{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,29]],"date-time":"2026-03-29T21:44:40Z","timestamp":1774820680446,"version":"3.50.1"},"reference-count":99,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2019,10,28]],"date-time":"2019-10-28T00:00:00Z","timestamp":1572220800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["17K17777"],"award-info":[{"award-number":["17K17777"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["17K05075."],"award-info":[{"award-number":["17K05075."]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In electromagnetic systems, duality is manifested in various forms: circuit, Keller\u2013Dykhne, electromagnetic, and Babinet dualities. These dualities have been developed individually in different research fields and frequency regimes, leading to a lack of unified perspective. In this paper, we establish a unified view of these dualities in electromagnetic systems. The underlying geometrical structures behind the dualities are elucidated by using concepts from algebraic topology and differential geometry. Moreover, we show that seemingly disparate phenomena, such as frequency-independent effective response, zero backscattering, and critical response, can be considered to be emergent phenomena of self-duality.<\/jats:p>","DOI":"10.3390\/sym11111336","type":"journal-article","created":{"date-parts":[[2019,10,28]],"date-time":"2019-10-28T11:26:13Z","timestamp":1572261973000},"page":"1336","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Geometric Structure behind Duality and Manifestation of Self-Duality from Electrical Circuits to Metamaterials"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4629-5134","authenticated-orcid":false,"given":"Yosuke","family":"Nakata","sequence":"first","affiliation":[{"name":"Research Center for Advanced Science and Technology, The University of Tokyo, Meguro-ku, Tokyo 153-8904, Japan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6580-5497","authenticated-orcid":false,"given":"Yoshiro","family":"Urade","sequence":"additional","affiliation":[{"name":"Center for Emergent Matter Science, RIKEN, Wako, Saitama 351-0198, Japan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6010-7318","authenticated-orcid":false,"given":"Toshihiro","family":"Nakanishi","sequence":"additional","affiliation":[{"name":"Department of Electronic Science and Engineering, Kyoto University, Kyoto 615-8510, Japan"}]}],"member":"1968","published-online":{"date-parts":[[2019,10,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1117","DOI":"10.1063\/1.1704215","article-title":"Exact Critical Percolation Probabilities for Site and Bond Problems in Two Dimensions","volume":"5","author":"Sykes","year":"1964","journal-title":"J. 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