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Lett."],"published-print":{"date-parts":[[2026,8,1]]},"abstract":"<jats:p>We propose a continuous-scaling angular spectrum (CSAS) method for efficient long-distance free-space optical (FSO) propagation simulation. By combining multistep propagation with continuously updated sampling intervals, the method maintains a constant sampling size and avoids the large computational grids required by conventional angular spectrum (AS) approaches. Under an aperture-limited framework, only the spatial-frequency components contributing to the received optical power (ROP) are preserved, and a low-frequency energy ratio is introduced to quantify the relevant spectral content. Numerical simulations and a 4.3\u2009km outdoor FSO experiment demonstrate that CSAS provides consistent ROP estimation compared with conventional AS, while significantly reducing computational cost. At a propagation distance of 4.3\u2009km, the proposed method achieves approximately 98% reduction in computation time without degrading power estimation performance. The results indicate that CSAS offers an efficient propagation framework for long-distance FSO systems, particularly for scenarios involving multi-step turbulence modeling and system-level evaluation.<\/jats:p>","DOI":"10.1364\/ol.599162","type":"journal-article","created":{"date-parts":[[2026,6,30]],"date-time":"2026-06-30T18:54:29Z","timestamp":1782845669000},"page":"4256","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Computationally efficient long-distance free-space optical simulation using a continuous-scaling angular spectrum method"],"prefix":"10.1364","volume":"51","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7820-7189","authenticated-orcid":true,"given":"Chaoxu","family":"Chen","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/04pmg2p90","id-type":"ROR","asserted-by":"publisher"}]},{"name":"Fudan University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Haoyu","family":"Zhang","sequence":"additional","affiliation":[{"name":"Fudan University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-2647-2688","authenticated-orcid":true,"given":"Yuan","family":"Wei","sequence":"additional","affiliation":[{"name":"Fudan University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fang","family":"Dong","sequence":"additional","affiliation":[{"name":"Fudan University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8041-1608","authenticated-orcid":true,"given":"Junwen","family":"Zhang","sequence":"additional","affiliation":[{"name":"Fudan University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4966-3844","authenticated-orcid":true,"given":"Nan","family":"Chi","sequence":"additional","affiliation":[{"name":"Fudan University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Haiwen","family":"Cai","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/04pmg2p90","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6621-8403","authenticated-orcid":true,"given":"Wei","family":"Chu","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/04pmg2p90","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5478-3704","authenticated-orcid":true,"given":"Jianyang","family":"Shi","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/04pmg2p90","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2026,7,24]]},"reference":[{"key":"ol-51-15-4256-R1","volume":"186","author":"Majumdar","year":"2014"},{"key":"ol-51-15-4256-R2","doi-asserted-by":"publisher","first-page":"2231","DOI":"10.1109\/COMST.2014.2329501","type":"journal-article","volume":"16","author":"Khalighi","year":"2014","journal-title":"IEEE Commun. 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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"}]}}