Superoscillations and Physical Applications

Andrew N. Jordan (), John C. Howell (), Nicholas Vamivakas () and Ebrahim Karimi ()
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Andrew N. Jordan: Chapman University, The Kennedy Chair in Physics
John C. Howell: Chapman University, Institute for Quantum Studies
Nicholas Vamivakas: University of Rochester, The Institute of Optics
Ebrahim Karimi: Chapman University, Institute for Quantum Studies

Chapter 96 in Operator Theory, 2026, pp 2929-2961 from Springer

Abstract: Abstract This book chapter gives a selective review of physical implementations and applications of superoscillations and associated phenomena. We introduce the field by reviewing simple examples of superoscillations and showing how their existence naturally follows from the real part of the quantum mechanical weak value, which the parallel phenomena of supergrowth naturally follows from the imaginary part. Focusing on electromagnetic applications, we review the topics of superoscillation and supergrowth in speckle, creating superoscillating hot spots with patterned filters, superspectroscopic discrimination of two molecules, noise mitigation, and the engineering of superbehavior in point spread functions for the purpose of optical superresolution. We also cover a variety of different methods for creating superoscillatory and supergrowing functions, reviewing both mathematical and physical ways to create this class of functions, and beyond. Promising directions for future research, including superoscillations in other wave phenomena, superradar, and generalized superphenomena in quantum physics, are outlined.

Keywords: Superoscillation; Bandlimited function; Supergrowth; Bandlimited approximation theory; Optical superresolution; Imaging; Speckle; Spatial light modulator; Hologram (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/978-3-032-16356-1_101

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