Comparison between the Propagation Properties of Bessel–Gauss and Generalized Laguerre–Gauss Beams
The connections between Laguerre–Gauss and Bessel–Gauss beams, and between Hermite–Gauss and cosine-Gauss beams are investigated. We review different asymptotic expressions for generalized Laguerre and Hermite polynomials of large radial/transverse order. The amplitude variations of generalized Lagu...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-09-01
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| Series: | Photonics |
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| Online Access: | https://www.mdpi.com/2304-6732/10/9/1011 |
| _version_ | 1797577870189527040 |
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| author | Colin J. R. Sheppard Miguel A. Porras |
| author_facet | Colin J. R. Sheppard Miguel A. Porras |
| author_sort | Colin J. R. Sheppard |
| collection | DOAJ |
| description | The connections between Laguerre–Gauss and Bessel–Gauss beams, and between Hermite–Gauss and cosine-Gauss beams are investigated. We review different asymptotic expressions for generalized Laguerre and Hermite polynomials of large radial/transverse order. The amplitude variations of generalized Laguerre–Gauss beams, including standard and elegant Laguerre–Gauss beams as special cases, are compared with Bessel–Gauss beams. Bessel–Gauss beams can be well-approximated by elegant Laguerre–Gauss beams. For non-integral values of the Laguerre function radial order, a generalized Laguerre–Gauss beam with integer order matches the width of the central lobe well, even for low radial orders. Previous approximations are found to be inaccurate for large azimuthal mode number (topolgical charge), and an improved approximation for this case is also introduced. |
| first_indexed | 2024-03-10T22:14:05Z |
| format | Article |
| id | doaj.art-3230355c7ca44c5ba38fc42edab5a8d9 |
| institution | Directory Open Access Journal |
| issn | 2304-6732 |
| language | English |
| last_indexed | 2024-03-10T22:14:05Z |
| publishDate | 2023-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Photonics |
| spelling | doaj.art-3230355c7ca44c5ba38fc42edab5a8d92023-11-19T12:29:49ZengMDPI AGPhotonics2304-67322023-09-01109101110.3390/photonics10091011Comparison between the Propagation Properties of Bessel–Gauss and Generalized Laguerre–Gauss BeamsColin J. R. Sheppard0Miguel A. Porras1Molecular Horizons, School of Chemistry and Molecular Biology, University of Wollongong, Wollongong, NSW 2522, AustraliaComplex Systems Group, ETSIME, Universidad Politécnica de Madrid, Ríos Rosas 21, 28003 Madrid, SpainThe connections between Laguerre–Gauss and Bessel–Gauss beams, and between Hermite–Gauss and cosine-Gauss beams are investigated. We review different asymptotic expressions for generalized Laguerre and Hermite polynomials of large radial/transverse order. The amplitude variations of generalized Laguerre–Gauss beams, including standard and elegant Laguerre–Gauss beams as special cases, are compared with Bessel–Gauss beams. Bessel–Gauss beams can be well-approximated by elegant Laguerre–Gauss beams. For non-integral values of the Laguerre function radial order, a generalized Laguerre–Gauss beam with integer order matches the width of the central lobe well, even for low radial orders. Previous approximations are found to be inaccurate for large azimuthal mode number (topolgical charge), and an improved approximation for this case is also introduced.https://www.mdpi.com/2304-6732/10/9/1011beam propagationBessel–Gauss beamsLaguerre–Gauss beamscosine-Gauss beamsHermite–Gauss beamsvortex beams |
| spellingShingle | Colin J. R. Sheppard Miguel A. Porras Comparison between the Propagation Properties of Bessel–Gauss and Generalized Laguerre–Gauss Beams Photonics beam propagation Bessel–Gauss beams Laguerre–Gauss beams cosine-Gauss beams Hermite–Gauss beams vortex beams |
| title | Comparison between the Propagation Properties of Bessel–Gauss and Generalized Laguerre–Gauss Beams |
| title_full | Comparison between the Propagation Properties of Bessel–Gauss and Generalized Laguerre–Gauss Beams |
| title_fullStr | Comparison between the Propagation Properties of Bessel–Gauss and Generalized Laguerre–Gauss Beams |
| title_full_unstemmed | Comparison between the Propagation Properties of Bessel–Gauss and Generalized Laguerre–Gauss Beams |
| title_short | Comparison between the Propagation Properties of Bessel–Gauss and Generalized Laguerre–Gauss Beams |
| title_sort | comparison between the propagation properties of bessel gauss and generalized laguerre gauss beams |
| topic | beam propagation Bessel–Gauss beams Laguerre–Gauss beams cosine-Gauss beams Hermite–Gauss beams vortex beams |
| url | https://www.mdpi.com/2304-6732/10/9/1011 |
| work_keys_str_mv | AT colinjrsheppard comparisonbetweenthepropagationpropertiesofbesselgaussandgeneralizedlaguerregaussbeams AT miguelaporras comparisonbetweenthepropagationpropertiesofbesselgaussandgeneralizedlaguerregaussbeams |