Observation of full-parameter Jones matrix in bilayer metasurface

Metasurfaces, artificial 2D structures, have been widely used for the design of various functionalities in optics. Jones matrix, a 2×2 matrix with eight parameters, provides the most complete characterization of the metasurface structures in linear optics, and the number of free parameters (i.e., degrees of freedom, DOFs) in the Jones matrix determines the limit to what functionalities we can realize. Great efforts have been made to continuously expand the number of DOFs, and a maximal number of six has been achieved recently. However, the realization of the ultimate goal with eight DOFs (full free parameters) has been proven as a great challenge so far. Here, we show that by cascading two layer metasurfaces and utilizing the gradient descent optimization algorithm, a spatially varying Jones matrix with eight DOFs is constructed and verified numerically and experimentally in optical frequencies. Such ultimate control unlocks opportunities to design optical functionalities that are unattainable with previously known methodologies and may find wide potential applications in optical fields.