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.
© 2006 Optical Society of America
Original Manuscript: March 10, 2006
Revised Manuscript: May 25, 2006
Manuscript Accepted: May 26, 2006
Published: August 9, 2006
Hong-Yi Fan and Hai-Liang Lu, "Collins diffraction formula studied in quantum optics," Opt. Lett. 31, 2622-2624 (2006)