Controlling electromagnetic surface waves with conformal transformation optics

• Published in: Communications physics Vol. 6; no. 1; pp. 201 - 8
• Main Authors: Zhao, Xiaoyu, Deng, Hong, Gao, Xiaoke, Ma, Xikui, Dong, Tianyu
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 05.08.2023; Nature Publishing Group; Nature Portfolio
• Subjects: 639/624/400/1105; 639/766/400/1105; Anisotropic media; Anisotropy; Conformal mapping; Coordinate transformations; Electromagnetic radiation; Electromagnetic surface waves; Euclidean space; Illusions; Isotropic media; Optical illusions; Optics; Parameterization; Physics; Physics and Astronomy; Surface waves; Transformations
• ISSN: 2399-3650; 2399-3650
• DOI: 10.1038/s42005-023-01322-w

The application of transformation optics to the development of intriguing electromagnetic devices can produce weakly anisotropic or isotropic media with the assistance of quasi-conformal and/or conformal mapping, as opposed to the strongly anisotropic media produced by general mappings; however, it is typically limited to two-dimensional applications. By addressing the conformal mapping between two manifolds embedded in three-dimensional space, we demonstrate that electromagnetic surface waves can be controlled without introducing singularity and anisotropy into the device parameters. Using fruitful surface conformal parameterization methods, a near-perfect conformal mapping between smooth manifolds with arbitrary boundaries can be obtained. Illustrations of concealing and illusions, including surface Luneburg and Eaton lenses and black holes for surface waves, are provided. Our work brings the manipulation of surface waves at microwave and optical wavelengths one step closer. Transformation optics has shown a powerful way in controlling the light flow. This study provides the conformal mapping between two manifolds embedded in three-dimensional space, enabling the control of surface electromagnetic waves on arbitrary two-dimensional manifold and potentially extends to other fields such as acoustics, mechanics, and thermodynamics.