  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 'holy grail' 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 new opportunities to design optical
functionalities that are unattainable with previously known methodologies and
may find wide potential applications in optical fields.
