Abstract
Abstract It is now well-appreciated that a bandlimited wave can possess oscillations much more rapidly than those predicted by the bandlimit itself, in a phenomenon known as superoscillation. Such superoscillations are required to be of dramatically smaller amplitude than the signal they are embedded in, and this has initially led researchers to consider them of limited use in applications. However, this view has changed in recent years and superoscillations have been employed in a number of systems to beat the limits of conventional diffraction theory. In this review, we discuss the current state of research on superoscillations in terms of superresolved imaging and subwavelength focusing, including the use of special non-diffracting and Airy beams to carry transverse superoscillating patterns. In addition, we discuss recent analogous works on using superoscillations to break the temporal resolution limit, and also consider the recently introduced inverse of superoscillations, known as suboscillations.
Highlights
It has long been assumed that a bandlimited signal has a maximum oscillation frequency, in space or in time, naturally dictated by the largest frequency in the band
It is well-appreciated that a bandlimited wave can possess oscillations much more rapidly than those predicted by the bandlimit itself, in a phenomenon known as superoscillation
We discuss the current state of research on superoscillations in terms of superresolved imaging and subwavelength focusing, including the use of special nondiffracting and Airy beams to carry transverse superoscillating patterns
Summary
It has long been assumed that a bandlimited signal has a maximum oscillation frequency, in space or in time, naturally dictated by the largest frequency in the band. Any set of overasmpling points may coincide with the zeros of a superoscillatory function; obviously, that function would not provide any contribution to the extrapolation To overcome this issue, Landau required that the energy of the total signal be bounded – a strategy that would restrict the size of any superoscillating components of a solution. In 2006, Berry and Popescu [15] presented the first discussion of superresolution via superoscillations, in which they demonstrate that superoscillations are surprisingly robust on propagation and can carry sub-wavelength structure beyond the range of evanescent waves Spurred by this insight, multiple researchers began in earnest to investigate the possibility of using superoscillations in applications, and this is the subject of the current review.
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