Theory of patch-antenna metamaterial perfect absorbers

A metasurface that absorbs waves from all directions of incidence can be achieved if the surface impedance is made to vary as a function of incidence angle in a specific manner. Here we show that a periodic array of planar nanoparticles coupled to a metal film can act as an absorbing metasurface with an angle-dependent impedance. Through a semi-analytical calculation based on coupled-mode theory, we find the perfect absorbing condition is equivalent to balancing the Ohmic and radiative losses of the nanoparticles at normal incidence. Absorption over a wide range of incidence angles can then be obtained by tailoring the scattered far-field pattern of the individual planar nanoparticles such that their radiative losses remain constant. The theory provides a means of understanding the behavior of perfect absorbing structures that have been observed experimentally or numerically, reconciling previously published theories and enabling the optimization of absorbing surfaces.