# Metasurface-Based Polarimeters
## 3 Metasurface-Based Polarimeters
### Metasurface-Only Polarimeters  
In recent years, on-chip metasurface-only polarimeters have been proposed and were demonstrated to determine the entire SOP simultaneously. These polarimeters involve different configurations, including gap surface plasmon resonators [67; 73], metallic nanoantennas [74; 75], and all-dielectric nanoposts [76]. Starting with GSPMs, Figure 3a conveniently illustrates the basic working principle of the metagrating-based polarimeter, composed of three interweaved metasurfaces. An arbitrary polarized incident beam is spatially diffracted into six different directions, corresponding to different polarization states, since each metasurface functions as a polarization splitter for a certain polarization basis (\(|x\rangle,|y\rangle\)), (\(|a\rangle,|b\rangle\)), or (\(|r\rangle,|l\rangle\)) [67]. As such, the proposed metagrating responds uniquely to all possible polarization states and the most pronounced differences in the corresponding diffractions occur for the six extreme polarizations \(|x\rangle\), \(|y\rangle\), \(|a\rangle\), \(|b\rangle\), \(|r\rangle\), and \(|l\rangle\). Hence, the entire SOP can be determined. By conducting simultaneous measurements of the corresponding far-field diffraction intensities in the six predesigned directions, the Stokes parameters can be quickly retrieved, thereby allowing one to easily analyze the SOP of the incident light. At the design wavelength of 800 nm, the experimental diffraction contrasts obtained by averaging three successive measurements are in good agreement with the input Stokes parameters, and lay on the Poincare sphere, with points covering all octants of the 3D parameter space (Figure 3b). The two-norm deviation between Stokes parameters and experimental diffraction contrasts is estimated to be around \(\sim\)0.1, which can be significantly reduced with better fabrication facilities. Importantly, due to the rather broadband response of the GSPM, the designed metagrating could work over a wide wavelength range. In the wavelength range of 750-850 nm, there is no significant degradation of the metagrating performance observed in the experiments; the experimentally diffraction contrasts closely represent the Stokes parameters. In a later work [74], an ultracompact in-line polarimeter was demonstrated for transmission-type polarimetry by using a two-dimensional (2D) metasurface made up of a thin array of subwavelength metallic antennae embedded in a polymer film (Figure 3c). By placing two pairs of gold nanorod rows superimposed at a 45\({}^{\circ}\) relative angle, incident beams with four elliptical polarization states are directionally scattered. Based on the measured polarization-selective directional scattering in four directions from the corresponding out-coupling gratings, the SOP could be precisely obtained after calibration. From Figure 3d, one can clearly see that the measurement of several arbitrarily selected polarizations using the metasurface polarimeter agrees well with the result from the commercial polarimeter at a wavelength of 1550 nm. Considering the potential compactness, speed, and stability, this design is clearly superior to the commercial polarimeter. Following this concept, a compact fiber-coupled polarimeter with high sampling rates wasdemonstrated [75]. Here, we note that the degree of polarization (DOP) cannot be measured in the present four-output design. For DOP measurements, a more complex antenna array design is needed [74]. As complementary to compact polarimeters with plasmonic metasurfaces, all-dielectric metasurfaces may be tailored to design ultracompact polarimeters [76]. Compared with the GSPM-based polarimeters, such all-dielectric polarimeters could relax the difficulty of system  
Figure 3: Metasurface-only polarimeters.