Fig. 1. (a) Simplified top view of the PhC system. The two black pentagrams represent two distant identical topological corner cavities (appearing at the intersections of the I–IV regions), and the red line indicates a topological interface state. (b) Three-dimensional photonic crystals with two pairs of gold plates placed in the xy and yz planes. h is the height of the cylinders. (c) Schematic of a triangular photonic crystal composed of six Al2O3 cylinders (ε=7.5). Right panel: magnified view of the unit cell. The radius of the hexagon (solid black line) is R, while the radius of the large (small) cylinder is marked with ra (rb). (d) Eigen-energy spectrum of the topological corner state. (e) Calculated band diagram based on a supercell composed of regions IV and V, where a periodic (absorbing) boundary condition is applied in the x (y) direction. Blue lines are for topological edge states.

Fig. 2. (a) Coherent (red solid curve) and incoherent (blue dashed curve) couplings between two molecules with parameters L2=20a and L1=L3=19a. (b) Energy transfer efficiency η and (c) energy transfer time tf as a function of the frequency with (red solid lines) and without (blue dashed lines) coherent coupling. (d) Populations of acceptor under three typical frequencies marked in (a), (b), and (c).

Fig. 3. (a) Energy transfer efficiency and (b) transfer time between two molecules separated by a longer distance L2=60a (red solid lines). The black dashed lines represent the case of L2=20a.

Fig. 4. Topologically protected energy transfer. (a), (b), (c) Case of the first kind of defect; (d), (e), (f) case of the second kind of defect. (a), (d) Energy transfer efficiency (solid red lines) under the two cases; (b), (e) corresponding energy transfer time (solid red lines). The dashed black curves represent the case without defect. (c), (f) Simulated unidirectional propagations of excited interface state along interfaces with disorders (deformed hexagons inside black dashed box) and 60° and 120° turns, respectively. The white star represents the excited chiral light source.