  In this paper, we propose a novel electromagnetic (EM) cloaking structure
that consists of two annular layers between three spherical shells and model
its performance numerically and theoretically by using a Global and Local EM
field (GL) method. The two annular layers contain distinct cloaking materials:
the outer layer provides invisibility; the inner layer is fully absorbing. The
cloaking materials are weakly degenerative. The wavefield from an EM source
located outside the cloak propagates as in free space outside the outer shell,
never be disturbed by the cloak and does not penetrate into the inner absorbing
layer and concealment.
  The field of a source located inside inner layer or the cloaked concealment
is completely absorbed by the inner layer and never reaches the outside of the
middle shell, Moreover, the EM wavefield excited in concealment is not
disrupted by the cloak. There exists no Maxwell EM wavefield can be excited in
a single layer cloaked concealment which is filled by normal material.
Moreover, we find a negative dielectric and positive susceptibility
metamaterial to fill into the concealment, such that the interior EM wave
propagates from the concealment to free space through the single layer cloak.
Therefore, the double layer cloak is important and necessary for complete
invisibility. Numerical simulations and theoretical analysis verifying these
properties are performed using the GL EM modeling method that we described in
this paper.
