The mathematical phenomenon of super-oscillation, 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 beyond the lower band limit. 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.
The relevance of super-oscillations to varied fields such as quantum measurement, optical beam shaping and super-resolution, particle manipulation, electron beam shaping and radio frequency antenna design, suggest that sub-oscillations could find interesting uses in varied fields as well. Our demonstration of super defocusing by itself might be relevant for optical dark-field microscopy.
 Y. Eliezer and A. Bahbad, Optica 4, 440 (2017)
Yaniv Eliezer and Alon Bahabad, "Suboscillations in optics (Conference Presentation)," Proc. SPIE 10677, Unconventional Optical Imaging, 106770Z (Presented at SPIE Photonics Europe: April 24, 2018; Published: 24 May 2018); https://doi.org/10.1117/12.2302785.5789396234001.
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