Bohmian-Based Approach to Gauss-Maxwell Beams
Usual Gaussian beams are particular scalar solutions to the paraxial Helmholtz equation, which neglect the vector nature of light. In order to overcome this inconvenience, Simon et al. (<i>J. Opt. Soc. Am. A</i> <b>1986</b>, <i>3</i>, 536−540) found a pa...
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MDPI AG
2020-03-01
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| Online Access: | https://www.mdpi.com/2076-3417/10/5/1808 |
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| author | Ángel S. Sanz Milena D. Davidović Mirjana Božić |
| author_facet | Ángel S. Sanz Milena D. Davidović Mirjana Božić |
| author_sort | Ángel S. Sanz |
| collection | DOAJ |
| description | Usual Gaussian beams are particular scalar solutions to the paraxial Helmholtz equation, which neglect the vector nature of light. In order to overcome this inconvenience, Simon et al. (<i>J. Opt. Soc. Am. A</i> <b>1986</b>, <i>3</i>, 536−540) found a paraxial solution to Maxwell’s equation in vacuum, which includes polarization in a natural way, though still preserving the spatial Gaussianity of the beams. In this regard, it seems that these solutions, known as Gauss-Maxwell beams, are particularly appropriate and a natural tool in optical problems dealing with Gaussian beams acted or manipulated by polarizers. In this work, inspired in the Bohmian picture of quantum mechanics, a hydrodynamic-type extension of such a formulation is provided and discussed, complementing the notion of electromagnetic field with that of (electromagnetic) flow or streamline. In this regard, the method proposed has the advantage that the rays obtained from it render a bona fide description of the spatial distribution of electromagnetic energy, since they are in compliance with the local space changes undergone by the time-averaged Poynting vector. This feature confers the approach a potential interest in the analysis and description of single-photon experiments, because of the direct connection between these rays and the average flow exhibited by swarms of identical photons (regardless of the particular motion, if any, that these entities might have), at least in the case of Gaussian input beams. In order to illustrate the approach, here it is applied to two common scenarios, namely the diffraction undergone by a single Gauss-Maxwell beam and the interference produced by a coherent superposition of two of such beams. |
| first_indexed | 2024-12-14T17:04:07Z |
| format | Article |
| id | doaj.art-86c066557e4042c4b23ea7092c0912fd |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-12-14T17:04:07Z |
| publishDate | 2020-03-01 |
| publisher | MDPI AG |
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| series | Applied Sciences |
| spelling | doaj.art-86c066557e4042c4b23ea7092c0912fd2022-12-21T22:53:46ZengMDPI AGApplied Sciences2076-34172020-03-01105180810.3390/app10051808app10051808Bohmian-Based Approach to Gauss-Maxwell BeamsÁngel S. Sanz0Milena D. Davidović1Mirjana Božić2Department of Optics, Faculty of Physical Sciences, Universidad Complutense de Madrid, Pza. Ciencias 1, Ciudad Universitaria, 28040 Madrid, SpainDepartment of Mathematics, Physics and Descriptive Geometry, Faculty of Civil Engineering, University of Belgrade, Bulevar Kralja Aleksandra 73, 11000 Belgrade, SerbiaInstitute of Physics Belgrade, University of Belgrade, Pregrevica 118, 11080 Belgrade, SerbiaUsual Gaussian beams are particular scalar solutions to the paraxial Helmholtz equation, which neglect the vector nature of light. In order to overcome this inconvenience, Simon et al. (<i>J. Opt. Soc. Am. A</i> <b>1986</b>, <i>3</i>, 536−540) found a paraxial solution to Maxwell’s equation in vacuum, which includes polarization in a natural way, though still preserving the spatial Gaussianity of the beams. In this regard, it seems that these solutions, known as Gauss-Maxwell beams, are particularly appropriate and a natural tool in optical problems dealing with Gaussian beams acted or manipulated by polarizers. In this work, inspired in the Bohmian picture of quantum mechanics, a hydrodynamic-type extension of such a formulation is provided and discussed, complementing the notion of electromagnetic field with that of (electromagnetic) flow or streamline. In this regard, the method proposed has the advantage that the rays obtained from it render a bona fide description of the spatial distribution of electromagnetic energy, since they are in compliance with the local space changes undergone by the time-averaged Poynting vector. This feature confers the approach a potential interest in the analysis and description of single-photon experiments, because of the direct connection between these rays and the average flow exhibited by swarms of identical photons (regardless of the particular motion, if any, that these entities might have), at least in the case of Gaussian input beams. In order to illustrate the approach, here it is applied to two common scenarios, namely the diffraction undergone by a single Gauss-Maxwell beam and the interference produced by a coherent superposition of two of such beams.https://www.mdpi.com/2076-3417/10/5/1808gauss-maxwell beamsoptical raybohmian mechanicsdiffractiontwo-slit interferencecoherence |
| spellingShingle | Ángel S. Sanz Milena D. Davidović Mirjana Božić Bohmian-Based Approach to Gauss-Maxwell Beams Applied Sciences gauss-maxwell beams optical ray bohmian mechanics diffraction two-slit interference coherence |
| title | Bohmian-Based Approach to Gauss-Maxwell Beams |
| title_full | Bohmian-Based Approach to Gauss-Maxwell Beams |
| title_fullStr | Bohmian-Based Approach to Gauss-Maxwell Beams |
| title_full_unstemmed | Bohmian-Based Approach to Gauss-Maxwell Beams |
| title_short | Bohmian-Based Approach to Gauss-Maxwell Beams |
| title_sort | bohmian based approach to gauss maxwell beams |
| topic | gauss-maxwell beams optical ray bohmian mechanics diffraction two-slit interference coherence |
| url | https://www.mdpi.com/2076-3417/10/5/1808 |
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