In this work, we present a closed-form model of silicon-on-insulator (SOI) micro-ring resonators, based on the conformal transformation method. We compute the propagation characteristics of the whispering gallery modes at resonance wavelengths. The results of the proposed model are compared to numerical simulations based on the finite element method (FEM). The proposed method allows comparable accuracy to that of FEM simulations, with a significant reduction in computer resource requirements (time, speed, memory). To further validate the proposed modelling, we also compare the modelling results to experimental data. Finally, we model a ring resonator for biosensing applications. We compute the bulk refractive index sensitivity (S), the figure of merit (FOM) and the intrinsic limit of detection (ILOD). In the geometry under study, our proposed model predicts an ideal ILOD of refractive index units, which is 0.24 smaller than what has been reported in SOI optimized structure. These results validate the proposed modelling technique for the fast design of optical biosensors where both the figure of merit and the geometries can be optimized.
