Superoscillation is a phenomenon in which a signal which is globally band-limited can contain local segments that oscillate faster than its fastest Fourier components.
The idea is originally attributed to Yakir Aharonov, and has been made more popularly known through the work of Michael Berry, who also notes that a similar result was known to Ingrid Daubechies.
[1][2] In 2007, Huang experimentally observed optical superoscillation phenomenon in the diffraction patterns of light transmitted through quasi-periodic nanohole arrays.
[4] In 2009, Huang et al further developed theoretical models to design superoscillation masks that can achieve extreme light concentration and imaging with arbitrary resolution.
Superoscillatory wave forms are being considered as a possible practical tool for engineering applications, such as optical superresolution, i.e., resolution beyond the diffraction limit.