Necessary and sufficient conditions for reflectionless transformation media in an isotropic and homogenous background

Abstract

It has been known that, keeping the outer boundary coordinates intact before and after a coordinate transformation is a sufficient condition for obtaining a reflectionless transformation medium. Here we prove that it is also a necessary condition for reflectionless transformation media in an isotropic and homogenous background. Our analytical results show that the outer boundary coordinates of a reflectionless transformation medium must be the same as the original coordinates with a combination of rotation and displacement, which is equivalent to situation that the boundary coordinates are kept intact before and after transformation.

9 pages, 4 figures

References in corpus (2)

• Cylindrical Superlens by a Coordinate Transformation
• Effectiveness and improvement of cylindrical cloaking with the SHS lining

Cited by in corpus (5)

• A complementary media invisibility cloak that can cloak objects at a distance outside the cloaking shell
• A General Class of Metamaterial Transformation Slabs
• Electromagnetic fields and boundary conditions at the interface of generalized transformation media
• Watching outside while under a carpet cloak of invisibility
• Inverse Transformation Optics and Reflection Analysis for Two-Dimensional Finite Embedded Coordinate Transformation