Astigmatic-Invariant Structured Singular Beams
We investigate the transformation of structured Laguerre–Gaussian (sLG) beams after passing through a cylindrical lens. The resulting beam, ab astigmatic structured Laguerre–Gaussian (asLG) beam, depends on quantum numbers <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-11-01
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| Series: | Photonics |
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| Online Access: | https://www.mdpi.com/2304-6732/9/11/842 |
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| author | Alexander Volyar Eugeny Abramochkin Yana Akimova Mikhail Bretsko |
| author_facet | Alexander Volyar Eugeny Abramochkin Yana Akimova Mikhail Bretsko |
| author_sort | Alexander Volyar |
| collection | DOAJ |
| description | We investigate the transformation of structured Laguerre–Gaussian (sLG) beams after passing through a cylindrical lens. The resulting beam, ab astigmatic structured Laguerre–Gaussian (asLG) beam, depends on quantum numbers <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mo>ℓ</mo><mo>)</mo></mrow></semantics></math></inline-formula> and three parameters. Two of them are control parameters of the initial sLG beam, the amplitude <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϵ</mi></semantics></math></inline-formula> and phase <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>θ</mi></semantics></math></inline-formula>. The third one is the ratio of the Rayleigh length <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>z</mi><mn>0</mn></msub></semantics></math></inline-formula> and the focal length <i>f</i> of the cylindrical lens. It was theoretically revealed and experimentally confirmed that the asLG beam keeps the intensity shape of the initial sLG beam when the parameters satisfy simple conditions: <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϵ</mi></semantics></math></inline-formula> is unity and the tangent of the phase parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>θ</mi><mo>/</mo><mn>2</mn></mrow></semantics></math></inline-formula> is equal to the above ratio. We also found sharp bursts and dips of the orbital angular momentum (OAM) in the asLG beams in the vicinity of the point where the OAM turns to zero. The heights and depths of these bursts and dips significantly exceed the OAM maximum and minimum values of the initial sLG beam and are controlled by the radial number <i>n</i>. |
| first_indexed | 2024-03-09T18:43:58Z |
| format | Article |
| id | doaj.art-5374994c0b4a4a0f84cfb32a0a8dcedf |
| institution | Directory Open Access Journal |
| issn | 2304-6732 |
| language | English |
| last_indexed | 2024-03-09T18:43:58Z |
| publishDate | 2022-11-01 |
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| series | Photonics |
| spelling | doaj.art-5374994c0b4a4a0f84cfb32a0a8dcedf2023-11-24T06:23:13ZengMDPI AGPhotonics2304-67322022-11-0191184210.3390/photonics9110842Astigmatic-Invariant Structured Singular BeamsAlexander Volyar0Eugeny Abramochkin1Yana Akimova2Mikhail Bretsko3V.I. Vernadsky Crimean Federal University, Vernadsky Prospect 4, 295007 Simferopol, RussiaLebedev Physical Institute, 443011 Samara, RussiaV.I. Vernadsky Crimean Federal University, Vernadsky Prospect 4, 295007 Simferopol, RussiaV.I. Vernadsky Crimean Federal University, Vernadsky Prospect 4, 295007 Simferopol, RussiaWe investigate the transformation of structured Laguerre–Gaussian (sLG) beams after passing through a cylindrical lens. The resulting beam, ab astigmatic structured Laguerre–Gaussian (asLG) beam, depends on quantum numbers <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mo>ℓ</mo><mo>)</mo></mrow></semantics></math></inline-formula> and three parameters. Two of them are control parameters of the initial sLG beam, the amplitude <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϵ</mi></semantics></math></inline-formula> and phase <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>θ</mi></semantics></math></inline-formula>. The third one is the ratio of the Rayleigh length <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>z</mi><mn>0</mn></msub></semantics></math></inline-formula> and the focal length <i>f</i> of the cylindrical lens. It was theoretically revealed and experimentally confirmed that the asLG beam keeps the intensity shape of the initial sLG beam when the parameters satisfy simple conditions: <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϵ</mi></semantics></math></inline-formula> is unity and the tangent of the phase parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>θ</mi><mo>/</mo><mn>2</mn></mrow></semantics></math></inline-formula> is equal to the above ratio. We also found sharp bursts and dips of the orbital angular momentum (OAM) in the asLG beams in the vicinity of the point where the OAM turns to zero. The heights and depths of these bursts and dips significantly exceed the OAM maximum and minimum values of the initial sLG beam and are controlled by the radial number <i>n</i>.https://www.mdpi.com/2304-6732/9/11/842vortex beamsstructured lightorbital angular momentumastigmatic-invariant beams |
| spellingShingle | Alexander Volyar Eugeny Abramochkin Yana Akimova Mikhail Bretsko Astigmatic-Invariant Structured Singular Beams Photonics vortex beams structured light orbital angular momentum astigmatic-invariant beams |
| title | Astigmatic-Invariant Structured Singular Beams |
| title_full | Astigmatic-Invariant Structured Singular Beams |
| title_fullStr | Astigmatic-Invariant Structured Singular Beams |
| title_full_unstemmed | Astigmatic-Invariant Structured Singular Beams |
| title_short | Astigmatic-Invariant Structured Singular Beams |
| title_sort | astigmatic invariant structured singular beams |
| topic | vortex beams structured light orbital angular momentum astigmatic-invariant beams |
| url | https://www.mdpi.com/2304-6732/9/11/842 |
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