Poincaré sphere trajectory encoding metasurfaces based on generalized Malus' law.

As a fundamental property of light, polarization serves as an excellent information encoding carrier, playing significant roles in many optical applications, including liquid crystal displays, polarization imaging, optical computation and encryption. However, conventional polarization information encoding schemes based on Malus' law usually consider 1D polarization projections on a linear basis, implying that their encoding flexibility is largely limited. Here, we propose a Poincaré sphere (PS) trajectory encoding approach with metasurfaces that leverages a generalized form of Malus' law governing universal 2D projections between arbitrary elliptical polarization pairs spanning the entire PS. Arbitrary polarization encodings are realized by engineering PS trajectories governed by either arbitrary analytic functions or aligned modulation grids of interest, leading to versatile polarization image transformation functionalities, including histogram stretching, thresholding and image encryption within non-orthogonal PS loci. Our work significantly expands the encoding dimensionality of polarization information, unveiling new opportunities for metasurfaces in polarization optics for both quantum and classical regimes.

Multifunctional Metasurfaces Enabled by Multifold Geometric Phase Interference.

Geometric phase is frequently used in artificially designed metasurfaces; it is typically used only once in reported works, leading to conjugate responses of two spins. Supercells containing multiple nanoantennas can break this limitation by introducing more degrees of freedom to generate new modulation capabilities. Here, we provide a method for constructing supercells for geometric phases using triple rotations, each of which achieves a specific modulation function. The physical meaning of each rotation is revealed by stepwise superposition. Based on this idea, spin-selective holography, nanoprinting, and their hybrid displays are demonstrated. As a typical application, we have designed a metalens that enables spin-selective transmission, allowing for high-quality imaging with only one spin state, which can serve as a plug-and-play chiral detection device. Finally, we analyzed how the size of supercells and the phase distribution inside it can affect the higher order diffraction, which may help in designing supercells for different scenarios.