The Fano resonance with a distinctive ultra-sharp, asymmetric line shape and high quality factor, is a widely occurring phenomena, that has a large variety of optical, plasmonic and microwave manifestations. In this paper, we explore the characteristic robustness of a Fano resonance mode, which is topologically protected by engineering a band inversion, induced by breaking the mirror symmetry of a two-dimensional honeycomb photonic crystal (HPC), associated with $C_6$ point group symmetry. Dark and bright topological edge modes appear in the band gap which arise when Dirac cone is opened up. Destructive and constructive interference of the dark and bright modes leads to the asymmetric line shape of the Fano resonance. The Fano resonance is very sensitive to the material changes and structural perturbations. This property can be applied to obtain new sensor designs. Here we demonstrate that the topological Fano resonance mode preserves its asymmetric, ultra-sharp line shape in the presence of the disorder, defects and cavities.The stability of the Fano resonance mode has useful optical device applications such as in low threshold lasers, and extremely precise interferometers.

法诺共振具有独特的超锐利、不对称线形和高品质因数，是一种广泛发生的现象，具有多种光学、等离子体和微波表现形式。在本文中，我们探索了 Fano 共振模式的特征鲁棒性，该模式通过设计能带反转得到拓扑保护，通过破坏二维蜂窝光子晶体 (HPC) 的镜像对称性引起，与$C_6$点群对称。当狄拉克锥打开时，带隙中出现暗和亮拓扑边缘模式。暗模式和明模式的破坏性和建设性干扰导致 Fano 共振的不对称线形。Fano 共振对材料变化和结构扰动非常敏感。此属性可用于获得新的传感器设计。在这里，我们证明了拓扑 Fano 共振模式在存在无序、缺陷和空腔的情况下保持其不对称、超锐利的线形状。 Fano 共振模式的稳定性具有有用的光学器件应用，例如低阈值激光器，以及精密干涉仪。