A generalized Collins formula derived by virtue of the displacement-squeezing related squeezed coherent state representation |
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| Authors: | Xie Chuan-Mei Fan Hong-Yi Wan Shao-Long |
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| Affiliation: | Institute for Theoretical Physics and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China; Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China; College of Physics and Material Science, Anhui University, Hefei 230039, China |
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| Abstract: | Based on the displacement-squeezing related squeezedcoherent state representation ≤ftvert zrightrangle _{g} andusing the technique of integration within an ordered product ofoperators, this paper finds a generalized Fresnel operator, whosematrix element in the coordinate representation leads to ageneralized Collins formula (Huygens--Fresnel integrationtransformation describing optical diffraction). The generalizedFresnel operator isderived by a quantum mechanical mapping from z to sz-rz^{ast } in the %≤ftvert zrightrangle _{g} representation, while ≤ftvertzrightrangle _{g} in phase space is graphically denoted by anellipse. |
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| Keywords: | generalized Fresnel operator generalized Collins formula phase space IWOP technique squeezed coherent state |
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