Bohm approach to the Gouy phase shift
Optics
2022-06-20 v1
Abstract
By adapting the Madelung-Bohm formalism to paraxial wave propagation we show, by using Ermakov-Lewis techniques, that the Gouy phase is related to the form of the phase chosen in order to produce a Gaussian function as a propagated field. For this, we introduce a quantum mechanical invariant, that it is explicitly time dependent despite the fact that the Hamiltonian is itself time-independent. We finally show that the effective Bohm {\it index of refraction} generates a GRIN medium that produces the focusing needed for the Gouy phase.
Cite
@article{arxiv.2109.12373,
title = {Bohm approach to the Gouy phase shift},
author = {Héctor M. Moya-Cessa and Sergio A. Hojman and Felipe A. Asenjo and Francisco Soto-Eguibar},
journal= {arXiv preprint arXiv:2109.12373},
year = {2022}
}