Polarization optics plays a pivotal role in diffractive, refractive, and emerging flat optics, and has been widely employed in contemporary optical industries and daily life. Advanced polarization manipulation leads to robust control of the polarization direction of light. Nevertheless, polarization control has been studied largely independent of the phase or intensity of light. Here, we propose and experimentally validate a Malus-metasurface-assisted paradigm to enable simultaneous and independent control of the intensity and phase properties of light simply by polarization modulation. The orientation degeneracy of the classical Malus's law implies a new degree of freedom and enables us to establish a one-to-many mapping strategy for designing anisotropic plasmonic nanostructures to engineer the Pancharatnam-Berry phase profile, while keeping the continuous intensity modulation unchanged. The proposed Malus metadevice can thus generate a near-field greyscale pattern, and project an independent far-field holographic image using an ultrathin and single-sized metasurface. This concept opens up distinct dimensions for conventional polarization optics, which allows one to merge the functionality of phase manipulation into an amplitudemanipulation-assisted optical component to form a multifunctional nano-optical device without increasing the complexity of the nanostructures. It can empower advanced applications in information multiplexing and encryption, anti-counterfeiting, dual-channel display for virtual/augmented reality, and many other related fields.

Metasurfaces have recently been used for multichannel image displays with pixel-size lower than a wavelength, which indicates the potential application in ultracompact anticounterfeiting with high-density and hidden information. However, current multichannel metasurfaces applied in anticounterfeiting are based on the sophisticated nanostructure design or at the cost of giving up some controls on the optical transmission matrix to encode multiple information channels. That is, the overall degrees of freedom offered by these metasurfaces are a "zero-sum game". Here, inspired by the orientation degeneracy indicated in Malus law, we propose a multiplexed anticounterfeiting metasurface consisting of single-sized nanostructures, which provide a new degree of freedom to increase the information capacity of anticounterfeiting without burdening the nanostructure design and fabrication. Specifically, the proposed metasurfaces can record a continuous grayscale image (channel 1) multiplexed with a totally/partially independent, interrelated, or watermarked anticounterfeiting pattern (channel 2). The two channels can be readily switched by polarization control. All experimental metasurface-images (meta-images) with high fidelity agree well with our design. With advantages such as ultracompactness, high-density information, multichannel displays, and strong concealment, the anticounterfeiting metasurfaces can empower advanced research and applications of metasurfaces in high-end optical anticounterfeiting and many other related fields.

Metasurfaces are flat structured surfaces that are designed to control the two-dimensional distributions of phase, polarization, and intensity profiles of optical waves. Usually, the optical response of metasurfaces is dispersive and polarization-dependent, which indicates the capability of using metasurfaces for information multiplexing using wavelengths and polarization states. However, most multiplexing techniques based on metasurfaces reported so far occur only in the spatial domain. Here, we experimentally demonstrate metasurface multiplexing by exploiting the degree of freedom of the spatial frequency domain. Specifically, we overlap two independent holographic images at high and low spatial frequencies and record them onto a single piece of metasurface hologram (meta-hologram). These two holographic images can be successfully separated from the reconstructed overlapped images by using two digital Gaussian filters. In addition, we demonstrate spatial frequency multiplexing by meta-nanoprinting, in which a complex multiplexed image (the combination of a cat image and a dog image) is recorded and demultiplexed with high fidelity. The presented spatial frequency multiplexing with metasurfaces suggests a route to increase the information channel and may contribute to the research and applications in optical information encoding, optical storage, optical information hiding, information security, compact displays, etc.

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