Theory and design of perfect invisibility devices

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Rapid progress in metamaterial sciences has made it possible to design cloaking devices that are able to guide electromagnetic fields around any object put inside has captured the attention of many researchers. In this research, we propose a novel method that uses three successive conformal maps and a combination of positive and negative refraction indices to enclose the trajectory of light rays. We show that our construction enables us not only to enclose the trajectory of light, but also to achieve perfect invisibility in isotropic media, without both phase delay and reflection.