{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:08:58Z","timestamp":1760231338139,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"18","license":[{"start":{"date-parts":[[2022,9,15]],"date-time":"2022-09-15T00:00:00Z","timestamp":1663200000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program","doi-asserted-by":"publisher","award":["2018YFB0504400","63223052","62075106"],"award-info":[{"award-number":["2018YFB0504400","63223052","62075106"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Fundamental Re-search Funds for the Central Universities","award":["2018YFB0504400","63223052","62075106"],"award-info":[{"award-number":["2018YFB0504400","63223052","62075106"]}]},{"name":"National Natural Science Foundation of China (NSFC)","award":["2018YFB0504400","63223052","62075106"],"award-info":[{"award-number":["2018YFB0504400","63223052","62075106"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Ultra-short laser filamentation has been intensively studied due to its unique optical properties for applications in the field of remote sensing and detection. Although significant progress has been made, the quality of the laser beam still suffers from various optical aberrations during long-range transmission. Astigmatism is a typical off-axis aberration that is often encountered in the off-axis optical systems. An effective method needs to be proposed to suppress the astigmatism of the beam during filamentation. Herein, we numerically investigated the impact of the nonlinear effects on the focusing properties of the astigmatic Gaussian beams in air and obtained similar results in the experiment. As the single pulse energy increases, the maximum on-axis intensity gradually shifted from the sagittal focus to the tangential focus and the foci moved forward simultaneously. Moreover, the astigmatism could be suppressed effectively with the enhancement of the nonlinear effects, that is, the astigmatic difference and the degree of beam distortion were both reduced. Through this approach, the acoustic intensity of the filament (located at the tangential focal point) increased by a factor of 22.8. Our work paves a solid step toward the practical applications of the astigmatism beam as the nonlinear lidar.<\/jats:p>","DOI":"10.3390\/s22186981","type":"journal-article","created":{"date-parts":[[2022,9,16]],"date-time":"2022-09-16T01:35:10Z","timestamp":1663292110000},"page":"6981","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Investigation of Focusing Properties on Astigmatic Gaussian Beams in Nonlinear Medium"],"prefix":"10.3390","volume":"22","author":[{"given":"Shishi","family":"Tao","sequence":"first","affiliation":[{"name":"Institute of Modern Optics, Eye Institute, Nankai University, Tianjin 300350, China"},{"name":"Tianjin Key Laboratory of Micro-Scale Optical Information Science and Technology, Tianjin 300350, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiayun","family":"Xue","sequence":"additional","affiliation":[{"name":"Institute of Modern Optics, Eye Institute, Nankai University, Tianjin 300350, China"},{"name":"Tianjin Key Laboratory of Micro-Scale Optical Information Science and Technology, Tianjin 300350, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiewei","family":"Guo","sequence":"additional","affiliation":[{"name":"Institute of Modern Optics, Eye Institute, Nankai University, Tianjin 300350, China"},{"name":"Tianjin Key Laboratory of Micro-Scale Optical Information Science and Technology, Tianjin 300350, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4924-9080","authenticated-orcid":false,"given":"Xing","family":"Zhao","sequence":"additional","affiliation":[{"name":"Institute of Modern Optics, Eye Institute, Nankai University, Tianjin 300350, China"},{"name":"Tianjin Key Laboratory of Micro-Scale Optical Information Science and Technology, Tianjin 300350, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhi","family":"Zhang","sequence":"additional","affiliation":[{"name":"Institute of Modern Optics, Eye Institute, Nankai University, Tianjin 300350, China"},{"name":"Tianjin Key Laboratory of Optoelectronic Sensor and Sensing Network Technology, Tianjin 300350, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lie","family":"Lin","sequence":"additional","affiliation":[{"name":"Institute of Modern Optics, Eye Institute, Nankai University, Tianjin 300350, China"},{"name":"Tianjin Key Laboratory of Optoelectronic Sensor and Sensing Network Technology, Tianjin 300350, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6036-9641","authenticated-orcid":false,"given":"Weiwei","family":"Liu","sequence":"additional","affiliation":[{"name":"Institute of Modern Optics, Eye Institute, Nankai University, Tianjin 300350, China"},{"name":"Tianjin Key Laboratory of Micro-Scale Optical Information Science and Technology, Tianjin 300350, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/j.physrep.2006.12.005","article-title":"Femtosecond filamentation in transparent media","volume":"441","author":"Couairon","year":"2007","journal-title":"Phys. Rep."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1126\/science.1085020","article-title":"White-light filaments for atmospheric analysis","volume":"301","author":"Kasparian","year":"2003","journal-title":"Science"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"863","DOI":"10.1139\/p05-048","article-title":"The propagation of powerful femtosecond laser pulses in opticalmedia: Physics, applications, and new challenges","volume":"83","author":"Chin","year":"2005","journal-title":"Can. J. Phys."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"466","DOI":"10.1364\/OE.16.000466","article-title":"Physics and applications of atmospheric nonlinear optics and filamentation","volume":"16","author":"Kasparian","year":"2008","journal-title":"Opt. Express"},{"key":"ref_5","first-page":"465","article-title":"Intensity clamping during femtosecond laser filamentation","volume":"52","author":"Liu","year":"2014","journal-title":"Chin. J. Phys."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1016\/S0030-4018(99)00691-4","article-title":"Fast pulsed electric field created from the self-generated filament of a femtosecond Ti: Sapphire laser pulse in air","volume":"174","author":"Proulx","year":"2000","journal-title":"Opt. Commun."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"753","DOI":"10.1007\/s003400050699","article-title":"Electrical conductivity of long plasma channels in air generated by self-guided femtosecond laser pulses","volume":"68","author":"Schillinger","year":"1999","journal-title":"Appl. Phys. B Lasers Opt."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"026001","DOI":"10.1088\/1361-6633\/aa8488","article-title":"Short-pulse lasers for weather control","volume":"81","author":"Wolf","year":"2017","journal-title":"Rep. Prog. Phys."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1002\/lpor.201500283","article-title":"Spaceborne laser filamentation for atmospheric remote sensing","volume":"10","author":"Dicaire","year":"2016","journal-title":"Laser Photonics Rev."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"036607","DOI":"10.1103\/PhysRevE.69.036607","article-title":"Kilometer-range nonlinear propagation of femtosecond laser pulses","volume":"69","author":"Rodriguez","year":"2004","journal-title":"Phys. Rev. E"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1214","DOI":"10.1364\/OL.37.001214","article-title":"Laser-filamentation-induced condensation and snow formation in a cloud chamber","volume":"37","author":"Ju","year":"2012","journal-title":"Opt. Lett."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1007\/s00340-004-1466-x","article-title":"Remote detection and identification of biological aerosols using a femtosecond terawatt lidar system","volume":"78","author":"Kasparian","year":"2004","journal-title":"Appl. Phys. B"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1002\/lpor.201400208","article-title":"Femtosecond laser ionization and fragmentation of molecules for environmental sensing","volume":"9","author":"Xu","year":"2015","journal-title":"Laser Photonics Rev."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00340-009-3381-7","article-title":"Filamentation \u201cremote\u201d sensing of chemical and biological agents\/pollutants using only one femtosecond laser source","volume":"95","author":"Chin","year":"2009","journal-title":"Appl. Phys. B"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"8962","DOI":"10.1364\/AO.55.008962","article-title":"Off-axis three-mirror freeform telescope with a large linear field of view based on an integration mirror","volume":"55","author":"Meng","year":"2016","journal-title":"Appl. Opt."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Garoli, D., Rodriguez De Marcos, L.V., Larruquert, J.I., Corso, A.J., Proietti Zaccaria, R., and Pelizzo, M.G. (2020). Mirrors for space telescopes: Degradation issues. Appl. Sci., 10.","DOI":"10.20944\/preprints202010.0141.v1"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1007\/s11433-006-0129-9","article-title":"Five hundred meter aperture spherical radio telescope (FAST)","volume":"49","author":"Nan","year":"2006","journal-title":"Sci. China Ser. G"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1687","DOI":"10.1364\/AO.8.001687","article-title":"Gaussian light beams with general astigmatism","volume":"8","author":"Arnaud","year":"1969","journal-title":"Appl. Opt."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"033819","DOI":"10.1103\/PhysRevA.75.033819","article-title":"Modes of a twisted optical cavity","volume":"75","author":"Habraken","year":"2007","journal-title":"Phys. Rev. A"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"043835","DOI":"10.1103\/PhysRevA.85.043835","article-title":"Nonparaxial wave beams and packets with general astigmatism","volume":"85","author":"Kiselev","year":"2012","journal-title":"Phys. Rev. A"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1085","DOI":"10.1070\/QE2014v044n12ABEH015472","article-title":"Plasma channels during filamentation of a femtosecond laser pulse with wavefront astigmatism in air","volume":"44","author":"Dergachev","year":"2014","journal-title":"Quantum Electron."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1772","DOI":"10.1364\/OL.29.001772","article-title":"Control of multiple filamentation in air","volume":"29","author":"Fibich","year":"2004","journal-title":"Opt. Lett."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"3867","DOI":"10.1364\/OL.36.003867","article-title":"Enhancement of filamentation postcompression by astigmatic focusing","volume":"36","author":"Alonso","year":"2011","journal-title":"Opt. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"168249","DOI":"10.1016\/j.ijleo.2021.168249","article-title":"Propagation and transformation properties of rotating sinh-Gaussian beam in nonlinear media with spatial nonlocality","volume":"250","author":"Liu","year":"2022","journal-title":"Optik"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"743","DOI":"10.1364\/OL.44.000743","article-title":"Propagation formulae and characteristics of partially coherent laser beams in nonlinear media","volume":"44","author":"Wang","year":"2019","journal-title":"Opt. Lett."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2737","DOI":"10.1364\/JOSAA.14.002737","article-title":"Characterization of aberrated laser beams","volume":"14","author":"Alda","year":"1997","journal-title":"J. Opt. Soc. Am. A"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/0079-6727(75)90003-8","article-title":"Self-focusing: Theory","volume":"4","author":"Marburger","year":"1975","journal-title":"Prog. Quantum Electron."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"877","DOI":"10.1007\/s003400000463","article-title":"The critical laser intensity of self-guided light filaments in air","volume":"71","author":"Kasparian","year":"2000","journal-title":"Appl. Phys. B"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"304","DOI":"10.1364\/OL.22.000304","article-title":"Moving focus in the propagation of ultrashort laser pulses in air","volume":"22","author":"Brodeur","year":"1997","journal-title":"Opt. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1063\/1.1654278","article-title":"Enhancement of self-focusing threshold in sapphire with elliptical beams","volume":"21","author":"Giuliano","year":"1972","journal-title":"Appl. Phys. Lett."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"074205","DOI":"10.7498\/aps.70.20201661","article-title":"Propagation characteristics of focused astigmatic Gaussian beams in Kerr nonlinear media","volume":"70","author":"Hu","year":"2021","journal-title":"Acta Phys. Sin."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1007\/s00340-004-1589-0","article-title":"Multi-parameter characterization of the longitudinal plasma profile of a filament: A comparative study","volume":"79","author":"Hosseini","year":"2004","journal-title":"Appl. Phys. B"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/18\/6981\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:32:01Z","timestamp":1760142721000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/18\/6981"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,9,15]]},"references-count":32,"journal-issue":{"issue":"18","published-online":{"date-parts":[[2022,9]]}},"alternative-id":["s22186981"],"URL":"https:\/\/doi.org\/10.3390\/s22186981","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2022,9,15]]}}}