학술논문

Geometric Structure behind Duality and Manifestation of Self-Duality from Electrical Circuits to Metamaterials
Document Type
article
Source
Symmetry, Vol 11, Iss 11, p 1336 (2019)
Subject
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
Mathematics
QA1-939
Language
English
ISSN
2073-8994
Abstract
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.