New relation between input and output fields based on Collins diffraction formula and the Wigner function in entangled state representation

Abstract

Based on the correspondence between the Collins diffraction formula (optical Fresnel transform) and the transform matrix element of a three-parameter two-mode squeezing operator in the entangled state representation 1 we further explore the relationship between output field intensity determined by the Collins formula and the input field's probability distribution along an infinitely thin phase space strip, both in the spatial domain and the frequency domain. The entangled Wigner function is introduced for recapitulating the result.

Keywords:

• Collins diffraction formula
• Wigner function
• entangled state representation

Acknowledgements

Work supported by the National Natural Science Foundation of China (Grant No. 10874174) and the President Foundation of the Chinese Academy of Science, and Research Foundation of the Education Department of Jiangxi Province.