The Fresnel-Weyl complementary transformation

摘要

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.