Surfaces are made to have optimum combinations of curvatures in orthogonal planes.

Coupling of light into and out of whispering- gallery-mode (WGM) optical resonators can be enhanced by designing and fabricating the resonators to have certain non- axisymmetric shapes (see figure). Such WGM resonators also exhibit the same ultrahigh values of the resonance quality factor (Q) as do prior WGM resonators. These WGM resonators are potentially useful as tunable narrow-band optical filters having throughput levels near unity, high-speed optical switches, and low-threshold laser resonators. These WGM resonators could also be used in experiments to investigate coupling between high-Q and chaotic modes within the resonators.