Controlling the degrees of freedom in metasurface designs for multi-functional optical devices

This review focuses on the control over the degrees of freedom (DOF) in metasurfaces, which include the input DOF (the polarization, wavelength and incident angle of the input light and some dynamic controls), parameter DOF (the complex geometric design of metasurfaces) and output DOF (the phase, polarization and amplitude of the output light). This framework could clearly show us the development process of metasurfaces, from single-functional to multi-functional ones. Advantages of the multi-functional metasurfaces are discussed in the context of various applications, including 3D holography, broadband achromatic metalenses and multi-dimensional encoded information. By combining all the input and output DOF together, we can realize ideal optical meta-devices with deep subwavelength thickness and striking functions beyond the reach of traditional optical components. Moreover, new research directions may emerge when merging different DOF in metasurfaces with other important concepts, such as parity-time symmetry and topology, so that we can have the complete control of light waves in a prescribed manner.