a College of Physics & Material Science, Anhui University, Hefei 230039, China;
b Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China
Abstract Based on the newly developed coherent-entangled state representation, we propose the so-called Fresnel-Weyl complementary transformation operator. The new operator plays the roles of both Fresnel transformation (for (a1-a2)√2 and the Weyl transformation (for (a1+a2)√2. Physically, (a1-a2)√2 and (a1+a2)√2 could be a symmetric beamsplitter's two output fields for the incoming fields a1 and a2. We show that the two transformations are concisely expressed in the coherent-entangled state representation as a projective operator in the integration form.
Fund: Project supported by the Doctoral Scientific Research Startup Fund of Anhui University, China (Grant No. 33190059), the Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20113401120004), and the Open Funds from National Laboratory for Infrared Physics, Chinese Academy of Sciences (Grant No. 201117).
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