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Controlling Electromagnetic Surface Waves with Conformal Transformation Optics

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 cloaking 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.