Causality Implications for Absorption by EM Metasurfaces

A causal electromagnetic (EM) metasurface is backed by a lossless substrate and partially absorbs obliquely incoming rays. The integral of the absorbed power along the entire frequency axis is analytically evaluated, and the obtained sum rules indicate the global absorption by such a generic configuration. The beneficial influence of the plasma frequency and damping factor on the total absorbance score as well as the opposite effect of the angle of excitation, is noted. An overall lossless behavior at the incidence direction where the propagating waves into the substrate turn into evanescent is identified, once the magnetic field is parallel to the interface. The reported results can be useful in the tailoring of spectrally dependent absorption by a whole class of planar structures and, accordingly, in the forward and inverse design of lossy photonic metasurface setups.