Fig. 1: Theoretical results of hyperbolic photonic topological insulator in the face-centered {6, 4} hyperbolic lattice.

a The illustration of face-centered {6, 4} hyperbolic lattice in the Poincaré disk. Lattice sites in the first, second, and third layers are represented by red, blue, and pink dots. Here, a half number of hexagons contain the staggered flux, as marked by triangles. b The coupling pattern in the hexagon possessing NN, NNN, and NNNN hoppings. c The coupling pattern in the hexagon only possessing NN hoppings. d, e The eigenspectra and real-space Chern numbers of the three-layer face-centered hyperbolic model with φ equaling to π and π/2, respectively. f The schematic diagram of the designed hyperbolic photonic topological lattice with two layers. g The illustration of detailed geometric parameters, including radius and widths of site and small-linking rings and the distance between linking rings and site rings. h, i Simulated transmission spectra by exciting the CPS and APS, respectively. Red and blue lines correspond to results of output ports at clockwise and counterclockwise positions with respect to the input port, respectively. j, k Simulation results of steady-state distributions of electric fields by exciting the CPS and APS with the wavelength being 1549.7 nm. l The steady-state distribution of electric fields with the excitation wavelength being 1550.3 nm.