{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T17:59:11Z","timestamp":1785434351360,"version":"3.56.0"},"reference-count":20,"publisher":"Optica Publishing Group","issue":"3","license":[{"start":{"date-parts":[[2024,1,26]],"date-time":"2024-01-26T00:00:00Z","timestamp":1706227200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/doi.org\/10.1364\/OA_License_v2#VOR"},{"start":{"date-parts":[[2024,1,26]],"date-time":"2024-01-26T00:00:00Z","timestamp":1706227200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/opg.optica.org\/policies\/opg-tdm-policy.json"}],"content-domain":{"domain":["opg.optica.org"],"crossmark-restriction":false},"short-container-title":["Opt. Lett."],"published-print":{"date-parts":[[2024,2,1]]},"abstract":"<jats:p>We derive the parametric equations for the geometric rays of a periodic orbit inside a confocal cavity. Based on the derived formula, we demonstrate a passively mode-locked solid-state laser with a low pulse repetition rate to obtain a pulse train traveling along zigzag multi-pass trajectories. We achieve a stable mode-locked pulse train with a pulse repetition rate of 18\u2005MHz by designing the cavity to satisfy the dual-M trajectory. Furthermore, by precisely adjusting cavity mirrors under the same experimental setup, we can reach pulse repetition rates of 12 and 9\u2005MHz for the mode-locked laser. It is believed that the numerical calculation and the developed experiment can provide a straightforward and convenient way to achieve a low pulse repetition rate for passively mode-locked lasers.<\/jats:p>","DOI":"10.1364\/ol.515603","type":"journal-article","created":{"date-parts":[[2024,1,2]],"date-time":"2024-01-02T11:00:09Z","timestamp":1704193209000},"page":"662","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Investigation of low pulse repetition passively mode-locked Nd:YVO\n                    <sub>4<\/sub>\n                    lasers via multi-pass periodic trajectories in a confocal cavity"],"prefix":"10.1364","volume":"49","author":[{"given":"Hsing-Chih","family":"Liang","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00se2k293","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yu-Hsin","family":"Hsu","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00se2k293","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pin-Wen","family":"Cheng","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00se2k293","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0752-175X","authenticated-orcid":true,"given":"Hai-Pang","family":"Chiang","sequence":"additional","affiliation":[{"name":"National Taiwan Ocean University"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2024,1,26]]},"reference":[{"key":"ol-49-3-662-R1","doi-asserted-by":"publisher","first-page":"S883","DOI":"10.1007\/s003390051552","volume":"69","author":"Lapczynal","year":"1999","journal-title":"Appl. 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