# Metasurface-Based Polarimeters
## 3 Metasurface-Based Polarimeters
### Metasurfaces Spectropolarimeters
Upon the excitation of a normally incident monochromatic beam, this center-symmetrical configuration would diffract any normally incident beam to six predesigned directions, whose contrasts in the corresponding diffraction intensities would provide a direct measure of the SOP and retrieval of the associated Stokes parameters, due to the direct mathematical equivalence between the normalized contrasts and Stokes parameters. At the same time, the polar angle of diffraction is approximately proportional to the wavelength, resulting in the spectral analysis of the incident beam. The fabricated 96 \(\upmu\)m diameter spectropolarimeters, operating in the wavelength range of 750-950 nm, are found to exhibit excellent capability of polarization detection (Figure 5b). Moreover, the experimentally measured angular dispersion \(\Delta\theta/\Delta\lambda\) for the \(|x\rangle\) channel is 0.0133 \({}^{\circ}\)/nm, corresponding to a measured spectral resolving power of \(\lambda/\Delta\lambda\approx 15.2\) (Figure 5c,d). Importantly, due to the circular-sector design, polarization analysis can be conducted for optical beams of different diameters without prior calibration, thereby demonstrating the beam-size invariant functionality. As a final comment, we would like to stress that uneven illumination of the three metasurfaces caused by misalignment or inhomogeneity of the laser beam will not affect the retrieved Stokes parameters and no calibration is needed since the Stokes parameters are only related to the relative diffraction contrasts for three polarization bases. To increase the spectral resolution of spectropolarimeters, interleaved metasurfaces have been designed to conduct spectropolarimetry, where different channels share the aperture of the device [79; 80]. A good example of interleaved metasurface-based spectropolarimeters is shown in Figure 6a, where three linear phase profiles associated with different nanoantenna subarrays, formed by  
Figure 5: Segmented spectropolarimeters. (**a**) Illustration of the gap-surface plasmon metasurface (GSPM)-based beam-size invariant spectropolarimeter; (**b**) Measured diffraction contrasts for the six extreme polarizations that represent the values of Stokes parameters at \(\lambda=800\) nm; (**c**) Normalized measured far-field intensity profile for different wavelengths of the \(|x\rangle\) channel; (**d**) Theoretical and measured spectral dispersions of different channels. Reproduced with permission from [78], Copyright American Chemical Society, 2017.  
the random interpersing, make up the configuration. This enables simultaneous characterization of the SOP and spectrum in the reflected beam [79]. In particular, by randomly mixing optical nanoantenna arrays with different phase functions, the PB-phase concept, spatially interleaved phase profiles are designed, which yield extraordinary information capability. When a probe beam with an arbitrary SOP is incident on the spectropolarimeter metasurface (SPM), two beams of intensities \(I_{\sigma+}\) and \(I_{\sigma-}\), consisting of opposite helicity states, and two additional beams emerge. The latter two beams are projected onto linear polarizers at \(0^{\circ}\) and \(45^{\circ}\), determining the linearly polarized components \(I_{L0}\) and \(I_{L45}\), respectively. The Stokes parameters of the incident beam are then calculated with a calibration experiment. Figure 6b shows the measured and calculated Stokes parameters on a Poincare sphere for an analyzed beam impinging the SPM at a wavelength of 760 nm with different polarizations, demonstrating the excellent capability of the polarization probe. Furthermore, such interleaved SPM shows good spectral resolving power, which was measured to be \(\lambda/\Delta\lambda\approx 13\) when the diameter is only 50 \(\upmu\)m (Figure 6c). To further improve the spectral resolving power while keeping the aperture size fixed, super-dispersive, off-axis metalenses that could simultaneously disperse and focus light of different wavelengths can be used [81; 82].