{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,24]],"date-time":"2026-01-24T14:16:58Z","timestamp":1769264218425,"version":"3.49.0"},"reference-count":32,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2024,4,29]],"date-time":"2024-04-29T00:00:00Z","timestamp":1714348800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Chongqing Local Universities and Institutions of Chinese Academy of Sciences","award":["HZ2021007"],"award-info":[{"award-number":["HZ2021007"]}]},{"name":"Chongqing Local Universities and Institutions of Chinese Academy of Sciences","award":["KJQN202200557"],"award-info":[{"award-number":["KJQN202200557"]}]},{"name":"Chongqing Local Universities and Institutions of Chinese Academy of Sciences","award":["KJQN202300525"],"award-info":[{"award-number":["KJQN202300525"]}]},{"name":"Chongqing Local Universities and Institutions of Chinese Academy of Sciences","award":["61975003"],"award-info":[{"award-number":["61975003"]}]},{"name":"Chongqing Local Universities and Institutions of Chinese Academy of Sciences","award":["61790584"],"award-info":[{"award-number":["61790584"]}]},{"name":"Chongqing Local Universities and Institutions of Chinese Academy of Sciences","award":["62025506"],"award-info":[{"award-number":["62025506"]}]},{"name":"Chongqing Local Universities and Institutions of Chinese Academy of Sciences","award":["23XLB003"],"award-info":[{"award-number":["23XLB003"]}]},{"name":"Chongqing Municipal Education Commission","award":["HZ2021007"],"award-info":[{"award-number":["HZ2021007"]}]},{"name":"Chongqing Municipal Education Commission","award":["KJQN202200557"],"award-info":[{"award-number":["KJQN202200557"]}]},{"name":"Chongqing Municipal Education Commission","award":["KJQN202300525"],"award-info":[{"award-number":["KJQN202300525"]}]},{"name":"Chongqing Municipal Education Commission","award":["61975003"],"award-info":[{"award-number":["61975003"]}]},{"name":"Chongqing Municipal Education Commission","award":["61790584"],"award-info":[{"award-number":["61790584"]}]},{"name":"Chongqing Municipal Education Commission","award":["62025506"],"award-info":[{"award-number":["62025506"]}]},{"name":"Chongqing Municipal Education Commission","award":["23XLB003"],"award-info":[{"award-number":["23XLB003"]}]},{"name":"National Natural Science Foundation of China","award":["HZ2021007"],"award-info":[{"award-number":["HZ2021007"]}]},{"name":"National Natural Science Foundation of China","award":["KJQN202200557"],"award-info":[{"award-number":["KJQN202200557"]}]},{"name":"National Natural Science Foundation of China","award":["KJQN202300525"],"award-info":[{"award-number":["KJQN202300525"]}]},{"name":"National Natural Science Foundation of China","award":["61975003"],"award-info":[{"award-number":["61975003"]}]},{"name":"National Natural Science Foundation of China","award":["61790584"],"award-info":[{"award-number":["61790584"]}]},{"name":"National Natural Science Foundation of China","award":["62025506"],"award-info":[{"award-number":["62025506"]}]},{"name":"National Natural Science Foundation of China","award":["23XLB003"],"award-info":[{"award-number":["23XLB003"]}]},{"name":"Chongqing Normal University (Talent Introduction\/Doctoral Initiation) Fund Project","award":["HZ2021007"],"award-info":[{"award-number":["HZ2021007"]}]},{"name":"Chongqing Normal University (Talent Introduction\/Doctoral Initiation) Fund Project","award":["KJQN202200557"],"award-info":[{"award-number":["KJQN202200557"]}]},{"name":"Chongqing Normal University (Talent Introduction\/Doctoral Initiation) Fund Project","award":["KJQN202300525"],"award-info":[{"award-number":["KJQN202300525"]}]},{"name":"Chongqing Normal University (Talent Introduction\/Doctoral Initiation) Fund Project","award":["61975003"],"award-info":[{"award-number":["61975003"]}]},{"name":"Chongqing Normal University (Talent Introduction\/Doctoral Initiation) Fund Project","award":["61790584"],"award-info":[{"award-number":["61790584"]}]},{"name":"Chongqing Normal University (Talent Introduction\/Doctoral Initiation) Fund Project","award":["62025506"],"award-info":[{"award-number":["62025506"]}]},{"name":"Chongqing Normal University (Talent Introduction\/Doctoral Initiation) Fund Project","award":["23XLB003"],"award-info":[{"award-number":["23XLB003"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Understanding the mechanism of mode-locking in a laser with high-order transverse mode is important for achieving an ultrashort pulses train under more complicated conditions. So far, mode-locking with high-order transverse mode has not been reported in other lasers except the multimode fiber laser. This paper demonstrates robust mode-locking with high-order transverse mode in a Kerr-lens mode-locked vertical-external-cavity surface-emitting laser for the first time, to the best of our knowledge. While the longitudinal modes are locked, continuous mode-locking accompanied by high-order transverse mode up to TEM40 is observed. The threshold of the mode-locking is only a little bigger than that of the lasing. After the laser oscillation is built up, the mode-locked pulse train can be obtained almost immediately and maintained until the thermal rollover of the laser. Output powers of 717 mW under fundamental mode and 666 mW under high-order transverse mode are achieved with a 4.3 ps pulse duration and 1.1 GHz pulses repetition rate, and some phenomenological explanations to the related characteristics of the mode-locked operation of high-order transverse mode in the vertical-external-cavity surface-emitting laser are proposed.<\/jats:p>","DOI":"10.3390\/s24092839","type":"journal-article","created":{"date-parts":[[2024,4,29]],"date-time":"2024-04-29T10:33:36Z","timestamp":1714386816000},"page":"2839","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Mode-Locked Operation of High-Order Transverse Modes in a Vertical-External-Cavity Surface-Emitting Laser"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5455-6333","authenticated-orcid":false,"given":"Tao","family":"Wang","sequence":"first","affiliation":[{"name":"College of Physics and Electronic Engineering, Chongqing Normal University, Chongqing 401331, China"}]},{"given":"Yunjie","family":"Liu","sequence":"additional","affiliation":[{"name":"National Center for Applied Mathematics in Chongqing, Chongqing Normal University, Chongqing 401331, China"}]},{"given":"Renjiang","family":"Zhu","sequence":"additional","affiliation":[{"name":"College of Physics and Electronic Engineering, Chongqing Normal University, Chongqing 401331, China"}]},{"given":"Lidan","family":"Jiang","sequence":"additional","affiliation":[{"name":"College of Physics and Electronic Engineering, Chongqing Normal University, Chongqing 401331, China"}]},{"given":"Huanyu","family":"Lu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Luminescence and Applications, Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China"}]},{"given":"Yanrong","family":"Song","sequence":"additional","affiliation":[{"name":"College of Applied Sciences, Beijing University of Technology, Beijing 100124, China"}]},{"given":"Peng","family":"Zhang","sequence":"additional","affiliation":[{"name":"National Center for Applied Mathematics in Chongqing, Chongqing Normal University, Chongqing 401331, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,4,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"831","DOI":"10.1038\/nature01938","article-title":"Recent Developments in Compact Ultrafast Lasers","volume":"424","author":"Keller","year":"2003","journal-title":"Nature"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"e149","DOI":"10.1038\/lsa.2014.30","article-title":"Ultrafast Lasers\u2014Reliable Tools for Advanced Materials Processing","volume":"3","author":"Sugioka","year":"2014","journal-title":"Light Sci. 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