{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,10]],"date-time":"2026-07-10T03:26:19Z","timestamp":1783653979939,"version":"3.55.0"},"reference-count":30,"publisher":"Optica Publishing Group","issue":"6","license":[{"start":{"date-parts":[[2025,5,20]],"date-time":"2025-05-20T00:00:00Z","timestamp":1747699200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/doi.org\/10.1364\/OA_License_v2#VOR"},{"start":{"date-parts":[[2025,5,20]],"date-time":"2025-05-20T00:00:00Z","timestamp":1747699200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/opg.optica.org\/policies\/opg-tdm-policy.json"}],"funder":[{"DOI":"10.13039\/501100006769","name":"Russian Science Foundation","doi-asserted-by":"publisher","award":["23-12-00236"],"award-info":[{"award-number":["23-12-00236"]}],"id":[{"id":"10.13039\/501100006769","id-type":"DOI","asserted-by":"publisher"}]},{"name":"State Assignment of NRC \u201cKurchatov Institute\u201d"}],"content-domain":{"domain":["opg.optica.org"],"crossmark-restriction":false},"short-container-title":["J. Opt. Soc. Am. A"],"published-print":{"date-parts":[[2025,6,1]]},"abstract":"<jats:p>In this work, we theoretically and numerically analyze helical Ince\u2013Gaussian (hIG) modes, hIG<jats:sub><jats:italic>p<\/jats:italic>,<jats:italic>q<\/jats:italic><\/jats:sub>(<jats:italic>x<\/jats:italic>,<jats:italic>y<\/jats:italic>,<jats:italic>\u03b5<\/jats:italic>). We derive explicit analytical relationships to describe the <jats:italic>\u03b5<\/jats:italic>-dependence (where <jats:italic>\u03b5<\/jats:italic> is the ellipticity parameter) of the orbital angular momentum (OAM) of hIG<jats:sub><jats:italic>p<\/jats:italic>,<jats:italic>q<\/jats:italic><\/jats:sub>(<jats:italic>x<\/jats:italic>,<jats:italic>y<\/jats:italic>,<jats:italic>\u03b5<\/jats:italic>) modes at <jats:italic>p<\/jats:italic>=2,3,4,5. The derivation procedure relies on expansions of the hIG modes in terms of Hermite\u2013Gaussian modes. It is shown that in the general case, the OAM is an even function of <jats:italic>\u03b5<\/jats:italic> and exhibits no monotonic behavior with <jats:italic>\u03b5<\/jats:italic> varying from zero to plus and minus infinity.<\/jats:p>","DOI":"10.1364\/josaa.558038","type":"journal-article","created":{"date-parts":[[2025,4,2]],"date-time":"2025-04-02T15:00:50Z","timestamp":1743606050000},"page":"780","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Helical Ince\u2013Gaussian laser beams as superpositions of Hermite\u2013Gaussian beams"],"prefix":"10.1364","volume":"42","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7813-8363","authenticated-orcid":true,"given":"Eugeny G.","family":"Abramochkin","sequence":"first","affiliation":[{"name":"Lebedev Physical Institute"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1737-0393","authenticated-orcid":true,"given":"Victor V.","family":"Kotlyar","sequence":"additional","affiliation":[{"name":"NRC \u201cKurchatov Institute"},{"name":"Samara National Research University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0488-4267","authenticated-orcid":true,"given":"Alexey A.","family":"Kovalev","sequence":"additional","affiliation":[{"name":"NRC \u201cKurchatov Institute"},{"name":"Samara National Research University"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2025,5,20]]},"reference":[{"key":"josaa-42-6-780-R1","doi-asserted-by":"publisher","first-page":"512","DOI":"10.1063\/1.522574","volume":"16","author":"Boyer","year":"1975","journal-title":"J. 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All rights, including for text and data mining (TDM), Artificial Intelligence (AI) training, and similar technologies, are reserved.","name":"copyright","label":"Copyright"}]}}