Quantum Mechanical Version for Bessel Beam＇s Propagation in ABCD Optical System

Daniela Mugnai

Fan Hong-Yi, Nian-Quan Jiang

By introducing the entangled state representation and the two-mode Fresnel operator we provide quantum mechanical version for Bessel beam's classical propagation in ABCD optical system. This provides the opportunity of studying various classical Fresnel transformations in the context of quantum optics.

Marco Ornigotti, Andrea Aiello

The ABCD matrix formalism describing paraxial propagation of optical beams across linear systems is generalized to arbitrary beam trajectories. As a by-product of this study, a one-to-one correspondence between the extended ABCD matrix formalism presented here and the quantum mechanical translation operator is established.

Nobuyuki Imoto, John Jeffers, R. Loudon

Izo I. Abram

Akihiro Ogura

We develop the mathematical properties of the ABCD -transformation from the classical and quantum mechanical points of view. First, we list the four types of generating function which generate the ABCD -transformation in classical mechanics. Second, we introduce the unitary operator of the ABCD -transformation. Next, we calculate the normal ordering of this unitary operator and derive the kernels in coordinate-momentum phase space. The kernels are comprised of the generating functions, which generate the ABCD -transformation in classical mechanics. This reveals a new correspondence between classical and quantum mechanics. As an application of these kernels, we show the propagation of coherent and Gaussian beams in the context of quantum optics which corresponds to the ABCD -transformation in matrix optics.