Abstract
We propose a new two-mode squeezed coherent state representation | z 1, z 2〉 g which is characteristic of the correlation between the squeezing and the displacement. Based on it and using the technique of integration within an ordered product of operators we obtain a generalized two-mode Fresnel operator (GTFO), which is an image of the mapping from ( z 1, z 2) to ( s z 1 + r z 2 * , r z 1 * + s z 2 ) in | z 1, z 2〉 g representation. The matrix element of GTFO in the coordinate representation leads to a generalized two-dimensional Collins formula (Huygens–Fresnel integration transformation describing optical diffraction) in entangled form.
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