Off-Axis Vortex Beam Propagation through Classical Optical System in Terms of Kummer Confluent Hypergeometric Function
The analytical solution for the propagation of the laser beam with optical vortex through the system of lenses is presented. The optical vortex is introduced into the laser beam (described as Gaussian beam) by spiral phase plate. The solution is general as it holds for the optical vortex of any inte...
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| Format: | Article |
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MDPI AG
2020-08-01
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| Series: | Photonics |
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| Online Access: | https://www.mdpi.com/2304-6732/7/3/60 |
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| author | Ireneusz Augustyniak Weronika Lamperska Jan Masajada Łukasz Płociniczak Agnieszka Popiołek-Masajada |
| author_facet | Ireneusz Augustyniak Weronika Lamperska Jan Masajada Łukasz Płociniczak Agnieszka Popiołek-Masajada |
| author_sort | Ireneusz Augustyniak |
| collection | DOAJ |
| description | The analytical solution for the propagation of the laser beam with optical vortex through the system of lenses is presented. The optical vortex is introduced into the laser beam (described as Gaussian beam) by spiral phase plate. The solution is general as it holds for the optical vortex of any integer topological charge, the off-axis position of the spiral phase plate and any number of lenses. Some intriguing conclusions are discussed. The higher order vortices are unstable and split under small phase or amplitude disturbance. Nevertheless, we have shown that off-axis higher order vortices are stable during the propagation through the set of lenses described in paraxial approximation, which is untypical behavior. The vortex trajectory registered at image plane due to spiral phase plate shift behaves like a rigid body. We have introduced a new factor which in our beam plays the same role as Gouy phase in pure Gaussian beam. |
| first_indexed | 2024-03-10T17:22:10Z |
| format | Article |
| id | doaj.art-24a4ad6042034f588811fea929bec4b2 |
| institution | Directory Open Access Journal |
| issn | 2304-6732 |
| language | English |
| last_indexed | 2024-03-10T17:22:10Z |
| publishDate | 2020-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Photonics |
| spelling | doaj.art-24a4ad6042034f588811fea929bec4b22023-11-20T10:16:52ZengMDPI AGPhotonics2304-67322020-08-01736010.3390/photonics7030060Off-Axis Vortex Beam Propagation through Classical Optical System in Terms of Kummer Confluent Hypergeometric FunctionIreneusz Augustyniak0Weronika Lamperska1Jan Masajada2Łukasz Płociniczak3Agnieszka Popiołek-Masajada4Department of Applied Mathematics, Faculty of Pure and Applied Mathematics, Wroclaw University of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, PolandDepartment of Optics and Photonics, Faculty of Fundamental Problems of Technology, Wroclaw University of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, PolandDepartment of Optics and Photonics, Faculty of Fundamental Problems of Technology, Wroclaw University of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, PolandDepartment of Applied Mathematics, Faculty of Pure and Applied Mathematics, Wroclaw University of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, PolandDepartment of Optics and Photonics, Faculty of Fundamental Problems of Technology, Wroclaw University of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, PolandThe analytical solution for the propagation of the laser beam with optical vortex through the system of lenses is presented. The optical vortex is introduced into the laser beam (described as Gaussian beam) by spiral phase plate. The solution is general as it holds for the optical vortex of any integer topological charge, the off-axis position of the spiral phase plate and any number of lenses. Some intriguing conclusions are discussed. The higher order vortices are unstable and split under small phase or amplitude disturbance. Nevertheless, we have shown that off-axis higher order vortices are stable during the propagation through the set of lenses described in paraxial approximation, which is untypical behavior. The vortex trajectory registered at image plane due to spiral phase plate shift behaves like a rigid body. We have introduced a new factor which in our beam plays the same role as Gouy phase in pure Gaussian beam.https://www.mdpi.com/2304-6732/7/3/60optical vortexangular momentumoptical microscopysingular opticshypergeometric functionKummer function |
| spellingShingle | Ireneusz Augustyniak Weronika Lamperska Jan Masajada Łukasz Płociniczak Agnieszka Popiołek-Masajada Off-Axis Vortex Beam Propagation through Classical Optical System in Terms of Kummer Confluent Hypergeometric Function Photonics optical vortex angular momentum optical microscopy singular optics hypergeometric function Kummer function |
| title | Off-Axis Vortex Beam Propagation through Classical Optical System in Terms of Kummer Confluent Hypergeometric Function |
| title_full | Off-Axis Vortex Beam Propagation through Classical Optical System in Terms of Kummer Confluent Hypergeometric Function |
| title_fullStr | Off-Axis Vortex Beam Propagation through Classical Optical System in Terms of Kummer Confluent Hypergeometric Function |
| title_full_unstemmed | Off-Axis Vortex Beam Propagation through Classical Optical System in Terms of Kummer Confluent Hypergeometric Function |
| title_short | Off-Axis Vortex Beam Propagation through Classical Optical System in Terms of Kummer Confluent Hypergeometric Function |
| title_sort | off axis vortex beam propagation through classical optical system in terms of kummer confluent hypergeometric function |
| topic | optical vortex angular momentum optical microscopy singular optics hypergeometric function Kummer function |
| url | https://www.mdpi.com/2304-6732/7/3/60 |
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