We discuss a first-order design tool for waveguidecoupled microring resonators based on an approximate solution of the wave propagation in a microring waveguide with micronsize 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.

Microdisk structures have been used to achieve low-threshold lasing. For these microcavity lasers, the spontaneous emission coupling factor p is an important parameter since it determines the threshold current of the laser. Theoretical calculation of p based on the exact solution of the modes in a microdisk is complicated. A simple, approximate method for solving the waveguide modes and the density of states is developed here, using conformal transformation and the Wentzel-Kramers-Brillouin approximation and taking into account the effect of the disk thickness. We find that the p value for a microdisk laser is smaller than that of an ideal laser that has a cylindrical waveguide structure with a strong index guiding. A considerably high value of 0 can still be achieved, however, in a microdisk laser.

We propose a two-ring resonator configuration that can provide optical switching with high extinction ratio (ER), large modulation depth (MD) and low switching threshold, and compare it with two other conventional one-ring configurations. The achievable input threshold is n2IIN ~10-5, while maintaining a large ER (> 10dB) and MD (~ 1) over a 10-GHz (0.1 nm) optical bandwidth. This performance can also be achieved by the ring-enhanced Mach-Zehnder interferometer, and is one to two orders of magnitude better than the simple bus-coupled one-ring structures, because of the use of asymmetric Fano resonance as opposed to the usual symmetric resonance of a single ring. The sharpness and the asymmetricity of the Fano resonance are linked to the low switching threshold and the high extinction ratio, respectively, and also accounts for the different dependence on ring dimensions between the one- and two-ring structures.

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