Information entropy of coding metasurface

Because of their exceptional capability to tailor the effective medium parameters, metamaterials have been widely used to control electromagnetic waves, which has led to the observation of many interesting phenomena, for example, negative refraction, invisibility cloaking, and anomalous reflections and transmissions. However, the studies of metamaterials or metasurfaces are mainly limited to their physical features; currently, there is a lack of viewpoints on metamaterials and metasurfaces from the information perspective. Here we propose to measure the information of a coding metasurface using Shannon entropy. We establish an analytical connection between the coding pattern of an arbitrary coding metasurface and its far-field pattern. We introduce geometrical entropy to describe the information of the coding pattern (or coding sequence) and physical entropy to describe the information of the far-field pattern of the metasurface. The coding metasurface is demonstrated to enhance the information in transmitting messages, and the amount of enhanced information can be manipulated by designing the coding pattern with different information entropies. The proposed concepts and entropy control method will be helpful in new information systems (for example, communication, radar and imaging) that are based on the coding metasurfaces.