A wave is called superoscillating when, in some interval, it oscillates much faster faster than the shortest wavelength contained in the entire wave.

Superoscillations are of interest in several fields. In quantum wave functions and fields they can act as "cooling rays", their use may be useful to improve measurement technology through superresolution or superabsorption and there is, for example, even a possibility that they may be useful in the field of optogenetics. We published quite a few papers on the topic. Here is a recent paper on this phenomenon, based on a talk I gave at a workshop on superoscillations in London, U.K., in October 2017:

Four aspects of Superoscillations.