{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,26]],"date-time":"2026-08-26T08:08:04Z","timestamp":1787731684585,"version":"build-2784847793"},"reference-count":34,"publisher":"Optica Publishing Group","issue":"13","license":[{"start":{"date-parts":[[2022,6,6]],"date-time":"2022-06-06T00:00:00Z","timestamp":1654473600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/doi.org\/10.1364\/OA_License_v2#VOR-OA"},{"start":{"date-parts":[[2022,6,6]],"date-time":"2022-06-06T00:00:00Z","timestamp":1654473600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/opg.optica.org\/policies\/opg-tdm-policy.json"}],"funder":[{"DOI":"10.13039\/501100003453","name":"Natural Science Foundation of Guangdong Province","doi-asserted-by":"publisher","award":["2020A1515010786"],"award-info":[{"award-number":["2020A1515010786"]}],"id":[{"id":"10.13039\/501100003453","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Guangdong Rural Science and Technology Commissioner Project","award":["ktp20200112"],"award-info":[{"award-number":["ktp20200112"]}]},{"DOI":"10.13039\/501100021171","name":"Basic and Applied Basic Research Foundation of Guangdong Province","doi-asserted-by":"publisher","award":["2021A1515012215"],"award-info":[{"award-number":["2021A1515012215"]}],"id":[{"id":"10.13039\/501100021171","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["opg.optica.org"],"crossmark-restriction":false},"short-container-title":["Opt. Express"],"published-print":{"date-parts":[[2022,6,20]]},"abstract":"<jats:p>We theoretically propose and experimentally demonstrate a novel ultra-compact four-mode silicon waveguide crossing device based on the asymmetric directional couplers for densely integrated on-chip mode division multiplexing systems. The crossing is based on the parallel crossing scheme where the two access waveguides are parallel to each other to have minimal area. The device utilizes an idle high order mode inside one bus waveguide to drop subsequently all the guided modes inside another bus waveguide, with the help of the asymmetric directional couplers (ADCs). We also optimize the structural parameters of these ADCs by using the particle swarm optimization method to obtain higher conversion efficiency and smaller coupling length. The simulation results show that the insertion losses of the input 1-8 ports are no more than 0.5\u2005dB at the central wavelength of 1550\u2005nm. And the crosstalks are less than \u221220\u2005dB in the broadband from 1530\u2005nm to 1580\u2005nm with a footprint of only 25\u2009\u00d7\u200970\u2009\u00b5m<jats:sup>2<\/jats:sup>. Furthermore, our scheme can be easily extended to accommodate more modes by cascading more ADCs for mode dropping and crossing, without obviously deteriorating the performance and greatly increasing the overall footprint.<\/jats:p>","DOI":"10.1364\/oe.459968","type":"journal-article","created":{"date-parts":[[2022,5,27]],"date-time":"2022-05-27T11:00:13Z","timestamp":1653649213000},"page":"22442","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":25,"title":["Four-mode parallel silicon multimode waveguide crossing scheme based on the asymmetric directional couplers"],"prefix":"10.1364","volume":"30","author":[{"given":"Runsen","family":"Zhang","sequence":"first","affiliation":[{"name":"South China Normal University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shangsen","family":"Sun","sequence":"additional","affiliation":[{"name":"South China Normal University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fengchun","family":"Zhang","sequence":"additional","affiliation":[{"name":"South China Normal University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kaixuan","family":"Chen","sequence":"additional","affiliation":[{"name":"South China Normal University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3651-544X","authenticated-orcid":true,"given":"Liu","family":"Liu","sequence":"additional","affiliation":[{"name":"Zhejiang University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5413-2258","authenticated-orcid":true,"given":"Ning","family":"Zhu","sequence":"additional","affiliation":[{"name":"South China Normal University"},{"name":"SCNU Qingyuan Institute of Science and Technology Innovation Co., Ltd."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2022,6,6]]},"reference":[{"key":"oe-30-13-22442-R1","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1515\/nanoph-2013-0021","volume":"3","author":"Dai","year":"2014","journal-title":"Nanophotonics"},{"key":"oe-30-13-22442-R2","doi-asserted-by":"publisher","first-page":"L18","DOI":"10.1002\/lpor.201300157","volume":"8","author":"Wang","year":"2014","journal-title":"Laser Photonics Rev."},{"key":"oe-30-13-22442-R3","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1038\/s41598-018-36763-9","volume":"9","author":"Jiang","year":"2019","journal-title":"Sci. Rep."},{"key":"oe-30-13-22442-R4","doi-asserted-by":"publisher","first-page":"5746","DOI":"10.1109\/JLT.2018.2878529","volume":"36","author":"He","year":"2018","journal-title":"J. Lightwave Technol."},{"key":"oe-30-13-22442-R5","doi-asserted-by":"publisher","first-page":"3069","DOI":"10.1038\/ncomms4069","volume":"5","author":"Luo","year":"2014","journal-title":"Nat. Commun."},{"key":"oe-30-13-22442-R6","doi-asserted-by":"publisher","first-page":"10376","DOI":"10.1364\/OE.21.010376","volume":"21","author":"Ding","year":"2013","journal-title":"Opt. Express"},{"key":"oe-30-13-22442-R7","doi-asserted-by":"publisher","first-page":"530","DOI":"10.1364\/OPTICA.2.000530","volume":"2","author":"Stern","year":"2015","journal-title":"Optica"},{"key":"oe-30-13-22442-R8","doi-asserted-by":"publisher","first-page":"20698","DOI":"10.1364\/OE.25.020698","volume":"25","author":"Jia","year":"2017","journal-title":"Opt. Express"},{"key":"oe-30-13-22442-R9","doi-asserted-by":"publisher","first-page":"3004","DOI":"10.1364\/OL.42.003004","volume":"42","author":"Sun","year":"2017","journal-title":"Opt. Express"},{"key":"oe-30-13-22442-R10","doi-asserted-by":"publisher","first-page":"2100162","DOI":"10.1002\/lpor.202100162","volume":"15","author":"Sun","year":"2021","journal-title":"Laser Photonics Rev."},{"key":"oe-30-13-22442-R11","doi-asserted-by":"publisher","first-page":"29374","DOI":"10.1364\/OE.21.029374","volume":"21","author":"Ma","year":"2013","journal-title":"Opt. Express"},{"key":"oe-30-13-22442-R12","doi-asserted-by":"publisher","first-page":"2260","DOI":"10.1109\/LPT.2006.884726","volume":"18","author":"Chen","year":"2006","journal-title":"IEEE Photonics Technol. Lett."},{"key":"oe-30-13-22442-R13","doi-asserted-by":"publisher","first-page":"3608","DOI":"10.1364\/OL.38.003608","volume":"38","author":"Zhang","year":"2013","journal-title":"Opt. Express"},{"key":"oe-30-13-22442-R14","doi-asserted-by":"publisher","first-page":"16146","DOI":"10.1364\/OE.18.016146","volume":"18","author":"Bock","year":"2010","journal-title":"Opt. Express"},{"key":"oe-30-13-22442-R15","doi-asserted-by":"publisher","first-page":"659","DOI":"10.1038\/s41566-018-0246-9","volume":"12","author":"Molesky","year":"2018","journal-title":"Nat. Photonics"},{"key":"oe-30-13-22442-R16","doi-asserted-by":"publisher","first-page":"25602","DOI":"10.1364\/OE.26.025602","volume":"26","author":"Han","year":"2018","journal-title":"Opt. Express"},{"key":"oe-30-13-22442-R17","doi-asserted-by":"publisher","first-page":"5381","DOI":"10.1364\/OL.41.005381","volume":"41","author":"Xu","year":"2016","journal-title":"Opt. Express"},{"key":"oe-30-13-22442-R18","doi-asserted-by":"publisher","first-page":"14705","DOI":"10.1364\/OE.392445","volume":"28","author":"Wu","year":"2020","journal-title":"Opt. Express"},{"key":"oe-30-13-22442-R19","doi-asserted-by":"publisher","first-page":"7","DOI":"10.1038\/s41467-018-07761-2","volume":"10","author":"Liu","year":"2019","journal-title":"Nat. Commun."},{"key":"oe-30-13-22442-R20","doi-asserted-by":"publisher","first-page":"660","DOI":"10.1364\/PRJ.6.000660","volume":"6","author":"Chang","year":"2018","journal-title":"Photonics Res."},{"key":"oe-30-13-22442-R22","doi-asserted-by":"publisher","first-page":"042003","DOI":"10.35848\/1347-4065\/ac54fc","volume":"61","author":"Muratsubaki","year":"2022","journal-title":"Jpn. J. Appl. Phys."},{"key":"oe-30-13-22442-R24","doi-asserted-by":"publisher","first-page":"1549","DOI":"10.1364\/OPTICA.5.001549","volume":"5","author":"Li","year":"2018","journal-title":"Optica"},{"key":"oe-30-13-22442-R25","doi-asserted-by":"publisher","first-page":"1800094","DOI":"10.1002\/lpor.201800094","volume":"12","author":"Xu","year":"2018","journal-title":"Laser Photonics Rev."},{"key":"oe-30-13-22442-R26","doi-asserted-by":"publisher","first-page":"2437","DOI":"10.1364\/JOSAB.392644","volume":"37","author":"Badri","year":"2020","journal-title":"J. Opt. Soc. Am. B"},{"key":"oe-30-13-22442-R27","doi-asserted-by":"publisher","first-page":"4913","DOI":"10.1364\/OL.42.004913","volume":"42","author":"Sun","year":"2017","journal-title":"Opt. Express"},{"key":"oe-30-13-22442-R28","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1109\/JPHOT.2018.2847762","volume":"10","author":"Chang","year":"2018","journal-title":"IEEE Photonics J."},{"key":"oe-30-13-22442-R29","doi-asserted-by":"publisher","first-page":"2264","DOI":"10.1364\/AO.58.002264","volume":"58","author":"Huang","year":"2019","journal-title":"Appl. Opt."},{"key":"oe-30-13-22442-R30","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1109\/JPHOT.2020.3046361","volume":"13","author":"Chen","year":"2021","journal-title":"IEEE Photonics J."},{"key":"oe-30-13-22442-R31","doi-asserted-by":"publisher","first-page":"30701","DOI":"10.1364\/OE.408432","volume":"28","author":"Chen","year":"2020","journal-title":"Opt. Express"},{"key":"oe-30-13-22442-R32","doi-asserted-by":"publisher","first-page":"1310","DOI":"10.1364\/OE.21.001310","volume":"21","author":"Zhang","year":"2013","journal-title":"Opt. Express"},{"key":"oe-30-13-22442-R33","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1109\/JPHOT.2019.2941742","volume":"11","author":"Shu","year":"2019","journal-title":"IEEE Photonics J."},{"key":"oe-30-13-22442-R34","doi-asserted-by":"publisher","first-page":"20021","DOI":"10.1364\/OE.20.020021","volume":"20","author":"Ding","year":"2012","journal-title":"Opt. Express"},{"key":"oe-30-13-22442-R35","doi-asserted-by":"publisher","first-page":"6069","DOI":"10.1364\/OE.25.006069","volume":"25","author":"Wu","year":"2017","journal-title":"Opt. Express"},{"key":"oe-30-13-22442-R36","doi-asserted-by":"publisher","first-page":"151101","DOI":"10.1063\/1.3579243","volume":"98","author":"Lin","year":"2011","journal-title":"Appl. Phys. Lett."}],"container-title":["Optics Express"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/opg.optica.org\/viewmedia.cfm?URI=oe-30-13-22442&seq=0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,6]],"date-time":"2024-08-06T19:29:11Z","timestamp":1722972551000},"score":1,"resource":{"primary":{"URL":"https:\/\/opg.optica.org\/abstract.cfm?URI=oe-30-13-22442"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,6,6]]},"references-count":34,"journal-issue":{"issue":"13","published-online":{"date-parts":[[2022]]},"published-print":{"date-parts":[[2022]]}},"URL":"https:\/\/doi.org\/10.1364\/oe.459968","relation":{},"ISSN":["1094-4087"],"issn-type":[{"value":"1094-4087","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,6,6]]},"assertion":[{"value":"Optica Publishing Group","name":"publisher","label":"This article is maintained by"},{"value":"https:\/\/doi.org\/10.1364\/OE.459968","name":"articlelink","label":"Crossref DOI link to publisher maintained version"},{"value":"research-article","name":"content_type","label":"Article type"},{"value":"Screened by Similarity Check","name":"cross_check","label":"Similarity check"},{"value":"Yes","order":0,"name":"peer_reviewed","label":"Peer reviewed","group":{"name":"peer_review","label":"Peer review"}},{"value":"Single blind","order":1,"name":"review_process","label":"Review process","group":{"name":"peer_review","label":"Peer review"}},{"value":"31 March 2022","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"25 May 2022","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"6 June 2022","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}},{"value":"\u00a9 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement","name":"copyright","label":"Copyright"}]}}