New methods for creating superoscillations

TL;DR

This paper introduces new computational methods for constructing high-frequency, long-duration superoscillations and non-singular Schrödinger potentials with superoscillating ground states, advancing applications in physics and engineering.

Contribution

The authors develop efficient algorithms for creating arbitrarily high-frequency superoscillations and non-singular Schrödinger potentials with superoscillating ground states, a novel approach in the field.

Findings

Able to construct superoscillations of arbitrarily high frequency

Developed methods for non-singular Schrödinger potentials with superoscillating ground states

Enhanced computational efficiency in generating superoscillations

Abstract

Superoscillating functions, i.e., functions that locally oscillate at a rate faster than their highest Fourier component, are of interest for applications from fundamental physics to engineering. Here, we develop a new method which allows one to construct superoscillations of arbitrarily high frequency and arbitrarily long duration in a computationally efficient way. We also present a method for constructing non-singular Schr\"odinger potentials whose ground state is a superoscillating wave function.