  Control of electromagnetic waves using engineered materials is very important
in a wide range of applications, therefore there is always a continuous need
for new and more efficient solutions. Known natural and artificial materials
and surfaces provide a particular functionality in the frequency range they
operate but cast a "shadow" and produce reflections at other frequencies. Here,
we introduce a concept of multifunctional engineered materials that possess
different predetermined functionalities at different frequencies. Such response
can be accomplished by cascading metasurfaces (thin composite layers) that are
designed to perform a single operation at the desired frequency and are
transparent elsewhere. Previously, out-of-band transparent metasurfaces for
control over reflection and absorption were proposed. In this paper, to
complete the full set of functionalities for wave control, we synthesize
transmitarrays that tailor transmission in a desired way, being "invisible"
beyond the operational band. The designed transmitarrays for wavefront shaping
and anomalous refraction are tested numerically and experimentally. To
demonstrate our concept of multifunctional engineered materials, we have
designed a cascade of three metasurfaces that performs three different
functions for waves at different frequencies. Remarkably, applied to volumetric
metamaterials, our concept can enable a single composite possessing desired
multifunctional response.
