{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T09:28:42Z","timestamp":1785403722070,"version":"3.56.0"},"reference-count":24,"publisher":"Optica Publishing Group","issue":"7","license":[{"start":{"date-parts":[[2026,6,30]],"date-time":"2026-06-30T00:00:00Z","timestamp":1782777600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/doi.org\/10.1364\/OA_License_v2#VOR"},{"start":{"date-parts":[[2026,6,30]],"date-time":"2026-06-30T00:00:00Z","timestamp":1782777600000},"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":["J. Opt. Soc. Am. A"],"published-print":{"date-parts":[[2026,7,1]]},"abstract":"<jats:p>This paper presents a closed-form analytical derivation of the wave structure function (WSF) for an underwater optical Gaussian beam propagating through oceanic turbulence with attenuation caused by absorption and scattering. Using the extended first-order Rytov approximation together with the oceanic turbulence optical power spectrum (OTOPS) model, attenuation is incorporated into the propagation path integral, leading to compact hypergeometric-function solutions. Numerical results show that, at a propagation distance of 20\u00a0m, the Gaussian-beam WSF increases by 32.08%, 52.61%, and 65.33% for wavelengths of 400, 450, and 532\u00a0nm, respectively, when compared with no-attenuation scenarios, while at 40\u00a0m, these values increase to 55.76%, 80.36%, and 90.51%. These results demonstrate that attenuation significantly modifies the effective weighting of turbulence-induced phase perturbations as propagation distance increases, with shorter wavelengths exhibiting stronger proportional growth in the predicted WSF. The proposed model extends existing turbulence-only formulations and provides a unified analytical framework for underwater optical wireless communication systems under combined turbulence and attenuation effects.<\/jats:p>","DOI":"10.1364\/josaa.599212","type":"journal-article","created":{"date-parts":[[2026,6,11]],"date-time":"2026-06-11T12:00:10Z","timestamp":1781179210000},"page":"1116","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Wave structure function of an underwater optical Gaussian beam including attenuation"],"prefix":"10.1364","volume":"43","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-7618-4031","authenticated-orcid":true,"given":"Shideh","family":"Tayebnaimi","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/049emcs32","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2662-9010","authenticated-orcid":true,"given":"Kamran","family":"Kiasaleh","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/049emcs32","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2026,6,30]]},"reference":[{"key":"josaa-43-7-1116-R1","doi-asserted-by":"publisher","first-page":"684","DOI":"10.1007\/s10043-025-01002-w","type":"journal-article","volume":"32","author":"Zayed","year":"2025","journal-title":"Opt. 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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"}]}}