We discuss a first-order design tool for waveguide-coupled microring resonators based on an approximate solution of the wave propagation in a microring waveguide with micron-size radius of curvature and a large lateral index contrast. The model makes use of the conformal transformation method and a linear approximation of the refractive index profile, and takes into account the effect of waveguide thickness, dispersion, and diffraction. Based on this model, we develop general design rules for the major physical characteristics of a waveguide-coupled microring resonator, including the resonance wavelength, the free spectral range, the coupling ratio, the bending radiation loss and the substrate leakage loss. In addition, the physical model provides leads to alternative coupling designs. We present two examples, one using a phase-matching parallel waveguide with a smaller width than the ring waveguide, and the other using a vertical coupling structure. Both these designs significantly increase the coupling length and reduce or eliminate the dependence on a narrow air gap in a waveguide-coupled microring resonator.
M. K. Chin and S. T. Ho, "Design and Modeling of Waveguide-Coupled Single-Mode Microring Resonators," J. Lightwave Technol. 16, 1433- (1998)