We propose a theory to characterize the information and information processing abilities of metasurfaces, and demonstrate the relation between the information of metasurface and its radiation pattern in the far-field region. By incorporating a general aperture model with uncertainty relation in L²-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 that can be realized. The proposed theory also provides guidance for inverse design of the metasurface with respect to given functionalities. Through investigating the information of disordered-phase modulated metasurfaces, we find the information invariance (1-γ) of chaotic radiation patterns. That is to say, the information of the disordered-phase modulated radiation patterns is always equal to 1-γ (γ is the Euler’s constant), no matter how the size, the number of elements, and the phase pattern of metasurface vary. This value might be the lower bound of radiation-pattern information of the metasurface, which can provide theoretical limit for information modulation applications, including computational imaging, stealth technologies and wireless communications.

中文翻译：

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超表面信息论

我们提出了一种表征超表面信息和信息处理能力的理论，并证明了超表面信息与其远场区域辐射模式之间的关系。通过在 L ^{2 中}加入具有不确定性关系的通用孔径模型-space，我们提出了一种预测超表面辐射模式中包含的信息上限的理论，并揭示了可以实现的正交辐射态的理论上限。所提出的理论还为关于给定功能的超表面逆向设计提供了指导。通过研究无序相位调制超表面的信息，我们发现了混沌辐射模式的信息不变性（1-γ）。也就是说，无论超表面的大小、元素数量和相位图如何变化，无序相位调制辐射图的信息总是等于1-γ（γ是欧拉常数）。这个值可能是超表面辐射模式信息的下限，