title: Symplectic-dilation mixed wavelet transform and its correspondence in quantum optics.
abstract: The symplectic wavelet transform, which is related to the quantum optical Fresnel transform, is developed to the symplectic-dilation mixed wavelet transform (SDWT). The SDWT involves both a real-variable dilation-transform and a complex-variable symplectic transform and possesses well-behaved properties such as the Parseval theorem and the inversion formula. The entangled-coherent state representation not only underlies the SDWT but also helps to derive the corresponding quantum transform operator whose counterpart in classical optics is the lens-Fresnel mixed transform.
authors.affiliation: Department of Material Science and Engineering, University of Science and Technology of China, Hefei, Anhui, China.
authors.forename: Hong-Yi
authors.initials: HY
authors.lastname: Fan
authors.forename: Shu-Guang
authors.initials: SG
authors.lastname: Liu
authors.forename: Li-Yun
authors.initials: LY
authors.lastname: Hu