Superoscillations and Physical Applications

TL;DR

This chapter reviews physical implementations and applications of superoscillations, highlighting their theoretical basis, methods of creation, and diverse applications in optics and quantum physics.

Contribution

It provides a comprehensive overview of superoscillation phenomena, connecting quantum weak values to practical electromagnetic applications and exploring new directions for future research.

Findings

Superoscillations can be generated using various mathematical and physical methods.

Applications include optical superresolution and molecule discrimination.

Future prospects include super radar and generalized super-phenomena.

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 super behavior 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, super radar, and generalized super-phenomena in quantum physics, are outlined.