Role of semiclassical description in the quantumlike theory of light rays

An alternative procedure to the one by Gloge and Marcuse [J. Opt. Sec. Am. 59, 1629 (1969)] for performing the transition from geometrical optics to w ave optics in the paraxial approximation is presented. This is done by empl oying a recent ''deformation" method used to give: a quantumlike phase-spac e description of charged-particle-beam transport in the semiclassical appro ximation. By taking into account the uncertainty relation (diffraction limi t) that holds between the transverse-beam-spot size and the rms of the ligh t-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, (h) over ba r and the time are replaced by the inverse of the wave number, X, and the p ropagation coordinate, respectively. In this framework, the corresponding W igner-like picture is given and the quantumlike corrections for an arbitrar y refractive index are considered. In particular, it is shown that the para xial-radiation-beam transport can also be described in terms of a fluid mot ion equation, where the pressure term is replaced by a quantumlike potentia l in the semiclassical approximation that accounts for the diffraction of t he beam. Finally, a comparison of this fluid model with Madelung's fluid mo del is made, and the classical-like picture given by the tomographic approa ch to radiation beams is advanced as a future perspective. [S1063-651X(99)1 8110-8].