Fig. 1. (a) Schematic of sandwich structure (DCD)u(ABA)vM with two coupled TISs. (b) Band structure of (ABA) PC. Red stripe represents the first bandgap with positive reflection phase. The Zak phase of each band is displayed next to it, and the sum of Zak phases below the first gap is shown in parentheses. (c) Band structure of (DCD) PC. Yellow stripe represents the first bandgap with negative reflection phase. (d) Reflectance for TIS 1 in (DCD)u(ABA)9. The blue solid, red dotted, black dashed, and green solid lines represent u=11, 9, 7, and 6, respectively. (e) Reflectance for TIS 2 in (ABA)9M. (f) Reflectance for coupled TISs in (DCD)7(ABA)vM. The blue solid, red dotted, and black dashed lines represent v=9, 13, and 15, respectively.

Fig. 2. Distribution of normalized electric field amplitude for different topological states. The yellow, red, gray, and white shaded areas represent the photonic crystal DCD, ABA, silver, and air background, respectively. (a) TIS 1 in (DCD)7(ABA)9. (b) TIS 2 in (ABA)9M. (c), (d) Super-modes with (c) lower and (d) higher energy in (DCD)7(ABA)9M with strong coupling. (e) Merged TISs in (DCD)7(ABA)13M with critical coupling. (f) Merged TISs in (DCD)7(ABA)13M with weak coupling. The red dashed lines represent the interfaces between different PCs and metal.

Fig. 3. (a) Reflectance spectra of TIS 1 in (DCD)6(ABA)10 calculated by TMM (blue solid line) and Lorentz model (red hexagonal points). (b) Same as in (a), but for TIS 2 in (ABA)10M.

Fig. 4. (a) Eigenvalue spectra of effective PT-symmetric system [(DCD)6(ABA)pM] versus coupling rate |κ| (period number p) between two TISs. Blue circles represent absorption peaks with varied period numbers p. (b) Reflectance and normalized electric field distribution of system for forward (F)/backward (B) propagation with p=12. Red/blue line stands for forward/backward propagation. The layers at two ends are air layers.

Fig. 5. Calculated absorption spectra of (DCD)6(ABA)pM with different period numbers p by using TMM (blue solid line) and CMT (red hexagonal points).

Fig. 6. (a) Schematic of PC heterostructure (D′C′D′)M′(A′B′A′)qM. (b), (c) Calculated absorption spectra of (b) TIS 1 in (D′C′D′)M′(A′B′A′)10 and (c) TIS 2 in (A′B′A′)10M, using TMM (blue solid line) and Lorentz model (red hexagonal points). (d), (e) Corresponding distribution of normalized electric field amplitude. The yellow (red) dashed line represents the interface between silver layers M′ and D′ (A′).

Fig. 7. (a) Eigenvalue spectra of non-ideal PT symmetric system [(D′C′D′)M′(A′B′A′)qM] versus different coupling rates |κ| (period number q). Blue circles represent absorption peaks of the system with varied period numbers q=6–12 calculated by TMM. Green star represents the case where the Hamiltonian of the system has a real eigenvalue (one-channel CPA is achieved). (b) SEM image of one sample of q=6. (c) Absorption spectra calculated from TMM (solid lines) and CMT (hexagonal dots). (d) Measured absorption spectra.