Opposing trends of geometrical parameters in maximisation of micro-ring resonator quality factor

Opposing trends of geometrical parameters in minimisation of bending loss and thus in maximising the quality factor are briefly discussed for micro-ring resonators. It is shown that, while the quality factor of low order modes is an oscillatory function of geometrical parameters, the quality factor of high order modes is a monotonic function. The former has discrete pairs of optimum inner and outer ring radii which maximises the quality factor. In contrast, the quality factor of the latter has no local maximum. Introduction of slight inhomogeneities does not change the overall behaviour of the quality factor but can increase its overall level when the refractive index of the ring region increases at its outer radius.