Topological charge of optical vortices in the far field with an initial fractional charge: optical "dipoles"
In this work, using the Rayleigh-Sommerfeld integral and the Berry formula, the topological charge (TC) of a Gaussian optical vortex with an initial fractional TC is calculated. It is shown that for different fractional parts of the TС, the beam contains a different number of screw dislocations, whi...
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| Format: | Article |
| Language: | English |
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Samara National Research University
2022-04-01
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| Series: | Компьютерная оптика |
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| Online Access: | https://computeroptics.ru/eng/KO/Annot/KO46-2/460203e.html |
| _version_ | 1797826179426680832 |
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| author | A.G. Nalimov V.V. Kotlyar |
| author_facet | A.G. Nalimov V.V. Kotlyar |
| author_sort | A.G. Nalimov |
| collection | DOAJ |
| description | In this work, using the Rayleigh-Sommerfeld integral and the Berry formula, the topological charge (TC) of a Gaussian optical vortex with an initial fractional TC is calculated. It is shown that for different fractional parts of the TС, the beam contains a different number of screw dislocations, which determine the TС of the entire beam. With a small fractional part of the TС, the beam consists of the main optical vortex centered on the optical axis with the TС equal to the nearest integer (let be n), and two edge dislocations located on the vertical axis (above and below the center). With an increase in the fractional part of the initial TC, a "dipole" is formed from the upper edge dislocation, consisting of two vortices with TC+1 and –1. With a further increase in the fractional part, the additional vortex with TC+1 is displaced to the center of the beam, and the vortex with TC–1 is displaced to the periphery. With a further increase in the fractional part of the TC, another "dipole" is formed from the lower edge dislocation, in which, on the contrary, the vortex with TC–1 is displaced to the optical axis (to the center of the beam), and the vortex with TC+1 is displaced to the beam periphery. When the fractional part of the TC becomes equal to 1/2, the "lower" vortex with TC–1, which was displaced to the center of the beam, begins to shift to the periphery, and the "upper" vortex with TC+1 moves closer and closer to the center of the beam and merges with the main vortex when the fractional part approaches 1. Such dynamics of additional vortices with upper TC+1 and lower TC–1 determine the whole TC the beam have (n or n+1) for different values of the fractional part from the segment [n, n+1]. |
| first_indexed | 2024-03-13T11:03:55Z |
| format | Article |
| id | doaj.art-e5bd1bae1bd449a786c901b13decffe9 |
| institution | Directory Open Access Journal |
| issn | 0134-2452 2412-6179 |
| language | English |
| last_indexed | 2024-03-13T11:03:55Z |
| publishDate | 2022-04-01 |
| publisher | Samara National Research University |
| record_format | Article |
| series | Компьютерная оптика |
| spelling | doaj.art-e5bd1bae1bd449a786c901b13decffe92023-05-16T12:35:05ZengSamara National Research UniversityКомпьютерная оптика0134-24522412-61792022-04-0146218919510.18287/2412-6179-CO-1073Topological charge of optical vortices in the far field with an initial fractional charge: optical "dipoles"A.G. Nalimov0V.V. Kotlyar1IPSI RAS – Branch of the FSRC "Crystallography and Photonics" RAS; Samara National Research UniversityIPSI RAS – Branch of the FSRC "Crystallography and Photonics" RAS; Samara National Research UniversityIn this work, using the Rayleigh-Sommerfeld integral and the Berry formula, the topological charge (TC) of a Gaussian optical vortex with an initial fractional TC is calculated. It is shown that for different fractional parts of the TС, the beam contains a different number of screw dislocations, which determine the TС of the entire beam. With a small fractional part of the TС, the beam consists of the main optical vortex centered on the optical axis with the TС equal to the nearest integer (let be n), and two edge dislocations located on the vertical axis (above and below the center). With an increase in the fractional part of the initial TC, a "dipole" is formed from the upper edge dislocation, consisting of two vortices with TC+1 and –1. With a further increase in the fractional part, the additional vortex with TC+1 is displaced to the center of the beam, and the vortex with TC–1 is displaced to the periphery. With a further increase in the fractional part of the TC, another "dipole" is formed from the lower edge dislocation, in which, on the contrary, the vortex with TC–1 is displaced to the optical axis (to the center of the beam), and the vortex with TC+1 is displaced to the beam periphery. When the fractional part of the TC becomes equal to 1/2, the "lower" vortex with TC–1, which was displaced to the center of the beam, begins to shift to the periphery, and the "upper" vortex with TC+1 moves closer and closer to the center of the beam and merges with the main vortex when the fractional part approaches 1. Such dynamics of additional vortices with upper TC+1 and lower TC–1 determine the whole TC the beam have (n or n+1) for different values of the fractional part from the segment [n, n+1].https://computeroptics.ru/eng/KO/Annot/KO46-2/460203e.htmlvector light beamfractional topological chargeoptical vortexdipole from two vortices |
| spellingShingle | A.G. Nalimov V.V. Kotlyar Topological charge of optical vortices in the far field with an initial fractional charge: optical "dipoles" Компьютерная оптика vector light beam fractional topological charge optical vortex dipole from two vortices |
| title | Topological charge of optical vortices in the far field with an initial fractional charge: optical "dipoles" |
| title_full | Topological charge of optical vortices in the far field with an initial fractional charge: optical "dipoles" |
| title_fullStr | Topological charge of optical vortices in the far field with an initial fractional charge: optical "dipoles" |
| title_full_unstemmed | Topological charge of optical vortices in the far field with an initial fractional charge: optical "dipoles" |
| title_short | Topological charge of optical vortices in the far field with an initial fractional charge: optical "dipoles" |
| title_sort | topological charge of optical vortices in the far field with an initial fractional charge optical dipoles |
| topic | vector light beam fractional topological charge optical vortex dipole from two vortices |
| url | https://computeroptics.ru/eng/KO/Annot/KO46-2/460203e.html |
| work_keys_str_mv | AT agnalimov topologicalchargeofopticalvorticesinthefarfieldwithaninitialfractionalchargeopticaldipoles AT vvkotlyar topologicalchargeofopticalvorticesinthefarfieldwithaninitialfractionalchargeopticaldipoles |