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Open AccessArticle

Geometric Structure behind Duality and Manifestation of Self-Duality from Electrical Circuits to Metamaterials

1
Research Center for Advanced Science and Technology, The University of Tokyo, Meguro-ku, Tokyo 153-8904, Japan
2
Center for Emergent Matter Science, RIKEN, Wako, Saitama 351-0198, Japan
3
Department of Electronic Science and Engineering, Kyoto University, Kyoto 615-8510, Japan
*
Author to whom correspondence should be addressed.
Current address: Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan.
Symmetry 2019, 11(11), 1336; https://doi.org/10.3390/sym11111336
Received: 31 August 2019 / Revised: 6 October 2019 / Accepted: 14 October 2019 / Published: 28 October 2019
(This article belongs to the Special Issue Duality Symmetry)
In electromagnetic systems, duality is manifested in various forms: circuit, Keller–Dykhne, 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. View Full-Text
Keywords: duality; self-duality; Poincaré duality; circuit duality; Keller–Dykhne duality; electromagnetic duality; Babinet’s principle; constant-resistance circuit; zero backscattering; critical response; self-complementary antenna; metamaterials; metasurfaces duality; self-duality; Poincaré duality; circuit duality; Keller–Dykhne duality; electromagnetic duality; Babinet’s principle; constant-resistance circuit; zero backscattering; critical response; self-complementary antenna; metamaterials; metasurfaces
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MDPI and ACS Style

Nakata, Y.; Urade, Y.; Nakanishi, T. Geometric Structure behind Duality and Manifestation of Self-Duality from Electrical Circuits to Metamaterials. Symmetry 2019, 11, 1336.

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