Fourier optics theory for invisibility cloaks

Currently, the most popular method for technically obtaining the geometric and electromagnetic parameters of invisibility cloaks is mainly based upon transformation optics. In this paper, by introducing transfer functions to elucidate the roles of the invisibility cloaks played on angular spectrum of the objects, we present an optical imaging theory to unify both Pendry cloaks and complementary media-based invisibility cloaks. The theory can not only give an analytical insight into the physical mechanism behind the invisibility cloaks and perfect lenses in hiding objects, creating illusions, and performing perfect imaging, but also provide a way for getting the electromagnetic parameters of the systems. The results are strictly of consistence with that obtained from transformation optics, confirming the validity of our Fourier optics theory. (C) 2011 Optical Society of America