# Metasurface-Based Polarimeters
## 3 Metasurface-Based Polarimeters
### Metasurface OAM Spectropolarimeters  
Besides the spectrum and polarization, the orbital angular momentum (OAM) is also an intrinsic property of light, which processes a helical phase front, such that the Poynting vector within the beam is twisted with respect to the principal axis of light propagation [89]. In contrast to the spin angular momentum (SAM) that can take only two values, OAM is unbounded since the topological charge \(l\) can take any integer value. Thus OAM beams have recently gained tremendous interest in optical trapping, high-resolution microscopy, and quantum information processing, as they introduces an additional degree of freedom for encoding the light beam and increasing communication capabilities [20; 90]. A variety of metasurfaces have been demonstrated to generate OAM beams [91; 92; 20; 93; 94], which have, in turn, motivated the implementation of OAM polarimetry, enabling direct detection of topological changes to a structured optical wavefront. Very recently, [PERSON]'s group incorporated spectropolarimetry and OAM sensing into a silicon metasurface, which would ultimately facilitate a simultaneous detection of the wavelength, polarization, and OAM of light by projecting an incident mode \(|l_{in}\rangle\) on a set of orthogonal OAM states \(|l_{j}\rangle\)[80].  
The OAM spectropolarimeter metasurface (OSPM), designed with the combination of the shared-aperture and PB-phase concepts, consists of interleaved antenna sub-arrays with multiplexed geometric-phase profiles. These result in a finite number of dominant multiplexed OAM harmonic  
Figure 7: On-chip spectropolarimetry by fingerprinting with random metasurfaces. (**a**) Schematic of surface plasmon polariton (SPP) excitation and scattering occurring upon illumination of random nanoparticle (NP) arrays at normal incidence; (**b**) Sketch of an individual gold NP atop a 70-nm-thick gold film deposited on a silica wafer; (**c**) Corresponding leakage radiation microscopy (LRM) image in the Fourier plane introducing the azimuthal angle \(\theta\) that denotes the SPP scattering direction. The bright circle is formed by SPP waves scattered in different directions with its radius being related to the SPP effective index; (**d**) Correlation between SPP scattering spectra obtained for different linear polarizations (at 800 nm) with differently sized random NP arrays as a function of the angle between the polarizations; (**e**) Correlation between SPP scattering spectra obtained with linear horizontal polarization as a function of the incident wavelength, when using different reference wavelengths of 750, 800, 850, and 900 nm. Reproduced with permission from [88], Copyright American Chemical Society, 2018.  
orders with identical intensities. Illuminating the OSPM with an arbitrarily polarized polychromatic light source results in four symmetric sets of annular spots with a bright spot at the center, as shown in Figure 8a. Given an incident beam possessing an arbitrary topological charge \(l_{in}\), the winding numbers of the diffracted orbital harmonics are modified by accumulating the value of \(l_{in}\). This shifts the bright spot from its original location \(l=0\) to \(l=-l_{in}\), thus enabling the determination of the incident OAM value (Figure 8b-g). From the far-field images, one can clearly see that the position of the bright spot changes in response to alternating the incident OAM. For instance, the bright spot moves to the right side if the incident OAM carries a topological change of \(l_{in}=1\) (Figure 8c), while the bright spot moves to the left side if \(l_{in}=-1\) (Figure 8e). Additionally, such OSPM can resolve the incident polarization states and wavelengths precisely.