# Metasurface-Based Polarimeters
## 3 Metasurface-Based Polarimeters
### On-Chip Spectropolarimetry by Fingerprinting with Random Metasurfaces  
Metasurfaces composed of disordered structure have been demonstrated to realize various functions, such as diffusing light [29], absorbing light [83], waveguiding [84], wavefront shaping [85; 86; 87], and polarimetry [88]. In Reference [88], a unique on-chip spectropolarimeter, by fingerprinting with a random gold nanoparticle (NP) array, in the near-infrared range is presented. This spectropolarimeter is based on analyzing scattering SPP patterns from micron-sized circular arrays of randomly distributed gold NPs (Figure 7a) through a leakage radiation microscope (LRM). Due to strong multiple scattering and the countless scattering routes between the closely packed NPs, the disordered media is able to generate unique and complicated scattering patterns that are sensitive to the wavelength and SOP, and thereby those scattering spectra can be employed as spectropolarimetric fingerprints to distinguish incident light carrying different polarization and spectrum components. The random metasurface consists of gold NPs with diameter of about 50 nm, thickness of 70 nm, and density of 75 \(\upmu\)m\({}^{-2}\), distributed in circular areas with radii of 1-5 \(\upmu\)m on top of a 70 nm thick gold film and 170 \(\upmu\)m thick silica substrate (Figure 7b). Larger array sizes generate more complex scattering patterns.  
In the experiment, the angular spectra of the scattering patterns are characterized along the azimuthal angle \(\theta\) through their Fourier plane images from the LRM (Figure 7c). The scattering spectra of different SOPs and wavelengths are quantitatively compared by calculating the correlation coefficients. The experimental results shows a substantial difference between the main SOPs: the orthogonal SOPs (horizontal and vertical linear, or left and right circular) exhibit virtually no correlation (\(<\)0.2). They also investigated the influence of the angle (\(\alpha\)) between two different linear polarizations, and the correlation coefficient exhibits similar angular dependence as the analytical expression of the polarizer transmission (\(\cos^{2}\!\alpha\)) with the increasing polarization angle difference (Figure 7d). In the case of varying wavelengths, the correlation coefficient also drops accordingly with increasing wavelength difference in the 700-1000 nm range, with the wavelength selectivity estimated to be \(\lambda^{2}/L_{spp}\) (\(L_{spp}\) is the propagation length of the SPP) (Figure 7e). Numerical simulations of angular SPP scattering spectra are also carried out and confirm the sensitivity of the SPP scattering spectra to different wavelength and SOPs, thereby validating the proposed concept of on-chip spectropolarimetry by fingerprinting based on SPP excitation and multiple scattering by random surface nanostructures. Compared to other metasurface-based polarimetry, the fingerprinting approach might require extra work for the careful calibration; the registration of different SPP scattering spectra to create a database of spectropolarimetric fingerprints. However, it also has the advantage of simple design and fabrication procedure, in addition to its potential applications for optical wavefront sensing, optical beam tracing and positioning, and so on.