Information theory of metasurfaces

We propose a theory to characterize the information and information processing abilities of metasurfaces, and demonstrate the relation between the information of the metasurface and its radiation pattern in the far-field region. By incorporating a general aperture model with uncertainty relation in L ²-space, we propose a theory to predict the upper bound of information contained in the radiation pattern of a metasurface, and reveal the theoretical upper limit of orthogonal radiation states. The proposed theory also provides guidance for inverse design of the metasurface with respect to given functionalities. Through investigation of the information of disordered-phase modulated metasurfaces, we find the information invariance (1-γ, where γ is Euler's constant) of chaotic radiation patterns. That is to say, the information of the disordered-phase modulated radiation patterns is always equal to 1-γ, regardless of variations in size, the number of elements and the phase pattern of metasurface. This value might be the lower bound of radiation-pattern information of the metasurface, which can provide a theoretical limit for information modulation applications, including computational imaging, stealth technologies and wireless communications.