{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,29]],"date-time":"2026-10-29T05:24:40Z","timestamp":1793251480699,"version":"4.5.0"},"reference-count":70,"publisher":"American Chemical Society (ACS)","issue":"18","license":[{"start":{"date-parts":[[2026,9,2]],"date-time":"2026-09-02T00:00:00Z","timestamp":1788307200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100019180","name":"HORIZON EUROPE European Research Council","doi-asserted-by":"publisher","award":["101116984"],"award-info":[{"award-number":["101116984"]}],"id":[{"id":"10.13039\/100019180","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003246","name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","doi-asserted-by":"publisher","award":["VI.Vidi.203.027"],"award-info":[{"award-number":["VI.Vidi.203.027"]}],"id":[{"id":"10.13039\/501100003246","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,9,16]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Metasurfaces leveraging nonlocal resonances enable narrowband spectral control and strong near-fields, with applications spanning augmented reality, biosensing, and nonlinear optics. However, the large spatial extent of these modes also poses new challenges: finite-size effects often deteriorate the performance of practical, footprint-limited devices. Here, we develop a spatiotemporal coupled-mode theory model that intuitively and quantitatively captures how finite size affects the scattering response of nonlocal metasurfaces. This reveals that, when the modal propagation length becomes constrained by the physical interaction length, the scattered field shows strong interference fringes and line width broadening. We derive an expression for the quality factor that incorporates an additional edge-loss channel, demonstrating that the stored energy and effective lifetime scale exponentially with the interaction length. We validate these predictions experimentally using position- and momentum-resolved spectroscopy on a 30-\u03bcm-wide metasurface. Overall, this work formalizes the impact of finite size on the scattering response of nonlocal photonic systems, and provides handles on how to minimize the impact of finite-size effects in metasurface design.<\/jats:p>","DOI":"10.1021\/acsphotonics.6c00860","type":"journal-article","created":{"date-parts":[[2026,9,3]],"date-time":"2026-09-03T17:34:35Z","timestamp":1788456875000},"page":"5337-5346","source":"Crossref","is-referenced-by-count":1,"title":["Finite-Size\nEffects in Nonlocal Metasurfaces"],"prefix":"10.1021","volume":"13","author":[{"given":"Tom","family":"Hoekstra","sequence":"first","affiliation":[{"name":"University of Amsterdam , , ,","place":["Amsterdam, The Netherlands, 1098 XH"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sander A.","family":"Mann","sequence":"additional","affiliation":[{"name":"University of Amsterdam , , ,","place":["Amsterdam, The Netherlands, 1098 XH"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3033-8005","authenticated-orcid":true,"given":"Jorik","family":"van de Groep","sequence":"additional","affiliation":[{"name":"University of Amsterdam , , ,","place":["Amsterdam, The Netherlands, 1098 XH"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"316","published-online":{"date-parts":[[2026,9,2]]},"reference":[{"key":"2026091609101276700_cit1","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1038\/nmat3839","article-title":"Flat Optics with Designer Metasurfaces","volume":"13","author":"Yu","year":"2014","journal-title":"Nat. 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Nanotechnol."},{"key":"2026091609101276700_cit6","doi-asserted-by":"publisher","first-page":"188","DOI":"10.1038\/nature12289","article-title":"Observation of Trapped\nLight within the Radiation Continuum","volume":"499","author":"Hsu","year":"2013","journal-title":"Nature"},{"key":"2026091609101276700_cit7","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.121.193903","article-title":"Asymmetric\nMetasurfaces with High-$Q$ Resonances Governed by Bound States in\nthe Continuum","volume":"121","author":"Koshelev","year":"2018","journal-title":"Phys. Rev. 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Commun."},{"key":"2026091609101276700_cit37","doi-asserted-by":"publisher","first-page":"4081","DOI":"10.1016\/j.physb.2012.03.053","article-title":"Collective\nResonances in Plasmonic Crystals: Size Matters","volume":"407","author":"Rodriguez","year":"2012","journal-title":"Phys. B"},{"key":"2026091609101276700_cit38","doi-asserted-by":"publisher","DOI":"10.1364\/OE.21.023640","article-title":"Finite-Size Limitations on Quality Factor of Guided\nResonance Modes in 2D Photonic Crystals","volume":"21","author":"Grepstad","year":"2013","journal-title":"Opt.\nExpress"},{"key":"2026091609101276700_cit39","doi-asserted-by":"publisher","DOI":"10.1038\/ncomms6753","article-title":"All-Dielectric\nMetasurface Analogue of Electromagnetically Induced Transparency","volume":"5","author":"Yang","year":"2014","journal-title":"Nat. Commun."},{"key":"2026091609101276700_cit40","doi-asserted-by":"publisher","DOI":"10.1088\/2515-7647\/aae8a2","article-title":"Finite-Size Effects on Periodic Arrays of Nanostructures","volume":"1","author":"Zundel","year":"2019","journal-title":"J. Phys.: Photonics"},{"key":"2026091609101276700_cit41","doi-asserted-by":"publisher","DOI":"10.1063\/1.4990753","article-title":"Quasi Bound States in the Continuum\nwith Few Unit Cells\nof Photonic Crystal Slab","volume":"111","author":"Taghizadeh","year":"2017","journal-title":"Appl. Phys. Lett."},{"key":"2026091609101276700_cit42","doi-asserted-by":"publisher","first-page":"3788","DOI":"10.1021\/acsphotonics.8b00835","article-title":"Finite-Size Effects in Metasurface\nLasers Based on Resonant Dark States","volume":"5","author":"Droulias","year":"2018","journal-title":"ACS Photonics"},{"key":"2026091609101276700_cit43","doi-asserted-by":"publisher","DOI":"10.1364\/JOSAA.7.001470","article-title":"Guided-Mode Resonances\nin Planar Dielectric-Layer Diffraction Gratings","volume":"7","author":"Wang","year":"1990","journal-title":"J. Opt. Soc. Am. A"},{"key":"2026091609101276700_cit44","doi-asserted-by":"publisher","DOI":"10.1364\/AO.32.002606","article-title":"Theory and Applications of Guided-Mode Resonance Filters","volume":"32","author":"Wang","year":"1993","journal-title":"Appl. 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Phys."},{"key":"2026091609101276700_cit51","doi-asserted-by":"publisher","DOI":"10.1364\/JOSAA.21.000981","article-title":"Effect\nof Finite Grating, Waveguide\nWidth, and End-Facet Geometry on Resonant Subwavelength Grating Reflectivity","volume":"21","author":"Peters","year":"2004","journal-title":"J. Opt. Soc. Am. A"},{"key":"2026091609101276700_cit52","doi-asserted-by":"publisher","first-page":"6567","DOI":"10.1364\/AO.48.006567","article-title":"Optimizing\nthe spatial resolution of photonic crystal label-free imaging","volume":"48","author":"Block","year":"2009","journal-title":"Appl. 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Optoelectron."},{"key":"2026091609101276700_cit59","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.109.115436","article-title":"Resonances\nin Finite-Size All-Dielectric\nMetasurfaces for Light Trapping and Propagation Control","volume":"109","author":"Ustimenko","year":"2024","journal-title":"Phys. Rev. B"},{"key":"2026091609101276700_cit60","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevResearch.7.013316","article-title":"Collective Nature\nof High-Q Resonances in Finite-Size\nPhotonic Metastructures","volume":"7","author":"Hoang","year":"2025","journal-title":"Phys. Rev. Res."},{"key":"2026091609101276700_cit61","doi-asserted-by":"publisher","DOI":"10.1364\/OE.23.019234","article-title":"Spatiotemporal\nCoupled-Mode Theory of Guided-Mode Resonant\nGratings","volume":"23","author":"Bykov","year":"2015","journal-title":"Opt. 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