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Express"],"published-print":{"date-parts":[[2026,1,26]]},"abstract":"<jats:p>Waveguide lenses based on mosaic structure are proposed and experimentally demonstrated. The devices are designed by an adjoint method based on the finite-element method (AM-FEM). In AM-FEM, it is easy to calculate the gradient of the objective function with respect to the refractive index distribution, and it is especially useful for multi-port and multi-mode problems. First, to demonstrate the effectiveness of the AM-FEM, simple 1\u2009\u00d7\u20092 power splitters are designed, and the importance of the initial structure is demonstrated together with experimental results. And then, the design of single-mode waveguide lenses is demonstrated. After passing through the mosaic lens, the wavefront of the light is aligned, and the light can traverse a slab region, which has no confinement mechanism in the transverse direction. Also, multimode waveguide lenses are presented for the first time, showing low-loss and almost wavelength-independent characteristics. The designed devices are fabricated, and the measured results are in good agreement with the theory. These devices can be useful for various wavefront controlling devices.<\/jats:p>","DOI":"10.1364\/oe.584131","type":"journal-article","created":{"date-parts":[[2026,1,2]],"date-time":"2026-01-02T06:00:08Z","timestamp":1767333608000},"page":"2047","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Mosaic-based waveguide lenses designed by the adjoint method based on the finite-element scheme"],"prefix":"10.1364","volume":"34","author":[{"given":"Takeshi","family":"Fujisawa","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00bx6dj65","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5213-6522","authenticated-orcid":true,"given":"Yasuhide","family":"Tsuji","sequence":"additional","affiliation":[{"name":"Muroran Institute of Technology"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Takuya","family":"Mitarai","sequence":"additional","affiliation":[{"name":"Transmission Devices Laboratory"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yusuke","family":"Sawada","sequence":"additional","affiliation":[{"name":"Transmission Devices Laboratory"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Takuya","family":"Okimoto","sequence":"additional","affiliation":[{"name":"Transmission Devices Laboratory"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Takuo","family":"Hiratani","sequence":"additional","affiliation":[{"name":"Transmission Devices Laboratory"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7818-5461","authenticated-orcid":true,"given":"Kento","family":"Komatsu","sequence":"additional","affiliation":[{"name":"Transmission Devices Laboratory"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hideki","family":"Yagi","sequence":"additional","affiliation":[{"name":"Transmission Devices Laboratory"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Naoki","family":"Fujiwara","sequence":"additional","affiliation":[{"name":"Transmission Devices Laboratory"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2026,1,15]]},"reference":[{"key":"oe-34-2-2047-R2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1109\/JSTQE.2018.2819893","type":"journal-article","volume":"24","author":"Horikawa","year":"2018","journal-title":"IEEE J. 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