Refined Theoretical Model for Microcavity Fano Resonance Lineshape Regulation using MRU Etching

In this article, we present a refinement theoretic model that utilizes the transfer matrix method (TMM) to describe the effect of etching a micro-ring resonator undercut (MRU) on a straight waveguide. The theoretical model quantifies the changes in transmission and reflection lineshape and intensity resulting from variations in MRU position and size. Compared to the single nanoparticle detection of micro-ring resonators (MRR), the MRU induces a strong counterclockwise (CCW) mode in the cavity. This enhanced sensitivity to reflections, arising from both single nanoparticles and rough cavity walls, leads to significant changes in the resonant lineshape. Consequently, this structure can be utilized for more precise single nanoparticle detection. Through numerical calculations and finite-difference time-domain (FDTD) simulations, we predict and observe the shifting and splitting of the Fano lineshape. The proposed model in this paper establishes a new foundation for the regulation and application of microcavity Fano resonance lineshape.'}