{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,15]],"date-time":"2026-04-15T01:33:49Z","timestamp":1776216829128,"version":"3.50.1"},"reference-count":52,"publisher":"MDPI AG","issue":"18","license":[{"start":{"date-parts":[[2022,9,12]],"date-time":"2022-09-12T00:00:00Z","timestamp":1662940800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["U20B2059"],"award-info":[{"award-number":["U20B2059"]}]},{"name":"National Natural Science Foundation of China","award":["61627901"],"award-info":[{"award-number":["61627901"]}]},{"name":"National Natural Science Foundation of China","award":["61901336"],"award-info":[{"award-number":["61901336"]}]},{"name":"National Natural Science Foundation of China","award":["61905186"],"award-info":[{"award-number":["61905186"]}]},{"name":"National Natural Science Foundation of China","award":["61621005"],"award-info":[{"award-number":["61621005"]}]},{"name":"National Natural Science Foundation of China","award":["YJS2208"],"award-info":[{"award-number":["YJS2208"]}]},{"name":"National Natural Science Foundation of China","award":["QTZX22037"],"award-info":[{"award-number":["QTZX22037"]}]},{"DOI":"10.13039\/501100012659","name":"Foundation for Innovative Research Groups of the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["U20B2059"],"award-info":[{"award-number":["U20B2059"]}],"id":[{"id":"10.13039\/501100012659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012659","name":"Foundation for Innovative Research Groups of the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61627901"],"award-info":[{"award-number":["61627901"]}],"id":[{"id":"10.13039\/501100012659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012659","name":"Foundation for Innovative Research Groups of the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61901336"],"award-info":[{"award-number":["61901336"]}],"id":[{"id":"10.13039\/501100012659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012659","name":"Foundation for Innovative Research Groups of the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61905186"],"award-info":[{"award-number":["61905186"]}],"id":[{"id":"10.13039\/501100012659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012659","name":"Foundation for Innovative Research Groups of the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61621005"],"award-info":[{"award-number":["61621005"]}],"id":[{"id":"10.13039\/501100012659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012659","name":"Foundation for Innovative Research Groups of the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["YJS2208"],"award-info":[{"award-number":["YJS2208"]}],"id":[{"id":"10.13039\/501100012659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012659","name":"Foundation for Innovative Research Groups of the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["QTZX22037"],"award-info":[{"award-number":["QTZX22037"]}],"id":[{"id":"10.13039\/501100012659","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Fundamental Research Funds for the Central Universities","award":["U20B2059"],"award-info":[{"award-number":["U20B2059"]}]},{"name":"Fundamental Research Funds for the Central Universities","award":["61627901"],"award-info":[{"award-number":["61627901"]}]},{"name":"Fundamental Research Funds for the Central Universities","award":["61901336"],"award-info":[{"award-number":["61901336"]}]},{"name":"Fundamental Research Funds for the Central Universities","award":["61905186"],"award-info":[{"award-number":["61905186"]}]},{"name":"Fundamental Research Funds for the Central Universities","award":["61621005"],"award-info":[{"award-number":["61621005"]}]},{"name":"Fundamental Research Funds for the Central Universities","award":["YJS2208"],"award-info":[{"award-number":["YJS2208"]}]},{"name":"Fundamental Research Funds for the Central Universities","award":["QTZX22037"],"award-info":[{"award-number":["QTZX22037"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>In this paper, we obtain the intensity and phase distributions of the scattering and external fields of a vector Bessel\u2013Gaussian vortex beam in the far-field region after being scattered by a particle. In our analysis, we use the Generalized Lorenz\u2013Mie theory (GLMT) and the angular spectrum decomposition method (ASDM). The orbital angular momentum (OAM) spectra of the fields are analyzed by using the spiral spectrum expansion method, which is a frequently used tool for studying the propagation of vortex beams in turbulent atmospheres. Both scattered and external fields show a significant difference in spiral spectra for particles with different characteristic parameters, such as the size and complex refractive index. We also examine sampling the phase along with a circle and show that it is unable to fully express the information of the fields. This study can provide a theoretical basis for the inversion of characteristic parameters of the Bessel\u2013Gaussian vortex beam and spherical particle by OAM spectra with applications in remote sensing engineering.<\/jats:p>","DOI":"10.3390\/rs14184550","type":"journal-article","created":{"date-parts":[[2022,9,13]],"date-time":"2022-09-13T04:05:41Z","timestamp":1663041941000},"page":"4550","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Particle Scattering Induced Orbital Angular Momentum Spectrum Change of Vector Bessel\u2013Gaussian Vortex Beam"],"prefix":"10.3390","volume":"14","author":[{"given":"Chenge","family":"Shi","sequence":"first","affiliation":[{"name":"College of Physics, Xidian University, Xi\u2019an 710071, China"}]},{"given":"Mingjian","family":"Cheng","sequence":"additional","affiliation":[{"name":"College of Physics, Xidian University, Xi\u2019an 710071, China"}]},{"given":"Lixin","family":"Guo","sequence":"additional","affiliation":[{"name":"College of Physics, Xidian University, Xi\u2019an 710071, China"}]},{"given":"Martin P. J.","family":"Lavery","sequence":"additional","affiliation":[{"name":"College of Engineering, University of Glasgow, Glasgow G12 8LT, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9707-4086","authenticated-orcid":false,"given":"Ping","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Communication Engineering, Xidian University, Xi\u2019an 710071, China"}]},{"given":"Songhua","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Physics, Xidian University, Xi\u2019an 710071, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7040-8672","authenticated-orcid":false,"given":"Renxian","family":"Li","sequence":"additional","affiliation":[{"name":"College of Physics, Xidian University, Xi\u2019an 710071, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3801-1058","authenticated-orcid":false,"given":"Jiangting","family":"Li","sequence":"additional","affiliation":[{"name":"College of Physics, Xidian University, Xi\u2019an 710071, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"8185","DOI":"10.1103\/PhysRevA.45.8185","article-title":"Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes","volume":"45","author":"Allen","year":"1992","journal-title":"Phys. Rev. A"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"041308","DOI":"10.1063\/5.0013276","article-title":"Optical trapping gets structure: Structured light for advanced optical manipulation","volume":"7","author":"Otte","year":"2020","journal-title":"Appl. Rhys. Rev."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"11873","DOI":"10.1109\/JSEN.2019.2937976","article-title":"Vortex SAR imaging method based on OAM beams design","volume":"19","author":"Wang","year":"2019","journal-title":"IEEE Sens. J."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"488","DOI":"10.1038\/nphoton.2012.138","article-title":"Terabit free-space data transmission employing orbital angular momentum multiplexing","volume":"6","author":"Wang","year":"2012","journal-title":"Nat. Photonics"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"645","DOI":"10.1515\/nanoph-2021-0527","article-title":"Orbital angular momentum and beyond in free-space optical communications","volume":"11","author":"Wang","year":"2022","journal-title":"Nanophotonics"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"041312","DOI":"10.1063\/5.0054885","article-title":"Orbital angular momentum of light for communications","volume":"8","author":"Willner","year":"2021","journal-title":"Appl. Phys. Rev."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1038\/s41377-019-0140-3","article-title":"Optical orbital-angular-momentum-multiplexed data transmission under high scattering","volume":"8","author":"Gong","year":"2019","journal-title":"Light Sci. Appl."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2316","DOI":"10.1109\/LAWP.2017.2716408","article-title":"Large-scale orbital angular momentum radar pulse generation with rotational antenna","volume":"16","author":"Zhang","year":"2017","journal-title":"IEEE Antennas Wirel. Propag. Lett."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"48769","DOI":"10.1109\/ACCESS.2021.3068792","article-title":"Dual-circularly polarized topological patch antenna with pattern diversity","volume":"9","author":"Barbuto","year":"2021","journal-title":"IEEE Access"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"6918","DOI":"10.1109\/JSEN.2017.2754554","article-title":"High-resolution electromagnetic vortex imaging based on sparse bayesian learning","volume":"17","author":"Liu","year":"2017","journal-title":"IEEE Sens. J."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1168","DOI":"10.1049\/el.2016.0237","article-title":"Super-resolution orbital angular momentum based radar targets detection","volume":"52","author":"Lin","year":"2016","journal-title":"Electron. Lett."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2069","DOI":"10.1364\/OL.41.002069","article-title":"Deep transmission of Laguerre-Gaussian vortex beams through turbid scattering media","volume":"41","author":"Wang","year":"2016","journal-title":"Opt. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"649","DOI":"10.1049\/iet-rsn.2017.0502","article-title":"Orbital-angular-momentum-carrying wave scattering by the chaff clouds","volume":"12","author":"Tang","year":"2018","journal-title":"IET Radar Sonar Nav."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"873","DOI":"10.1364\/OPEX.13.000873","article-title":"Digital spiral imaging","volume":"13","author":"Torner","year":"2005","journal-title":"Opt. Express"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"16056","DOI":"10.1364\/OE.416324","article-title":"Spiral spectrum of high-order elliptic Gaussian vortex beams in a non-Kolmogorov turbulent atmosphere","volume":"29","author":"Wang","year":"2021","journal-title":"Opt. Express"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"13171","DOI":"10.1364\/OE.420193","article-title":"Experimental demonstration of OAM-based transmitter mode diversity data transmission under atmosphere turbulence","volume":"29","author":"Wang","year":"2021","journal-title":"Opt. Express"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1016\/j.optcom.2019.04.026","article-title":"Mitigation of atmospheric turbulence with random light carrying OAM","volume":"446","author":"Li","year":"2019","journal-title":"Opt. Commun."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"093012","DOI":"10.1088\/1367-2630\/ac1fca","article-title":"The orbital angular momentum of a turbulent atmosphere and its impact on propagating structured light fields","volume":"23","author":"Klug","year":"2021","journal-title":"New J. Phys."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1423","DOI":"10.1364\/JOSAA.432607","article-title":"Weak turbulence effects on different beams carrying orbital angular momentum","volume":"38","author":"Ferlic","year":"2021","journal-title":"J. Opt. Soc. Am. A"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"924","DOI":"10.1364\/OE.380405","article-title":"Experimental probing of turbulence using a continuous spectrum of asymmetric OAM beams","volume":"28","author":"Watkins","year":"2020","journal-title":"Opt. Express"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"E8","DOI":"10.1364\/AO.56.0000E8","article-title":"Study of propagation of vortex beams in aerosol optical medium","volume":"56","author":"Porfirev","year":"2017","journal-title":"Appl. Opt."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"9794","DOI":"10.1364\/OE.24.009794","article-title":"Multi-gigabit\/s underwater optical communication link using orbital angular momentum multiplexing","volume":"24","author":"Baghdady","year":"2016","journal-title":"Opt. Express"},{"key":"ref_23","first-page":"1","article-title":"Capacity of communication link with carrier of vortex localized wave in absorptive turbulent seawater","volume":"12","author":"Deng","year":"2020","journal-title":"Waves Random Complex Media"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"9053","DOI":"10.1364\/OE.451981","article-title":"Bit-error rate and average capacity of an absorbent and turbulent underwater wireless communication link with perfect Laguerre-Gauss beam","volume":"30","author":"Yang","year":"2022","journal-title":"Opt. Express"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"7647","DOI":"10.1109\/TCOMM.2021.3101876","article-title":"Evolution properties and spatial-mode UWOC performances of the perfect vortex beam subject to oceanic turbulence","volume":"69","author":"Wang","year":"2021","journal-title":"IEEE Trans. Commun."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"869","DOI":"10.1364\/OL.37.000869","article-title":"Characterization of dielectric spheres by spiral imaging","volume":"37","author":"Petrov","year":"2012","journal-title":"Opt. Lett."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"4194","DOI":"10.1109\/TAP.2018.2839753","article-title":"Reflection, transmission, and absorption of vortex beams propagation in an inhomogeneous magnetized plasma slab","volume":"66","author":"Li","year":"2018","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1167","DOI":"10.1109\/LAWP.2020.2993687","article-title":"Backward scattering of electrically large standard objects illuminated by OAM Beams","volume":"19","author":"Liu","year":"2020","journal-title":"IEEE Antennas Wirel. Propag. Lett."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1080\/0010751042000275259","article-title":"Bessel beams: Diffraction in a new light","volume":"46","author":"Mcgloin","year":"2005","journal-title":"Contemp. Phys."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"9467","DOI":"10.1364\/OE.27.009467","article-title":"Highly efficient generation of Bessel beams with polarization insensitive metasurfaces","volume":"27","author":"Akram","year":"2019","journal-title":"Opt. Express"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"6819","DOI":"10.1364\/OL.39.006819","article-title":"Wave-optics description of self-healing mechanism in Bessel beams","volume":"39","author":"Aiello","year":"2014","journal-title":"Opt. Lett."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1140\/epjd\/e2012-30343-6","article-title":"Analytical study on the self-healing property of Bessel beam","volume":"66","author":"Chu","year":"2012","journal-title":"Eur. Phys. J. D"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"064018","DOI":"10.1088\/2040-8978\/13\/6\/064018","article-title":"Free-space orbital angular momentum division multiplexing with Bessel beams","volume":"13","author":"Gatto","year":"2011","journal-title":"J. Opt."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1007\/s00340-007-2707-6","article-title":"Propagation of higher order Bessel-Gaussian beams in turbulence","volume":"88","year":"2007","journal-title":"Appl. Phys. B"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"B61","DOI":"10.1364\/AO.55.000B61","article-title":"Integral momenta of vortex Bessel-Gaussian beams in turbulent atmosphere","volume":"55","author":"Lukin","year":"2016","journal-title":"Appl. Opt."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1016\/j.optcom.2019.01.027","article-title":"Bandwidth-limited orbital angular momentum mode of Bessel Gaussian beams in the moderate to strong non-Kolmogorov turbulence","volume":"438","author":"Xu","year":"2019","journal-title":"Opt. Commun."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"837","DOI":"10.1364\/JOSAA.28.000837","article-title":"Self-healing of tightly focused scalar and vector Bessel-Gauss beams at the focal plane","volume":"28","author":"Vyas","year":"2011","journal-title":"J. Opt. Soc. Am. A"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"5821","DOI":"10.1364\/OE.25.005821","article-title":"Generation and self-healing of vector Bessel-Gauss beams with variant state of polarizations upon propagation","volume":"25","author":"Li","year":"2017","journal-title":"Opt. Express"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"888","DOI":"10.1364\/OL.36.000888","article-title":"Vector-vortex Bessel-Gauss beams and their tightly focusing properties","volume":"36","author":"Huang","year":"2011","journal-title":"Opt. Lett."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"107552","DOI":"10.1016\/j.jqsrt.2021.107552","article-title":"Scattering of a high-order vector Bessel Gaussian beam by a spherical marine aerosol","volume":"265","author":"Shi","year":"2021","journal-title":"J. Quant. Spectrosc. Radiat. Transf."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"128138","DOI":"10.1016\/j.optcom.2022.128138","article-title":"Attenuation characteristics of Bessel Gaussian vortex beam by a wet dust particle","volume":"514","author":"Shi","year":"2022","journal-title":"Opt. Commun."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Gouesbet, G., and Gr\u00e9han, G. (2011). Generalized Lorenz-Mie Theories, Springer.","DOI":"10.1007\/978-3-642-17194-9"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1016\/j.jqsrt.2012.10.010","article-title":"The role of the angular momentum of light in Mie scattering. Excitation of dielectric spheres with Laguerre-Gaussian modes","volume":"126","year":"2013","journal-title":"J. Quant. Spectrosc. Radiat. Transf."},{"key":"ref_44","unstructured":"Bohren, C., and Huffman, D. (1983). Absorption and Scattering of Light by Small Particles, Wiley."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"170","DOI":"10.1016\/j.jqsrt.2007.01.016","article-title":"Scattering of electromagnetic waves by charged spheres and some physical consequences","volume":"106","author":"Kocifaj","year":"2007","journal-title":"J. Quant. Spectrosc. Radiat. Transf."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1364\/OL.37.000265","article-title":"Scattering of electromagnetic waves by charged spheres: Near-field external intensity distribution","volume":"37","author":"Kocifaj","year":"2012","journal-title":"Opt. Lett."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/j.optcom.2013.12.069","article-title":"Spreading of spiral spectrum of Bessel-Gaussian beam in non-Kolmogorov turbulence","volume":"318","author":"Ou","year":"2014","journal-title":"Opt. Commun."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"9411","DOI":"10.1364\/OE.16.009411","article-title":"The Poynting vector and angular momentum of Airy beams","volume":"16","author":"Sztul","year":"2008","journal-title":"Opt. Express"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1016\/j.optcom.2013.04.013","article-title":"Spiral spectrum of Laguerre-Gaussian beam propagation in non-Kolmogorov turbulence","volume":"303","author":"Jiang","year":"2013","journal-title":"Opt. Commun."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"9071","DOI":"10.1364\/OE.14.009071","article-title":"Fourier relationship between angular position and optical orbital angular momentum","volume":"14","author":"Yao","year":"2006","journal-title":"Opt. Express"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"103013","DOI":"10.1088\/1367-2630\/10\/10\/103013","article-title":"Angular diffraction","volume":"10","author":"Jack","year":"2008","journal-title":"New J. Phys."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"2166","DOI":"10.1109\/TAP.2019.2948711","article-title":"Ultrawideband reflection-type metasurface for generating integer and fractional orbital angular momentum","volume":"68","author":"Yang","year":"2020","journal-title":"IEEE Trans. Antennas Propag."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/18\/4550\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:29:52Z","timestamp":1760142592000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/18\/4550"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,9,12]]},"references-count":52,"journal-issue":{"issue":"18","published-online":{"date-parts":[[2022,9]]}},"alternative-id":["rs14184550"],"URL":"https:\/\/doi.org\/10.3390\/rs14184550","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,9,12]]}}}