Gs. Agarwal et R. Simon, A SIMPLE REALIZATION OF FRACTIONAL FOURIER-TRANSFORM AND RELATION TO HARMONIC-OSCILLATOR GREEN-FUNCTION, Optics communications, 110(1-2), 1994, pp. 23-26
A simple relation between the fractional Fourier transform (FRACFT) an
d the Green's function for the harmonic oscillator is demonstrated. Th
is relation enables us to understand easily the characteristics of FRA
CFT and leads to an elementary realization of FRACFT in terms of Fresn
el diffraction.