Conventional mirrors obey Snells 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.
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