Theoretical Model for Controlling Fano Resonance Linewidth in Microcavities for Nanoparticle Sensing

Fano resonance is considered an excellent candidate for nanoparticle sensing. However, generating Fano resonance linewidths on ultra-compact chips and applying them for nanoparticle detection remains a challenge, with some theories and mechanisms still relatively unclear. In this paper, we propose a theoretical model based on the transfer matrix method (TMM) to quantitatively explain the influence of micro-reflection units (MRUs) formed when a straight waveguide pore is coupled with a compact MRR. When the MRU is etched in the coupling region, the clockwise (CW) and counterclockwise (CCW) modes in the cavity will couple due to a single nanoparticle, leading to the shifting and splitting of the Fano resonance linewidth. In contrast to single particle sensing in the MRR, the CCW mode inside the cavity is not only affected by the particle and rough cavity walls, but also potentially by the MRU, resulting in a drastic change in the resonance linewidth. The proposed model is validated when applied to single nanoparticle sensing and is highly consistent with FDTD simulation results. These findings demonstrate the practicality of the proposed model and provide a new theoretical basis for controlling the Fano resonance linewidth in microcavities, opening up new possibilities for integrated sensing in high-sensitivity silicon photonic devices.