{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,25]],"date-time":"2026-09-25T16:03:19Z","timestamp":1790352199903,"version":"4.1.0"},"reference-count":58,"publisher":"National Academy of Sciences","issue":"39","license":[{"start":{"date-parts":[[2026,9,25]],"date-time":"2026-09-25T00:00:00Z","timestamp":1790294400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"content-domain":{"domain":["www.pnas.org"],"crossmark-restriction":true},"short-container-title":["Proc. Natl. Acad. Sci. U.S.A."],"published-print":{"date-parts":[[2026,9,29]]},"abstract":"<jats:p>Transient chaos is a hallmark of complex dynamics in nonlinear systems. Governed by chaotic saddles, it manifests as short-lived yet rich chaotic behavior preceding an abrupt transition to a stable attractor. However, real-time capture and quantitative characterization of such inherently unpredictable and nonrepetitive dynamics remain challenging, obscuring their physical origins. Here, we experimentally demonstrate transient chaos during the self-organization of dissipative optical solitons in a mode-locked fiber laser. By reconstructing phase-space trajectories from single-shot measurements, we quantify key dynamical invariants that confirm the deterministic nature of the underlying nonattracting chaotic set. Experimental and numerical results reveal that this complexity arises from coupled nonlinear interactions within unstable multipulse complexes. Furthermore, we identify the emergence of optical rogue waves with extreme amplitudes during the chaotic transient regime. Our results bridge the conceptual gap between optical chaos and mode-locking coherence, providing both an analytical framework and a versatile experimental platform for probing and manipulating transient chaotic dynamics in high-dimensional dissipative systems.<\/jats:p>","DOI":"10.1073\/pnas.2624826123","type":"journal-article","created":{"date-parts":[[2026,9,25]],"date-time":"2026-09-25T15:34:37Z","timestamp":1790350477000},"update-policy":"https:\/\/doi.org\/10.1073\/pnas.cm10313","source":"Crossref","is-referenced-by-count":0,"title":["Transient chaos in the self-organization of dissipative optical solitons"],"prefix":"10.1073","volume":"123","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-7169-0207","authenticated-orcid":false,"given":"Kun","family":"Chen","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00p991c53","id-type":"ROR","asserted-by":"publisher"}],"name":"School of Optical and Electronic Information, Huazhong University of Science and Technology","place":["Wuhan, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tao","family":"Cao","sequence":"additional","affiliation":[{"name":"Institute of Advanced Light Source Facilities","place":["Shenzhen, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shaozhen","family":"Liu","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00p991c53","id-type":"ROR","asserted-by":"publisher"}],"name":"School of Optical and Electronic Information, Huazhong University of Science and Technology","place":["Wuhan, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xinyi","family":"Yan","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00p991c53","id-type":"ROR","asserted-by":"publisher"}],"name":"School of Optical and Electronic Information, Huazhong University of Science and Technology","place":["Wuhan, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qi","family":"Xu","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00p991c53","id-type":"ROR","asserted-by":"publisher"}],"name":"School of Optical and Electronic Information, Huazhong University of Science and Technology","place":["Wuhan, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhou","family":"Li","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00p991c53","id-type":"ROR","asserted-by":"publisher"}],"name":"School of Optical and Electronic Information, Huazhong University of Science and Technology","place":["Wuhan, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Leyan","family":"Yang","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00p991c53","id-type":"ROR","asserted-by":"publisher"}],"name":"School of Optical and Electronic Information, Huazhong University of Science and Technology","place":["Wuhan, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6879-7840","authenticated-orcid":false,"given":"Alexei V.","family":"Sokolov","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/01f5ytq51","id-type":"ROR","asserted-by":"publisher"}],"name":"Institute for Quantum Science and Engineering, Texas A&M University","place":["College Station"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiahui","family":"Peng","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00p991c53","id-type":"ROR","asserted-by":"publisher"}],"name":"School of Optical and Electronic Information, Huazhong University of Science and Technology","place":["Wuhan, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"341","published-online":{"date-parts":[[2026,9,25]]},"reference":[{"key":"e_1_3_4_1_2","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(83)90126-4"},{"key":"e_1_3_4_2_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.48.1507"},{"key":"e_1_3_4_3_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.90.022917"},{"key":"e_1_3_4_4_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.87.035802"},{"key":"e_1_3_4_5_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.4917287"},{"key":"e_1_3_4_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-6987-3"},{"key":"e_1_3_4_7_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.112.044503"},{"key":"e_1_3_4_8_2","doi-asserted-by":"publisher","DOI":"10.1021\/j100054a001"},{"key":"e_1_3_4_9_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.460019"},{"key":"e_1_3_4_10_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.4790863"},{"key":"e_1_3_4_11_2","doi-asserted-by":"publisher","DOI":"10.1088\/2041-8205\/798\/1\/L9"},{"key":"e_1_3_4_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2019.109400"},{"key":"e_1_3_4_13_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41567-020-0784-1"},{"key":"e_1_3_4_14_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.89.103901"},{"key":"e_1_3_4_15_2","doi-asserted-by":"publisher","DOI":"10.1364\/OPTICA.540158"},{"key":"e_1_3_4_16_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-019-14013-4"},{"key":"e_1_3_4_17_2","doi-asserted-by":"publisher","DOI":"10.1364\/JOSAB.8.002068"},{"key":"e_1_3_4_18_2","doi-asserted-by":"publisher","DOI":"10.1109\/2944.571754"},{"key":"e_1_3_4_19_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.49.2806"},{"key":"e_1_3_4_20_2","doi-asserted-by":"publisher","DOI":"10.1038\/nphoton.2011.345"},{"key":"e_1_3_4_21_2","doi-asserted-by":"publisher","DOI":"10.1021\/acsphotonics.3c01210"},{"key":"e_1_3_4_22_2","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.74.99"},{"key":"e_1_3_4_23_2","doi-asserted-by":"publisher","DOI":"10.1364\/OE.476083"},{"key":"e_1_3_4_24_2","doi-asserted-by":"publisher","DOI":"10.1021\/acsphotonics.4c01623"},{"key":"e_1_3_4_25_2","doi-asserted-by":"publisher","DOI":"10.1088\/2040-8978\/15\/6\/060201"},{"key":"e_1_3_4_26_2","doi-asserted-by":"publisher","DOI":"10.1063\/5.0255282"},{"key":"e_1_3_4_27_2","doi-asserted-by":"publisher","DOI":"10.1038\/nphoton.2017.76"},{"key":"e_1_3_4_28_2","doi-asserted-by":"publisher","DOI":"10.1002\/lpor.202200763"},{"key":"e_1_3_4_29_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41566-018-0106-7"},{"key":"e_1_3_4_30_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-024-50236-w"},{"key":"e_1_3_4_31_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41598-019-50022-5"},{"key":"e_1_3_4_32_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.yofte.2024.103753"},{"key":"e_1_3_4_33_2","doi-asserted-by":"publisher","DOI":"10.1002\/adpr.202400049"},{"key":"e_1_3_4_34_2","doi-asserted-by":"publisher","DOI":"10.1038\/nphoton.2016.38"},{"key":"e_1_3_4_35_2","doi-asserted-by":"publisher","DOI":"10.1117\/1.AP.1.1.016003"},{"key":"e_1_3_4_36_2","doi-asserted-by":"publisher","DOI":"10.1364\/OL.425574"},{"key":"e_1_3_4_37_2","volume-title":"Lasers","author":"Siegman A. E.","year":"1986","unstructured":"A. E. Siegman, Lasers (University Science Books, Mill Valley, CA, 1986)."},{"key":"e_1_3_4_38_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.44.6954"},{"key":"e_1_3_4_39_2","doi-asserted-by":"crossref","unstructured":"I. Kudelin S. Sugavanam M. Chernysheva \u201cCorrelation of solitons in bidirectional mode-locked fibre laser\u201d in Nonlinear Optics and its Applications 2020 N. G. R. Broderick J. M. Dudley A. C. Peacock Eds. (SPIE Bellingham WA 2020) vol. 11358 p. 1135810.","DOI":"10.1117\/12.2555382"},{"key":"e_1_3_4_40_2","doi-asserted-by":"publisher","DOI":"10.1109\/JLT.2021.3098575"},{"key":"e_1_3_4_41_2","doi-asserted-by":"crossref","unstructured":"F. Takens \u201cDetecting strange attractors in turbulence\u201d in Dynamical Systems and Turbulence Warwick 1980 D. Rand L. S. Young Eds. (Springer Berlin Heidelberg Berlin Heidelberg 1981) pp. 366\u2013381.","DOI":"10.1007\/BFb0091924"},{"key":"e_1_3_4_42_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.59.1646"},{"key":"e_1_3_4_43_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.33.1134"},{"key":"e_1_3_4_44_2","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(83)90298-1"},{"key":"e_1_3_4_45_2","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(93)90009-P"},{"key":"e_1_3_4_46_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.aal5326"},{"key":"e_1_3_4_47_2","doi-asserted-by":"publisher","DOI":"10.1364\/JOSAB.25.001193"},{"key":"e_1_3_4_48_2","doi-asserted-by":"publisher","DOI":"10.1002\/2017MS000999"},{"key":"e_1_3_4_49_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.88.052911"},{"key":"e_1_3_4_50_2","doi-asserted-by":"publisher","DOI":"10.1146\/annurev.fluid.40.111406.102203"},{"key":"e_1_3_4_51_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.80.033610"},{"key":"e_1_3_4_52_2","doi-asserted-by":"publisher","DOI":"10.1038\/nature06402"},{"key":"e_1_3_4_53_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.90.013805"},{"key":"e_1_3_4_54_2","doi-asserted-by":"publisher","DOI":"10.1002\/lpor.202200470"},{"key":"e_1_3_4_55_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-021-25861-4"},{"key":"e_1_3_4_56_2","doi-asserted-by":"publisher","DOI":"10.1038\/nphoton.2014.220"},{"key":"e_1_3_4_57_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.85.013828"},{"key":"e_1_3_4_58_2","unstructured":"K. Chen Dataset for \u201cTransient chaos in the self-organization of dissipative optical solitons\u201d. Zenodo. https:\/\/doi.org\/10.5281\/zenodo.22284975. Deposited 3 September 2026."}],"container-title":["Proceedings of the National Academy of Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pnas.org\/doi\/pdf\/10.1073\/pnas.2624826123","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,25]],"date-time":"2026-09-25T15:34:46Z","timestamp":1790350486000},"score":1,"resource":{"primary":{"URL":"https:\/\/pnas.org\/doi\/10.1073\/pnas.2624826123"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,25]]},"references-count":58,"journal-issue":{"issue":"39","published-print":{"date-parts":[[2026,9,29]]}},"alternative-id":["10.1073\/pnas.2624826123"],"URL":"https:\/\/doi.org\/10.1073\/pnas.2624826123","relation":{},"ISSN":["0027-8424","1091-6490"],"issn-type":[{"value":"0027-8424","type":"print"},{"value":"1091-6490","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,25]]},"assertion":[{"value":"2026-07-19","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-08-23","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-09-25","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"e2624826123"}}