Upper limit on the polarization-assisted amplitude modulation capability of cascaded single-cell wave-plate-like metasurfaces

The Jones matrix method offers a robust framework for designing polarization multiplexed metasurfaces (PMMs). Traditional PMMs design involves initially defining functions and working channels, then mapping feature functions to adjustable parameters of metasurfaces. However, this approach makes it difficult to predict how working channels affect metasurface features. Here, we employ the generalized Malus law and Rodriguez rotation matrix on the Poincare Sphere to analyze diverse working channels' impact on PMMs' amplitude modulation capacity. For single-celled waveplate-like PMMs, up to three distinct images can be displayed. We demonstrate this in both theoretic method and numerical simulations. Our study establishes a framework for multi-channel amplitude modulation design of metasurfaces, applicable in information encryption, optical computation, diffraction neural networks, etc.