# Metasurface-Based Polarimeters
## 3 Metasurface-Based Polarimeters
### Metasurfaces Spectropolarimeters  
In addition to determining the SOP of an incident beam, spectral analysis is concomitantly required. This resulted in the recent developments of metasurface-based spectropolarimeters, which enable simultaneous measurements of the spectrum and SOP [77; 78; 79; 80]. As such, the spectropolarimeters are superior to the isolated spectrometers or polarimeters, regarding their capability of combining the uncorrelated information channels of intensity, wavelength, and SOP together. Starting with segmented spectropolarimeters [77; 78], a spectropolarimeter metadevice that steers different polarization and spectral components into predesigned spatial directions was proposed [77], which consists of six GSPMs arranged in a \(2\times 3\) array, corresponding to horizontal (0\({}^{\circ}\)), vertical (90\({}^{\circ}\)), \(\pm 45^{\circ}\), RCP, and LCP analyzers. Once a probe beam with a certain polarization state is incident on the metadevice, six diffraction spots are generated in the far-field, resulting from the anomalous reflection of each GSPM area. When the incident polarization is altered, the relative intensity distributions of diffraction spots change accordingly. As such, the polarization response of this spectropolarimeter at a given wavelength can be determined by carefully analyzing the relationship between the intensity of individual peaks and the incident SOP. Additionally, this metadevice could be used to analyze the wavelength due to the fact that the GSPMs are usually dispersive. The measured angular dispersion for the LCP and RCP channels are 0.053 \({}^{\circ}\)/nm and 0.024 \({}^{\circ}\)/nm, respectively. Hence, proving the potential of spectral measurement with spectral resolution up to \(\sim\)0.3 nm if this metadevice is inserted into a typical spectrometer setup. It should be noted that the spectral resolution of \(\sim\)0.3 nm is estimated with the aid of other optical components in a commercial spectrometer and the intrinsic resolution accessed with the metadevice itself is rather limited. Although the metadevice with rectangular configuration shows good performance, it is relatively sensitive to the illuminated area by the incident light. In particular, the incident light should cover the whole area of the metasurface with the same light intensity in order to ensure faithful comparison  
Figure 4: Metacoupler-based polarimeter. (**a**) Schematic of the unit cell; (**b**) Top view of the combined waveguide metacoupler; (**c**–**e**) Color map of the intensity in the center of the Poly(methyl methacrylate) (PMMA) layer for the metacoupler when the incident light is a Gaussian beam with a beam radius of 6 \(\upmu\)m. The polarization state \(|u\rangle\) of the beam is displayed in the upper right corner. Note that the scale bar is chosen to better highlight weak intensity features. Panel (**c**) shows the numbering of the six ports marked with gray lines; (**f**) Circles and asterisks indicate retrieved and exact polarization states of the incident beam for 42 different SOPs, plotted in \((s_{1},s_{2},s_{3})\)-space together with the Poincaré sphere. Reproduced with permission from [68], Copyright American Physical Society, 2016.  
of the corresponding diffraction orders. To increase the detection robustness and the compatibility with a circular laser beam that has a Gaussian profile, a segmented plasmonic spectropolarimeter has been demonstrated by using a center-symmetric configuration, featuring a self-calibrating nature [78]. The working principle of the self-calibrated spectropolarimeter is displayed in Figure 5a, which consists of three different types of GSPMs occupying 120\({}^{\circ}\) circular sectors each. Similar to the previous work [67], each sector-shaped GSPM operates as an efficient polarization splitter for one of the three polarization bases (\(|x\rangle\),\(|y\rangle\)), (\(|a\rangle\),\(|b\rangle\)), and (\(|r\rangle\),\(|l\rangle\)).