{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,13]],"date-time":"2026-09-13T18:03:50Z","timestamp":1789322630601,"version":"build-2803163510"},"reference-count":38,"publisher":"Wiley","issue":"15","license":[{"start":{"date-parts":[[2026,7,28]],"date-time":"2026-07-28T00:00:00Z","timestamp":1785196800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2026,7,28]],"date-time":"2026-07-28T00:00:00Z","timestamp":1785196800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62405308"],"award-info":[{"award-number":["62405308"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Nanophotonics"],"published-print":{"date-parts":[[2026,8,13]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>Heterogeneous integration of III\u2013V lasers on silicon is pivotal for scaling next\u2010generation photonic systems, yet it faces a fundamental bottleneck: the inherent trade\u2010off between coupler compactness and misalignment tolerance. In this work, we break this longstanding barrier by combining multi\u2010start adjoint optimization with a physics\u2010guided strategy that places dense control points in near\u2010phase\u2010matched regions. This approach produces a more extended phase\u2010near\u2010matched region that spatially overlaps with the region of controlled odd supermode excitation, which is the key condition for simultaneously achieving compactness and tolerance. Our design achieves 98.11% coupling efficiency within a footprint of just 20\u00a0\u03bcm. Remarkably, it sustains over 80% efficiency under substantial misalignments up to\u00a0\u00b1\u00a01.1\u00a0\u03bcm and waveguide width variations of\u00a0\u00b1\u00a00.4\u00a0\u03bcm\u2014representing the highest tolerance per unit length reported for vertical III\u2013V\u2010on\u2010silicon couplers. This achievement decouples the traditional conflict between size and robustness, offering a critical solution for high\u2010yield micro\u2010transfer printing and dense photonic integration. The successful extension of our optimization framework to the lithium niobate\u2010on\u2010silicon nitride platform confirms its generality, positioning it as a versatile and transformative design strategy for a broad range of heterogeneous photonic platforms.<\/jats:p>","DOI":"10.1002\/nap2.70211","type":"journal-article","created":{"date-parts":[[2026,7,28]],"date-time":"2026-07-28T07:14:48Z","timestamp":1785222888000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Breaking the Size\u2010Tolerance Trade\u2010off in Vertical Couplers via Adjoint\u2010Based Inverse Design"],"prefix":"10.1002","volume":"15","author":[{"given":"Ruiqi","family":"Liu","sequence":"first","affiliation":[{"name":"Nanometer Optoelectronics Lab Institute of Semiconductors, Chinese Academy of Sciences  Beijing China"},{"name":"College of Materials Science and Opto\u2010Electronic Technology University of Chinese Academy of Sciences  Beijing 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Optoelectronics Lab Institute of Semiconductors, Chinese Academy of Sciences  Beijing China"},{"name":"College of Materials Science and Opto\u2010Electronic Technology University of Chinese Academy of Sciences  Beijing China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Haiyang","family":"Yu","sequence":"additional","affiliation":[{"name":"Nanometer Optoelectronics Lab Institute of Semiconductors, Chinese Academy of Sciences  Beijing China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2226-5897","authenticated-orcid":false,"given":"Yulian","family":"Cao","sequence":"additional","affiliation":[{"name":"Nanometer Optoelectronics Lab Institute of Semiconductors, Chinese Academy of Sciences  Beijing 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