Theory of two-dimensional ´fingerprint´ resonators

The development of integrated optics demands high-quality resonators which can be embedded in the surface of small chips. The designs so far available, such as self-coupling fibres or rings, are intrinsically unsuitable for this, because the small bending resulting from the small size inevitably introduces severe radiation losses. The typical feature of a resonator is the existence of standing waves: these are established in classical resonators by reflection from a metal wall. However, this can also be achieved by a periodic perturbation on the surface of dielectric waveguides. A practical design for a two-dimensional perturbation is a series of concentric circular curves etched on a chip surface, which looks like human fingerprints. For such a resonator, a high quality value can be achieved in a small size.