Analysis of the equivalent scattering properties of a target embedded in transformation media

Transformation electromagnetics reveals that electromagnetic fields can be manipulated in almost any desired manner using specially tailored transformation media. The equivalent scattering property of an arbitrary target changes when it is embedded in such media. This study focuses on this phenomenon and provides a general description that any target embedded in transformation media can map to another object in free space through inverse spatial transformation. The structure and material parameters of the free object are analyzed in detail. A field expander is then obtained as a specific example to demonstrate that the embedded target and the corresponding free object have the same scattering pattern. A cloak with a fissure in the shell is also used to illustrate that the said equivalent scattering is helpful in designing illusion devices and in rigorously evaluating the deviation of scattering cross-section caused by the imperfect structures or parameters of the systems.