  This paper is concerned with the invisibility cloaking in electromagnetic
wave scattering from a new perspective. We are especially interested in
achieving the invisibility cloaking by completely regular and isotropic
mediums. Our study is based on an interior transmission eigenvalue problem. We
propose a cloaking scheme that takes a three-layer structure including a
cloaked region, a lossy layer and a cloaking shell. The target medium in the
cloaked region can be arbitrary but regular, whereas the mediums in the lossy
layer and the cloaking shell are both regular and isotropic. We establish that
there exists an infinite set of incident waves such that the cloaking device is
nearly-invisible under the corresponding wave interrogation. The set of waves
is generated from the Maxwell-Herglotz approximation of the associated interior
transmission eigenfunctions. We provide the mathematical design of the cloaking
device and sharply quantify the cloaking performance.
