{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T23:10:47Z","timestamp":1790723447020,"version":"4.1.0"},"reference-count":57,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T00:00:00Z","timestamp":1760313600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12322416"],"award-info":[{"award-number":["12322416"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["advanced.onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Advanced Science"],"published-print":{"date-parts":[[2026,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Geometric phase is a far\u2010reaching concept in quantum and classical physics, revealing deep connections between topology and wave dynamics in diverse systems. The Pancharatnam\u2010Berry (PB) geometric phase, which arises from 2D optical polarization evolution, has revolutionized light manipulation by enabling optical metasurfaces. The PB phase is commonly regarded as a unique property of light waves. Generalizing this concept to other classical waves can uncover new geometric phase properties and enable novel wave control mechanisms. Here, the first observation of the PB phase in surface water (gravity) waves is reported, achieved through the interaction with symmetry\u2010engineered scatterers. In contrast to the optical PB phase, the water\u2010wave PB phase is an intrinsic higher\u2010order geometric phase induced by 4D evolution of spin\u2010orbit states. It exhibits remarkable properties, including unbounded phase values, spin\u2010momentum\u2010locked unidirectional channels, and a Poincar\u00e9 hypersphere representation. PB metasurfaces are further realized for versatile manipulation of water wavefronts, including steering and focusing. This work reveals the universality of the PB phase across different wave systems and generalizes it to higher\u2010dimensional state evolutions. The results open new avenues for exploring the geometric and topological properties of water waves, with potential applications in coastal protection and wave energy\u00a0harvesting.<\/jats:p>","DOI":"10.1002\/advs.202515337","type":"journal-article","created":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T02:53:14Z","timestamp":1760410394000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Water\u2010Wave Pancharatnam\u2010Berry Phase Induced by 4D Spin\u2010Orbit State Evolution"],"prefix":"10.1002","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8133-1941","authenticated-orcid":false,"given":"Wanyue","family":"Xiao","sequence":"first","affiliation":[{"name":"Department of Physics City University of Hong Kong Tat Chee Avenue, Kowloon Hong Kong 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