Modeling of tuning of microresonator filters by perturbational evaluation of cavity mode phase shifts

Microresonator filters, realized by evanescent coupling of circular cavities with two parallel bus waveguides, are promising candidates for applications in dense wavelength division multiplexing. Tunability of these filters is an essential feature for their successful deployment. In this paper we present a framework for modeling of tuning of the microresonators by changes of their cavity core refractive index. Using a reciprocity theorem, a perturbational expression for changes in the cavity propagation constants due to slight modifications of the cavity core refractive index is derived. This expression permits to analytically calculate shifts in spectral response of the 2D resonators. Comparisons of the resultant shifts and spectra with direct simulations based on coupled mode theory show satisfactory agreement.