Collins diffraction formula studied in quantum optics.
We find that the Collins diffraction formula in cylindrical coordinates is just the transformation matrix element of a three-parameter two-mode squeezing operator in the deduced entangled state representation. This is a new tie connecting the unitary transform in quantum optics to the generalized Hankel transform in Fourier optics. The group multiplication rule of the squeezing operators maps to the Collins formula related to two successive Hankel transforms.
Fan
Hong-Yi
HY
Department of Physics, Shanghai Jiao Tong University, Shanghai, China.
Lu
Hai-Liang
HL