DESIGN AND MODELING OF WAVE-GUIDE-COUPLED SINGLE-MODE MICRORING RESONATORS

We discuss a first-order design tool for waveguide-coupled microring r esonators 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 transfor mation method and a linear approximation of the refractive index profi le, and takes into account the effect of waveguide thickness, dispersi on, and diffraction, Based on this model, we develop general design ru les for the major physical characteristics of a waveguide-coupled micr oring resonator, including the resonance wavelength, the free spectral range, the coupling ratio, the bending radiation loss and the substra te leakage loss, In addition, the physical model provides leads to alt ernative coupling designs. We present two examples, one using a phase- matching parallel waveguide with a smaller width than the ring wavegui de, and the other using a vertical coupling structure. Both these desi gns significantly increase the coupling length and reduce or eliminate the dependence on a narrow air gap in a waveguide-coupled microring r esonator.