Ince-Gaussian laser beams as superposition of Hermite-Gaussian or Laguerre-Gaussian beams
We obtain explicit analytic expressions for the Ince-Gaussian (IG) beams for several first indices p = 3, 4, 5, 6. Earlier, explicit expressions have been derived for amplitudes of the IG beams with p = 0, 1, 2 and without regard for the ellipticity parameter. Here, we give expressions for the ampli...
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Samara National Research University
2024-08-01
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| Series: | Компьютерная оптика |
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| Online Access: | https://www.computeroptics.ru/eng/KO/Annot/KO48-4/480404e.html |
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| author | E.G. Abramochkin V.V. Kotlyar A.A. Kovalev |
| author_facet | E.G. Abramochkin V.V. Kotlyar A.A. Kovalev |
| author_sort | E.G. Abramochkin |
| collection | DOAJ |
| description | We obtain explicit analytic expressions for the Ince-Gaussian (IG) beams for several first indices p = 3, 4, 5, 6. Earlier, explicit expressions have been derived for amplitudes of the IG beams with p = 0, 1, 2 and without regard for the ellipticity parameter. Here, we give expressions for the amplitudes of 24 IG beams written as superpositions of the Laguerre-Gaussian (LG) or Hermite-Gaussian (HG) beams, with the superposition coefficients explicitly depending on the ellipticity parameter. Simultaneously expressing the IG modes both via the LG and HG modes allows easily obtaining the IG modes in the extreme cases when the ellipticity parameter is zero or infinite. Explicit dependence of the obtained expressions for the IG modes on the ellipticity allows the intensity pattern at the beam cross-section to be varied by continuously varying the parameter value. For the first time, intensity distributions are obtained for the IG beams with negative ellipticity parameter. |
| format | Article |
| id | doaj-art-0736ed0a303d4f5aba29d170111a3834 |
| institution | Kabale University |
| issn | 0134-2452 2412-6179 |
| language | English |
| publishDate | 2024-08-01 |
| publisher | Samara National Research University |
| record_format | Article |
| series | Компьютерная оптика |
| spelling | doaj-art-0736ed0a303d4f5aba29d170111a38342025-02-08T16:02:09ZengSamara National Research UniversityКомпьютерная оптика0134-24522412-61792024-08-0148450151010.18287/2412-6179-CO-1466Ince-Gaussian laser beams as superposition of Hermite-Gaussian or Laguerre-Gaussian beamsE.G. Abramochkin0V.V. Kotlyar1A.A. Kovalev2Lebedev Physical Institute; Image Processing Systems Institute, NRC "Kurchatov Institute"Image Processing Systems Institute, NRC "Kurchatov Institute"; Samara National Research UniversityImage Processing Systems Institute, NRC "Kurchatov Institute"; Samara National Research UniversityWe obtain explicit analytic expressions for the Ince-Gaussian (IG) beams for several first indices p = 3, 4, 5, 6. Earlier, explicit expressions have been derived for amplitudes of the IG beams with p = 0, 1, 2 and without regard for the ellipticity parameter. Here, we give expressions for the amplitudes of 24 IG beams written as superpositions of the Laguerre-Gaussian (LG) or Hermite-Gaussian (HG) beams, with the superposition coefficients explicitly depending on the ellipticity parameter. Simultaneously expressing the IG modes both via the LG and HG modes allows easily obtaining the IG modes in the extreme cases when the ellipticity parameter is zero or infinite. Explicit dependence of the obtained expressions for the IG modes on the ellipticity allows the intensity pattern at the beam cross-section to be varied by continuously varying the parameter value. For the first time, intensity distributions are obtained for the IG beams with negative ellipticity parameter.https://www.computeroptics.ru/eng/KO/Annot/KO48-4/480404e.htmlince-gaussian beamslaguerre-gaussian beamshermite-gaussian beamselliptic beamscharacteristic equation |
| spellingShingle | E.G. Abramochkin V.V. Kotlyar A.A. Kovalev Ince-Gaussian laser beams as superposition of Hermite-Gaussian or Laguerre-Gaussian beams Компьютерная оптика ince-gaussian beams laguerre-gaussian beams hermite-gaussian beams elliptic beams characteristic equation |
| title | Ince-Gaussian laser beams as superposition of Hermite-Gaussian or Laguerre-Gaussian beams |
| title_full | Ince-Gaussian laser beams as superposition of Hermite-Gaussian or Laguerre-Gaussian beams |
| title_fullStr | Ince-Gaussian laser beams as superposition of Hermite-Gaussian or Laguerre-Gaussian beams |
| title_full_unstemmed | Ince-Gaussian laser beams as superposition of Hermite-Gaussian or Laguerre-Gaussian beams |
| title_short | Ince-Gaussian laser beams as superposition of Hermite-Gaussian or Laguerre-Gaussian beams |
| title_sort | ince gaussian laser beams as superposition of hermite gaussian or laguerre gaussian beams |
| topic | ince-gaussian beams laguerre-gaussian beams hermite-gaussian beams elliptic beams characteristic equation |
| url | https://www.computeroptics.ru/eng/KO/Annot/KO48-4/480404e.html |
| work_keys_str_mv | AT egabramochkin incegaussianlaserbeamsassuperpositionofhermitegaussianorlaguerregaussianbeams AT vvkotlyar incegaussianlaserbeamsassuperpositionofhermitegaussianorlaguerregaussianbeams AT aakovalev incegaussianlaserbeamsassuperpositionofhermitegaussianorlaguerregaussianbeams |