Analytical model for active racetrack resonators with intracavity reflections and its application in Fano resonance tailoring.

We present an analytical model for estimating the spectral properties of an active racetrack resonator/waveguide system. Under reasonable approximations, we show that the transfer function can be approximated by a rational function, the coefficients of which are determined by the parameters of the structure. The model takes into account intracavity reflections that can provide additional degrees of freedom in the design. We identify conditions under which asymmetric transitions around a spectral peak can occur, which are characteristic of Fano-type resonances. The accuracy of our model is verified by rigorous transfer matrix numerical simulations. We also discuss how the model can be applied for tailoring the transfer function in order to obtain sharper transitions from the spectral peaks to the minima in order for the structure to be used for sensing applications.