Controlling electromagnetic surface waves with conformal transformation optics

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