Spin Hall Effect in the Paraxial Light Beams with Multiple Polarization Singularities
Elements of micromachines can be driven by light, including structured light with phase and/or polarization singularities. We investigate a paraxial vectorial Gaussian beam with multiple polarization singularities residing on a circle. Such a beam is a superposition of a cylindrically polarized Lagu...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-03-01
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| Series: | Micromachines |
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| Online Access: | https://www.mdpi.com/2072-666X/14/4/777 |
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| author | Alexey A. Kovalev Victor V. Kotlyar Sergey S. Stafeev |
| author_facet | Alexey A. Kovalev Victor V. Kotlyar Sergey S. Stafeev |
| author_sort | Alexey A. Kovalev |
| collection | DOAJ |
| description | Elements of micromachines can be driven by light, including structured light with phase and/or polarization singularities. We investigate a paraxial vectorial Gaussian beam with multiple polarization singularities residing on a circle. Such a beam is a superposition of a cylindrically polarized Laguerre–Gaussian beam with a linearly polarized Gaussian beam. We demonstrate that, despite linear polarization in the initial plane, on propagation in space, alternating areas are generated with a spin angular momentum (SAM) density of opposite sign, that manifest about the spin Hall effect. We derive that in each transverse plane, maximal SAM magnitude is on a certain-radius circle. We obtain an approximate expression for the distance to the transverse plane with the maximal SAM density. Besides, we define the singularities circle radius, for which the achievable SAM density is maximal. It turns out that in this case the energies of the Laguerre–Gaussian and of the Gaussian beams are equal. We obtain an expression for the orbital angular momentum density and find that it is equal to the SAM density, multiplied by −<i>m</i>/2 with <i>m</i> being the order of the Laguerre–Gaussian beam, equal to the number of the polarization singularities. We consider an analogy with plane waves and find that the spin Hall affect arises due to the different divergence between the linearly polarized Gaussian beam and cylindrically polarized Laguerre–Gaussian beam. Application areas of the obtained results are designing micromachines with optically driven elements. |
| first_indexed | 2024-03-11T04:45:09Z |
| format | Article |
| id | doaj.art-e96f5bbae3b9449084d8313957632187 |
| institution | Directory Open Access Journal |
| issn | 2072-666X |
| language | English |
| last_indexed | 2024-03-11T04:45:09Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Micromachines |
| spelling | doaj.art-e96f5bbae3b9449084d83139576321872023-11-17T20:29:12ZengMDPI AGMicromachines2072-666X2023-03-0114477710.3390/mi14040777Spin Hall Effect in the Paraxial Light Beams with Multiple Polarization SingularitiesAlexey A. Kovalev0Victor V. Kotlyar1Sergey S. Stafeev2Image 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, RussiaImage Processing Systems Institute of the RAS—Branch of FSRC “Crystallography & Photonics” of the RAS, 151 Molodogvardeyskaya St., 443001 Samara, RussiaElements of micromachines can be driven by light, including structured light with phase and/or polarization singularities. We investigate a paraxial vectorial Gaussian beam with multiple polarization singularities residing on a circle. Such a beam is a superposition of a cylindrically polarized Laguerre–Gaussian beam with a linearly polarized Gaussian beam. We demonstrate that, despite linear polarization in the initial plane, on propagation in space, alternating areas are generated with a spin angular momentum (SAM) density of opposite sign, that manifest about the spin Hall effect. We derive that in each transverse plane, maximal SAM magnitude is on a certain-radius circle. We obtain an approximate expression for the distance to the transverse plane with the maximal SAM density. Besides, we define the singularities circle radius, for which the achievable SAM density is maximal. It turns out that in this case the energies of the Laguerre–Gaussian and of the Gaussian beams are equal. We obtain an expression for the orbital angular momentum density and find that it is equal to the SAM density, multiplied by −<i>m</i>/2 with <i>m</i> being the order of the Laguerre–Gaussian beam, equal to the number of the polarization singularities. We consider an analogy with plane waves and find that the spin Hall affect arises due to the different divergence between the linearly polarized Gaussian beam and cylindrically polarized Laguerre–Gaussian beam. Application areas of the obtained results are designing micromachines with optically driven elements.https://www.mdpi.com/2072-666X/14/4/777cylindrical vector beamradial polarizationpolarization singularityGaussian beamLaguerre–Gaussian beamspin angular momentum |
| spellingShingle | Alexey A. Kovalev Victor V. Kotlyar Sergey S. Stafeev Spin Hall Effect in the Paraxial Light Beams with Multiple Polarization Singularities Micromachines cylindrical vector beam radial polarization polarization singularity Gaussian beam Laguerre–Gaussian beam spin angular momentum |
| title | Spin Hall Effect in the Paraxial Light Beams with Multiple Polarization Singularities |
| title_full | Spin Hall Effect in the Paraxial Light Beams with Multiple Polarization Singularities |
| title_fullStr | Spin Hall Effect in the Paraxial Light Beams with Multiple Polarization Singularities |
| title_full_unstemmed | Spin Hall Effect in the Paraxial Light Beams with Multiple Polarization Singularities |
| title_short | Spin Hall Effect in the Paraxial Light Beams with Multiple Polarization Singularities |
| title_sort | spin hall effect in the paraxial light beams with multiple polarization singularities |
| topic | cylindrical vector beam radial polarization polarization singularity Gaussian beam Laguerre–Gaussian beam spin angular momentum |
| url | https://www.mdpi.com/2072-666X/14/4/777 |
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