  We extend the design of radially symmetric three-dimensional invisibility
cloaks through transformation optics to cloaks with a surface of revolution. We
derive the expression of the transformation matrix and show that one of its
eigenvalues vanishes on the inner boundary of the cloaks, while the other two
remain strictly positive and bounded. The validity of our approach is confirmed
by finite edge-elements computations for a non-convex cloak of varying
thickness.
