great consistency of field intensities in the topological frequency windows indicates the immunity of TVWSs to defects. Hz phase diagrams of TVWSs after transmission (f) without and (g) with defects.

Fig. 4. (a), (b) Simulated photonic Hz field distributions under the excitation of point sources at the input port 1 for two different configurations at 302.08 THz. Three ports labeled 2, 3, and 4 are located in B domain. (c), (d) Transmittance of TVWSs through port 2, port 3, and port 4 for (a) and (b), respectively.

Fig. 5. (a) Schematic of a topological concentrator. The width of B domain abruptly changes from 9 to 0.5 layers in the middle of the device. The waveguide with x=0.5 in the B domain is terminated by a mirror made up of a photonic crystal structure. Red stars: point sources. (b) Simulated H field distributions in the topological concentrator at 302.08 THz. (c) Simulated intensity profiles along black, red, and blue dashed lines in (a). (d) Schematic of a topological photonic power splitter. The width of B domain of the top waveguide is one and that of bottom waveguide is two. Red stars: point sources. (e) Simulated H field distributions in the topological photonic power splitter at 302.08 THz. (f) The power splitting ratio of the device varies with the top waveguide shift in units of the lattice constant a.