Adaption of Collins formula to fractional Fourier transform studied in the entangled state representation of quantum optics

摘要

Adaption of Collins diffraction formula to the fractional Fourier transform in complex form (FFT-C) is demonstrated in entangled state vertical bar eta > representation of quantum optics. The additivity property of FFT-C corresponding to Collins formula has been proved by using group multiplication of the Fresnel operator and the quantum mechanical version of the Collins formula.