Abstract
The close relationships that exist between vortex trajectories and their associated stationary point trajectories are studied for the phase and the intensity of optical beams. It is found that trajectories of these two different types of critical points join together at a junction to form what we call colloquially a bundle. This bundle has a definite topology and a small number of possible geometries. These geometries are illustrated using simple analytical models, and are shown to be present in realistic Gaussian laser beams using numerical simulations. The effects of different foliations of the beam are considered, and it is shown that there generally exists a broad range of foliations within which changes in foliation preserve the geometry of a bundle and simply slide its junction along the parent vortex trajectory.
Original language | English |
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Pages (from-to) | 71-90 |
Number of pages | 20 |
Journal | Optics Communications |
Volume | 187 |
Issue number | 1-3 |
DOIs | |
State | Published - 1 Jan 2001 |
Bibliographical note
Funding Information:We are indebted to Prof. Sir Michael Berry for a copy of (the sometimes difficult to obtain) Ref. [18] in which oriented trajectories were first introduced, as well as for a preprint of the paper by Berry and Dennis [27] that contains many useful results germane to the present study. D.A.K. acknowledges the support of the Israel Science Foundation.
Funding
We are indebted to Prof. Sir Michael Berry for a copy of (the sometimes difficult to obtain) Ref. [18] in which oriented trajectories were first introduced, as well as for a preprint of the paper by Berry and Dennis [27] that contains many useful results germane to the present study. D.A.K. acknowledges the support of the Israel Science Foundation.
Funders | Funder number |
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Israel Science Foundation |