  There has recently been considerable interest in the possibility, both
theoretical and practical, of invisibility (or "cloaking") from observation by
electromagnetic (EM) waves. Here, we prove invisibility, with respect to
solutions of the Helmholtz and Maxwell's equations, for several constructions
of cloaking devices. Previous results have either been on the level of ray
tracing [Le,PSS] or at zero frequency [GLU2,GLU3], but recent numerical [CPSSP]
and experimental [SMJCPSS] work has provided evidence for invisibility at
frequency $k\ne 0$. We give two basic constructions for cloaking a region $D$
contained in a domain $\Omega$ from measurements of Cauchy data of waves at $\p
\Omega$; we pay particular attention to cloaking not just a passive object, but
an active device within $D$, interpreted as a collection of sources and sinks
or an internal current.
