Fig. 1: Jones matrix with eight DOFs and an application example of advanced light control.
From: Observation of full-parameter Jones matrix in bilayer metasurface

a Schematic view of a bilayer metasurface with eight DOFs in the Jones matrix. The incident and output Jones vectors Ein and Eo are connected by 2×2 equivalent Jones matrix J. The two layer metasurfaces are separated by a distance z. The Jones matrix of each single layer is symmetric and endowed with six DOFs. MS: metasurface. b Schematic of the bilayer metasurface for independent amplitude and phase control of arbitrary set of two polarizations. The incident two arbitrary polarizations \(|{\alpha }_{1}\rangle\)and \(|{\alpha }_{2}\rangle\) can be transformed into arbitrary output polarizations \(|{\beta }_{1}\rangle\)and \(|{\beta }_{2}\rangle\) with independent complex-amplitude \({A}_{1}{e}^{i{\delta }_{1}}\)and \({A}_{2}{e}^{i{\delta }_{2}}\), respectively. There are no constraints imposed on the input and output polarizations. c Comparison of the independent controlled parameters and polarization constraints between metasurfaces with different DOFs in Jones matrix.