Fig. 1. Schematic of the PFDW structure and band structure. (a) PFDW structure consisting of domains A (blue), B (green), and C (yellow) with different configurations. The supercell used to calculate the projected band structure is denoted by a red rectangle in (a). (b1)–(b3) Illustration of honeycomb unit cells. (c1)–(c3) Corresponding bulk band structures of domains A, B, and C when domain A is biased by +H. The eigenfields of photonic orbitals at the Γ point hosted by the lattices A and C are presented on the right.

Fig. 2. Projected band gap and the eigenmodal field distributions (Ez) of the PFDW. (a) Projected band structures of the PFDW in the cases of +H (red) and −H (blue). The black dashed line denotes the typical frequency ωs=0.528 (2πc/a) that intersects with the red and blue dispersion curves at points 1 (+H) and 2 (−H), respectively. The red and blue triangles represent pseudospin-down and pseudospin-up states. (b) and (c) Eigenfield distributions and the time-averaged Poynting vector S→ of the supercell corresponding to points 1 and 2. The red and blue arrows indicate waveguide states propagating in negative and positive directions, respectively.

Fig. 3. (a) Width of the topological frequency window as a function of the number of layers n in domain B (n=1–20). (b) Eigenfield distributions when n=1, 10, 20.

Fig. 4. Transport phenomena of the PFDW. Simulated Ez field distributions for cases of domain A immersed in −H excited by (a) pseudospin-down source and (b1) pseudospin-up source; and in +H excited by (c) pseudospin-up source and (d1) pseudospin-down source. (b2) and (d2) are Poynting vector distributions of (b1) and (d1) denoted by the red frames. S+ (S−) represents the pseudospin-up (pseudospin-down) source oscillating at ωs.

Fig. 5. Transport phenomena of the PFDW. Simulated Ez field distributions excited by a trivial point source for cases of domain A immersed in (a1) −H and (b1) +H. (a2) and (b2) Poynting vector distributions corresponding to (a1) and (b1). (a3) and (b3) are an enlargement of (a2) and (b2) denoted by the black frames. Red star represents the trivial point source oscillating at ωs.

Fig. 6. Transport phenomena of EM transmission in PFDW-based topological intersection channel. (a1) and (b1) Ez field distributions of the intersection channel with different distributions of external magnetic fields. (a2) and (b2) Time-average Poynting vector distributions corresponding to (a1) and (b1). Domain A applied with −H and +H is depicted as blue and red, respectively. Domains B and C are depicted as green and yellow. (c) Normalized energy intensity distributions measured along the blue and red lines in (a1) and (b1), respectively. The red star on left side represents pseudospin-up source oscillating at ωs.

Fig. 7. Simulated Ez field distributions at ωs in PFDW with (a) void defects, (b) PEC obstacle, and (c) bends. The white block inset in (b) is the corresponding Poynting vector distributions. (d) Simulated transmission spectra in PFDW for three kinds of defects, respectively. Shaded area represents the photonic band gap.

Fig. 8. (a1) and (b1) Ez distributions using a point source excitation at ωs on the left and right boundaries of domain B in the PFDW structure, respectively. The number of layers in domain B drops from 10 to 1 (from the left to right sides). (a2) and (b2) Normalized intensity distribution measured along the red and blue lines in (a1) and (b1). (c) S21 and S12 are the simulated transmission spectra when the point source is excited from the left and right boundaries of domain B, respectively. The red star indicates the point source radiating at ωs.

Fig. 9. Topological large-area pseudospin splitter. Simulated distributions of (a) Ez field and (b1) and (b2) energy fluxes (time-averaged Poynting vector marked as the red arrows) in PFDW circled by red frames, with metallic obstacles inserted in the left and right sides of (a). (c) Simulated transmission spectra along left boundary and right boundary of the structure. White rectangle and red star denote the PEC obstacle of 1.5a and the out-of-plane point source, respectively. Shaded area indicates the photonic band gap.