Metamaterials are artificial structures composed of subwavelength unit cells to control electromagnetic (EM) waves. The spatial coding representation of metamaterial has the ability to describe the material in a digital way. The spatial coding metamaterials are typically constructed by unit cells that have similar shapes with fixed functionality. Here, the concept of frequency coding metamaterial is proposed, which achieves different controls of EM energy radiations with a fixed spatial coding pattern when the frequency changes. In this case, not only different phase responses of the unit cells are considered, but also different phase sensitivities are also required. Due to different frequency sensitivities of unit cells, two units with the same phase response at the initial frequency may have different phase responses at higher frequency. To describe the frequency coding property of unit cell, digitalized frequency sensitivity is proposed, in which the units are encoded with digits "0" and "1" to represent the low and high phase sensitivities, respectively. By this merit, two degrees of freedom, spatial coding and frequency coding, are obtained to control the EM energy radiations by a new class of frequency-spatial coding metamaterials. The above concepts and physical phenomena are confirmed by numerical simulations and experiments.
Keywords: energy radiations; frequency coding; metamaterials; multiple controls; phase sensitivity.