RESUMO
Within the framework of the thermal-wave model, the quantumlike description of electron optics in terms of the propagator is given. First we briefly review the standard description in configuration space by analogy to quantum mechanics and in connection with recent investigations of charged-particle-beam transport that have used the concept of propagator. Then new insights are given by extension of the analysis of the particle-beam propagator to the phase-space context for which our system is described by the Wigner quasi-distribution function, as well as to the tomography context for which our system is described by the marginal distribution. Furthermore, the integrals of motion of a charged-particle beam and their relation to the propagator concept are discussed. Finally, the perturbation theory for a charged-particle-beam propagator is developed in the above-described two contexts and is applied to some simple optical devices.
RESUMO
An alternative procedure to the one by Gloge and Marcuse [J. Opt. Soc. Am. 59, 1629 (1969)] for performing the transition from geometrical optics to wave optics in the paraxial approximation is presented. This is done by employing a recent "deformation" method used to give a quantumlike phase-space description of charged-particle-beam transport in the semiclassical approximation. By taking into account the uncertainty relation (diffraction limit) that holds between the transverse-beam-spot size and the rms of the light-ray slopes, the classical phase-space equation for light rays is deformed into a von Neumann-like equation that governs the phase-space description of the beam transport in the semiclassical approximation. Here, Planck's constant and the time are replaced by the inverse of the wave number, not lambda, and the propagation coordinate, respectively. In this framework, the corresponding Wigner-like picture is given and the quantumlike corrections for an arbitrary refractive index are considered. In particular, it is shown that the paraxial-radiation-beam transport can also be described in terms of a fluid motion equation, where the pressure term is replaced by a quantumlike potential in the semiclassical approximation that accounts for the diffraction of the beam. Finally, a comparison of this fluid model with Madelung's fluid model is made, and the classical-like picture given by the tomographic approach to radiation beams is advanced as a future perspective.
