帮我优化简化和从新表达下面这段话让逻辑和内容更加符合论文摘要书写要求： Fano resonance is considered to be an excellent candidate for nanoparticle sensing However generating Fano resonance lineshape on ultra-compact chips and applying f

Fano resonance is a promising candidate for nanoparticle sensing. However, generating Fano resonance on compact chips and using it for nanoparticle detection is challenging, and some theories and mechanisms are still unclear. In this study, we propose a theoretic model based on the transfer matrix method (TMM) to explain the effect of a micro-reflective unit (MRU) formed by an air hole in a straight waveguide when coupled to a compact MRR. The MRU, etched in the coupling region, couples the clock-wise (CW) and counter-clock-wise (CCW) modes in the cavity due to a single nanoparticle or the rough cavity wall, leading to a shift and split in the Fano lineshape. Compared to sensing with an MRR alone, the CCW mode in the cavity is not only affected by particles and rough cavity wall, but also by the MRU, resulting in a significant change in the resonance lineshape. The proposed model is validated through single nanoparticle sensing and FDTD simulation, demonstrating its practicality and providing a new theoretical basis for regulating microcavity Fano resonance lineshape. This opens up new possibilities for highly sensitive integrated sensing of silicon photonic devices