  The intriguing concept of "anti-cloaking" has been recently introduced within
the framework of transformation optics (TO), first as a "countermeasure" to
invisibility-cloaking (i.e., to restore the scattering response of a cloaked
target), and more recently in connection with "sensor invisibility" (i.e., to
strongly reduce the scattering response while maintaining the field-sensing
capabilities). In this paper, we extend our previous studies, which were
limited to a two-dimensional cylindrical scenario, to the three-dimensional
spherical case. More specifically, via a generalized (coordinate-mapped)
Mie-series approach, we derive a general analytical full-wave solution
pertaining to plane-wave-excited configurations featuring a spherical object
surrounded by a TO-based invisibility cloak coupled via a vacuum layer to an
anti-cloak, and explore the various interactions of interest. With a number of
selected examples, we illustrate the cloaking and field-restoring capabilities
of various configurations, highlighting similarities and differences with
respect to the cylindrical case, with special emphasis on sensor-cloaking
scenarios and ideas for approximate implementations that require the use of
double-positive media only.
