Rotation-tuned single hexagonal air cavity assisting in third-harmonic generation via hybrid modes

A fillable air cavity with a high quality (Q) factor and large-scale electric field confinement is highly desired in many optical applications. Yet, it remains challenging due to the dielectric transparency and metal loss in optical and near-infrared regimes. Here, we present a rotated hexagonal air cavity embedded in an Ag-air-Ag waveguide. Under near-infrared excitation, evanescent waves tunnel into the cavity. In addition to the whispering gallery mode and surface plasmon polaritons, the cavity also induces Fabry-P\'erot (FP) resonance, whose orientation is tunable via cavity rotation. Thus, our cavity possesses much stronger field confinement and higher Q than a circular cavity lacking FP resonance. The waveguide exhibits suppressed backward reflection filtering and Fano-type lineshapes. Then, integrating a silicon cylinder into the cavity, we demonstrate linear tuning of Mie resonances via radius adjustment. When the electric dipole (ED) resonance is excited, energy is predominantly confined within the cylinder. Different Mie modes will change the orientation of the FP resonance. Furthermore, the hybrid modes with ED resonance induce the third-harmonic wave of green light. These findings offer a promising strategy for designing high-Q air cavities for next-generation multifunctional electro-optical devices.