Super defocusing of light by optical sub-oscillations

The mathematical phenomenon of superoscillation, in which a spectrally bound function oscillates locally at a rate faster than its fastest Fourier component, has found use in both theoretical and applied areas of optical research. We show the existence of a complementary phenomenon we term sub-oscillation, in which a spectrally lower bound limited function oscillates locally at an arbitrarily low frequency. The relevance of superoscillations to various fields, such as weak measurements, beam shaping, and super-resolution imaging, suggests that sub-oscillations could also find various uses. Here, we construct a spatially sub-oscillatory optical beam to experimentally demonstrate optical super defocusing, i.e., a very fast, exceptional expansion of a partially blocked light beam.