Implementation of quantum and classical discrete fractional Fourier transforms.

ABSTRACT: Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Mo

SUBMITTER: Weimann S 

PROVIDER: S-EPMC4814576 | biostudies-literature | 2016 Mar

REPOSITORIES: biostudies-literature