Topologically protected Fano resonance in photonic valley Hall insulators

Rapidly developing photonics brings many interesting resonant optical phenomena, in which the Fano resonance (FR) always intrigues researchers because of its applications in optical switching and sensing. However, its sensitive dependence on environmental conditions makes it hard to implement in experiments. We in this work suggest a topologically-protected FR based on the photonic valley Hall insulators, immune to the system impurities. The topologically-protected FR is achieved by coupling the valley-dependent topological edge states (TESs) with one double-degenerate cavity. The $\delta$-type photonic transport theory we build reveals that this topological FR dates from the interference of the two transmissions that are attributed to the parity-odd cavity mode and the parity-even one. We confirm that the induced Fano line shape of the transmission spectra is robust against the bending domain walls and disorders. Our work may provoke exciting frontiers for manipulating the valley transport and pave a way for the topologically protected photonic devices such as optical switches, low-threshold lasers, and ultra-sensitive sensors.