  Conventional mirrors obey Snell's reflection law: a plane wave is reflected
as a plane wave, at the same angle. To engineer spatial distributions of fields
reflected from a mirror, one can either shape the reflector (for example,
creating a parabolic reflector) or position some phase-correcting elements on
top of a mirror surface (for example, designing a reflectarray antenna). Here
we show, both theoretically and experimentally, that full-power reflection with
general control over reflected wave phase is possible with a single-layer array
of deeply sub-wavelength inclusions. These proposed artificial surfaces,
metamirrors, provide various functions of shaped or nonuniform reflectors
without utilizing any mirror. This can be achieved only if the forward and
backward scattering of the inclusions in the array can be engineered
independently, and we prove that it is possible using electrically and
magnetically polarizable inclusions. The proposed sub-wavelength inclusions
possess desired reflecting properties at the operational frequency band, while
at other frequencies the array is practically transparent. The metamirror
concept leads to a variety of applications over the entire electromagnetic
spectrum, such as optically transparent focusing antennas for satellites,
multi-frequency reflector antennas for radio astronomy, low-profile conformal
antennas for telecommunications, and nano-reflectarray antennas for integrated
optics.
