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Volumes of sub-wavelength electromagnetic elements can act like homogeneousmaterials: metamaterials. In analogy, sheets of optical elements such as prismscan act ray-optically like homogeneous sheet materials. In this sense, suchsheets can be considered to be metamaterials for light rays (METATOYs).METATOYs realize new and unusual transformations of the directions oftransmitted light rays. We study here, in the ray-optics and scalar-wavelimits, the wave-optical analog of such transformations, and we show that suchan analog does not always exist. Perhaps, this is the reason why many of theray-optical possibilities offered by METATOYs have never before beenconsidered.

Metamaterials for light rays: ray optics without wave-optical analog in the ray-optics limit