  Transformation optics constructions have allowed the design of cloaking
devices that steer electromagnetic, acoustic and quantum waves around a region
without penetrating it, so that this region is hidden from external
observations. The proposed material parameters are anisotropic, and singular at
the interface between the cloaked region and the cloaking device. The presence
of these singularities causes various mathematical problems and physical
effects on the interface surface. In this paper, we analyze the 3-dimensional
cloaking for Maxwell's equations when there are sources or sinks present inside
the cloaked region. In particular, we consider nonsingular approximate
invisibility cloaks based on the truncation of the singular transformations. We
analyze the limit of solutions when the approximate cloaking approaches the
ideal cloaking in the sense of distributions. We show that the solutions in the
approximate cloaks converge to a distribution that contains Dirac's delta
distribution supported on the interface surface. In particular, this implies
that the limit of solutions are not measurable functions, making them outside
of those classes of functions that have earlier been used in the models of the
ideal invisibility cloaks. Also, we give a rigorous meaning for the
"extraordinary surface voltage effect" considered in physical literature of
invisibility cloaks.
