{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T05:00:06Z","timestamp":1787029206477,"version":"build-2736575974"},"reference-count":59,"publisher":"MDPI AG","issue":"14","license":[{"start":{"date-parts":[[2023,7,23]],"date-time":"2023-07-23T00:00:00Z","timestamp":1690070400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12274031"],"award-info":[{"award-number":["12274031"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2022CX01006"],"award-info":[{"award-number":["2022CX01006"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Beijing Institute of Technology Research Fund Program","award":["12274031"],"award-info":[{"award-number":["12274031"]}]},{"name":"Beijing Institute of Technology Research Fund Program","award":["2022CX01006"],"award-info":[{"award-number":["2022CX01006"]}]},{"name":"Beijing Institute of Technology Science and Technology Innovation Plan Innovative Talents Science and Technology Funding Special Plan","award":["12274031"],"award-info":[{"award-number":["12274031"]}]},{"name":"Beijing Institute of Technology Science and Technology Innovation Plan Innovative Talents Science and Technology Funding Special Plan","award":["2022CX01006"],"award-info":[{"award-number":["2022CX01006"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Nanomaterials"],"abstract":"<jats:p>Integrated frequency routers, which can guide light with different frequencies to different output ports, are an important kind of nanophotonic device. However, frequency routers with both a compact size and multiple channels are difficult to realize, which limits the application of these frequency routers in nanophotonics. Here, a kind of bandgap optimization algorithm, which consists of the finite element method and topology optimization, is proposed to design a multi-channel frequency router. Channels supporting photonic edge states with different frequencies are built through the synthetic dimension of translational deformation. Due to the help of the developed optimization algorithms, the number of channels and output ports can be increased up to nine while maintaining ultracompact device size. The device operates within a working band of 0.585\u20130.665 c\/a, corresponding to 1.504\u20131.709 \u03bcm when the lattice constant is set as 1 \u03bcm, covering the telecom wavelength of 1.55 \u03bcm. The average crosstalk is about \u221211.49 dB. The average extinction ratio is around 16.18 dB. Because the bus of the device can be regarded as a part of a topological rainbow, the results show that the structure is robust to fabrication errors. This method is general, which can be used for different materials and different frequency ranges. The all-dielectric planar configuration of our router is compact, robust, and easy to integrate, providing a new method for on-chip multi-channel broadband information processing.<\/jats:p>","DOI":"10.3390\/nano13142133","type":"journal-article","created":{"date-parts":[[2023,7,24]],"date-time":"2023-07-24T01:08:11Z","timestamp":1690160891000},"page":"2133","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["A Multi-Channel Frequency Router Based on an Optimization Algorithm and Dispersion Engineering"],"prefix":"10.3390","volume":"13","author":[{"given":"Hongyi","family":"Yuan","sequence":"first","affiliation":[{"name":"Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurements of Ministry of Education, Beijing Key Laboratory of Nanophotonics and Ultrafine Optoelectronic Systems, School of Physics, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nianen","family":"Zhang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurements of Ministry of Education, Beijing Key Laboratory of Nanophotonics and Ultrafine Optoelectronic Systems, School of Physics, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hongyu","family":"Zhang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurements of Ministry of Education, Beijing Key Laboratory of Nanophotonics and Ultrafine Optoelectronic Systems, School of Physics, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7789-1946","authenticated-orcid":false,"given":"Cuicui","family":"Lu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurements of Ministry of Education, Beijing Key Laboratory of Nanophotonics and Ultrafine Optoelectronic Systems, School of Physics, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"507","DOI":"10.1515\/nanoph-2016-0145","article-title":"Digital Optical Processing of Optical Communications: Towards an Optical Turing Machine","volume":"6","author":"Touch","year":"2017","journal-title":"Nanophotonics"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1267","DOI":"10.1016\/j.scib.2018.05.038","article-title":"On-Chip Silicon Photonic Signaling and Processing: A Review","volume":"63","author":"Wang","year":"2018","journal-title":"Sci. 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