Fig. 5: Realization of anomalous Hall phase by stitching coupling winding numbers.
From: Winding coupling phase for pseudo-spin-derived topological photonics
a Sketch of the implementation strategy based on stitching two types of resonator pairs in a 4-fold rotational symmetric (C4) square lattice [left panel]. The two stitching units consist of coupled A (red)-B (blue) and C (gray)-B MRRs, respectively. Various combinations of the coupling winding numbers of the two-resonator pairs lead to different topological phases, including the anomalous Hall phase (aHP) and the spin-valley Hall phase (SVHP) [right panel]. b Bulk band diagram of a designed photonic aHP. The band Chern numbers \({C}^{s}\) are indicated. The outer radii of the MRR A, B and C are set to \({r}_{A}=5.55\,\mathrm{\mu m}\) and \({r}_{B}={r}_{C}=5.45\,\mathrm{\mu m}\), with gap distances between the A–B MRRs and A–C MRRs being 100 nm and 200 nm, respectively. The other parameters keep the same as those in Figs. 3, 4. The TE-polarized AM modes with \({m}_{A}=53\) at \({\lambda }_{A}=1531.7\,\mathrm{nm}\) and \({m}_{B,C}=52\) at \({\lambda }_{B,C}=1531.7\,\mathrm{nm}\) are supported. The band frequency is offset by the central frequency of the involved modes, i.e., \(({\lambda }_{A}+{\lambda }_{B}+{\lambda }_{C})/3=1531.7\,\mathrm{nm}\). c Projected band diagram for an aHP slab [left panel], group index of ESs [middle panel], and transmission spectra of ESs under defects [right panel]. The pseudo-spin indices for the ESs are indicated on the upper interface of the aHP slab. The aHP slab is truncated along the [1 1] direction, so that the MRR B’s are located at the interfaces. The defects are created by removing MRRs randomly close to the interface. d, e Simulated field distributions shows that ESs (pseudo-spin \(\uparrow\)) detour around defects. The frequencies of the ESs are set to \(f=-50\,\mathrm{GHz}\) (d) and \(f=50\,\mathrm{GHz}\) (e).
