Spin Hall Effect of Two-Index Paraxial Vector Propagation-Invariant Beams
We investigate a simple paraxial vector beam, which is a coaxial superposition of two single-ringed Laguerre–Gaussian (LG) beams, linearly polarized along the horizontal axis, with topological charges (TC) <i>n</i> and −<i>n</i>, and of two LG beams, linearly polarized along...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-11-01
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| Series: | Photonics |
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| Online Access: | https://www.mdpi.com/2304-6732/10/11/1288 |
| _version_ | 1797458003467698176 |
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| author | Victor V. Kotlyar Alexey A. Kovalev |
| author_facet | Victor V. Kotlyar Alexey A. Kovalev |
| author_sort | Victor V. Kotlyar |
| collection | DOAJ |
| description | We investigate a simple paraxial vector beam, which is a coaxial superposition of two single-ringed Laguerre–Gaussian (LG) beams, linearly polarized along the horizontal axis, with topological charges (TC) <i>n</i> and −<i>n</i>, and of two LG beams, linearly polarized along the vertical axis, with the TCs <i>m</i> and −<i>m</i>. In the initial plane, such a vector beam has zero spin angular momentum (SAM). Upon propagation in free space, such a propagation-invariant beam has still zero SAM at several distances from the waist plane (initial plane). However, we show that at all other distances, the SAM becomes nonzero. The intensity distribution in the cross-section of such a beam has 2<i>m</i> (if <i>m</i> > <i>n</i>) lobes, the maxima of which reside on a circle of a certain radius. The SAM distribution has also several lobes, from 2<i>m</i> till 2(<i>m</i> + <i>n</i>), the centers of which reside on a circle with a radius smaller than that of the maximal-intensity circle. The SAM sign alternates differently: one lobe has a positive SAM, while two neighbor lobes on the circle have a negative SAM, or two neighbor pairs of lobes can have a positive and negative SAM. When passing through a plane with zero SAM, positive and negative SAM lobes are swapped. The maximal SAM value is achieved at a distance smaller than or equal to the Rayleigh distance. |
| first_indexed | 2024-03-09T16:31:55Z |
| format | Article |
| id | doaj.art-f191fc14fcd24f72b181b2fabbff8e38 |
| institution | Directory Open Access Journal |
| issn | 2304-6732 |
| language | English |
| last_indexed | 2024-03-09T16:31:55Z |
| publishDate | 2023-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Photonics |
| spelling | doaj.art-f191fc14fcd24f72b181b2fabbff8e382023-11-24T15:01:45ZengMDPI AGPhotonics2304-67322023-11-011011128810.3390/photonics10111288Spin Hall Effect of Two-Index Paraxial Vector Propagation-Invariant BeamsVictor V. Kotlyar0Alexey A. Kovalev1Image Processing Systems Institute of the RAS—Branch of FSRC “Crystallography & Photonics” of the RAS, 151 Molodogvardeyskaya St., 443001 Samara, RussiaImage Processing Systems Institute of the RAS—Branch of FSRC “Crystallography & Photonics” of the RAS, 151 Molodogvardeyskaya St., 443001 Samara, RussiaWe investigate a simple paraxial vector beam, which is a coaxial superposition of two single-ringed Laguerre–Gaussian (LG) beams, linearly polarized along the horizontal axis, with topological charges (TC) <i>n</i> and −<i>n</i>, and of two LG beams, linearly polarized along the vertical axis, with the TCs <i>m</i> and −<i>m</i>. In the initial plane, such a vector beam has zero spin angular momentum (SAM). Upon propagation in free space, such a propagation-invariant beam has still zero SAM at several distances from the waist plane (initial plane). However, we show that at all other distances, the SAM becomes nonzero. The intensity distribution in the cross-section of such a beam has 2<i>m</i> (if <i>m</i> > <i>n</i>) lobes, the maxima of which reside on a circle of a certain radius. The SAM distribution has also several lobes, from 2<i>m</i> till 2(<i>m</i> + <i>n</i>), the centers of which reside on a circle with a radius smaller than that of the maximal-intensity circle. The SAM sign alternates differently: one lobe has a positive SAM, while two neighbor lobes on the circle have a negative SAM, or two neighbor pairs of lobes can have a positive and negative SAM. When passing through a plane with zero SAM, positive and negative SAM lobes are swapped. The maximal SAM value is achieved at a distance smaller than or equal to the Rayleigh distance.https://www.mdpi.com/2304-6732/10/11/1288spin Hall effectpropagation-invariant beamLaguerre–Gaussian beamvector beam |
| spellingShingle | Victor V. Kotlyar Alexey A. Kovalev Spin Hall Effect of Two-Index Paraxial Vector Propagation-Invariant Beams Photonics spin Hall effect propagation-invariant beam Laguerre–Gaussian beam vector beam |
| title | Spin Hall Effect of Two-Index Paraxial Vector Propagation-Invariant Beams |
| title_full | Spin Hall Effect of Two-Index Paraxial Vector Propagation-Invariant Beams |
| title_fullStr | Spin Hall Effect of Two-Index Paraxial Vector Propagation-Invariant Beams |
| title_full_unstemmed | Spin Hall Effect of Two-Index Paraxial Vector Propagation-Invariant Beams |
| title_short | Spin Hall Effect of Two-Index Paraxial Vector Propagation-Invariant Beams |
| title_sort | spin hall effect of two index paraxial vector propagation invariant beams |
| topic | spin Hall effect propagation-invariant beam Laguerre–Gaussian beam vector beam |
| url | https://www.mdpi.com/2304-6732/10/11/1288 |
| work_keys_str_mv | AT victorvkotlyar spinhalleffectoftwoindexparaxialvectorpropagationinvariantbeams AT alexeyakovalev spinhalleffectoftwoindexparaxialvectorpropagationinvariantbeams |