Type-I Weyl points induced by negative coupling in photonic crystal

Weyl points,which are the degenerate points in three-dimensional momentum space,have been widely studied in the photonic system,and show some intriguing phenomena such as topologically protected surface states and chiral anomalies.Type-I Weyl systems possess a complete bandgap,and topologically protected surface states can be excited without disturbing the bulk states.In this work,we investigate the influence of the sign of coupling coefficient on the topological property of the system and find that type-I Weyl points can be realized by introducing a negative coupling between the stacking layers of the designed photonic crystal.We propose a new strategy to construct a type-I Weyl system by stacking the hexagonal photonic lattice.Different from the topological nontrivial photonic system with a positive coefficient,the negative couplings in the photonic system are realized by adding another resonating site between stacking layers.We theoretically demonstrate that the effective coupling between the resonating sites in adjacent layers sign-flips through the judicious design of the nearest coupling strength and eigenfrequency of the additional sites.The surface states at opposite boundaries of the proposed system have opposite group velocities,which is the feature of type-I Weyl points.Our study provides a new method of exploring topologically protected photonic systems and developing possible topological devices.