Topological Fano resonance of symmetric Lamb wave induced by antisymmetric trapped mode

The rapid development of topological physics in recent years has greatly enriched the methods for manipulating classic waves. Fano resonance is a widespread phenomenon featured with asymmetric and ultrasharp transmission line shape, which is induced by the constructive and destructive interference of two resonance modes with different quality factors. The temporal coupling mode theory is introduced to theoretically describe the physical process of Fano phenomena with two topological resonance states. The mechanism of the pass band led by the coupling between local resonance and Bragg scattering is introduced to design the antisymmetric topological resonance state and suppress the interference of the antisymmetric propagation mode. The complex eigenvalue analysis shows that the antisymmetric topological resonance state can be treated as the bound state in continuum (BIC). The periods of the phononic crystal (PnC) can be largely reduced by this scheme. The mechanism of coupling between two topological resonance modes attributed to geometric parameter variation is explained by the perturbing perspective and the temporal coupled mode theory. By theoretical analysis, the antisymmetric topological resonance state can be simultaneously treated as symmetric protected BIC and Friedrich-Wintgen BIC. Then, the design method for PnC with Fano resonance is proposed. The numerical results are in good agreement with the theoretical outcomes. The research results may find potential applications and offer the theoretical directive guideline for design in the fields of non-destructive testing, radio-frequency filters, resonators, and sensors.