# Metasurface-Based Polarimeters
## 3 Metasurface-Based Polarimeters
### PB-Phase Metasurfaces for Determining Part of the SOP  
In early approaches, PB-phase metasurfaces together with conventional optical elements, such as polarizers and retardation waveplates, were designed to determine the degree of circular polarization [69; 70; 71]. One example is depicted in Figure 2a, where an ultrathin (40 nm) gradient metasurface was formed and demonstrated to measure the ellipticity and handedness of polarized light [70]. Figure 2a shows the schematic and scanning electron microscope (SEM) image of the designed PB-phase metasurface, which consists of Au nanorods--with identical geometrical parameters but with spatially varying orientation--on top of anindium tin oxide (ITO) coated glass substrate. The angular orientation of each nanorod varies along the \(x\)-direction with an incremental \(\pi/8\) clockwise rotation, but remains invariant in the \(y\)-direction. Hence, each period in \(x\)-direction contains eight nanorods, resulting in a phase shift ranging from 0 to \(2\pi\). Due to the spin-selected opposite slope of the PB-phase gradient, the decomposed RCP and LCP beams are steered in opposite directions, exhibiting the photonic spin Hall effect (PSHE) [72]. Thus, the obtained intensity distribution of the anomalously refracted LCP and RCP light provides an accurate and simple method to measure the ellipticity of the incident light. To experimentally demonstrate the capability of determining the degree of circular polarization with the proposed metasurface approach, various polarization states of incident light were impinged on the metasurface by changing the angle \(\beta\) between the axis of polarization and the fast axis of the quarter waveplate. These show different intensity distributions after interacting with the metasurface, as shown in Figure 2b. Figure 2c clearly shows that the ellipticity and handedness of various incident polarization states can be well characterized, and are in good agreement with the predicted values. Additionally, the proposed method here is suitable to work at a wide range of wavelengths, ascribed to the broadband nature of PB-phase. It should be noted that the conversion efficiency of the metasurface is strictly limited and the maximum conversion efficiency is around 7.6% at 940 nm, which may affect the performance of the proposed metasurface since the ellipticity and handedness of various incident polarization states are determined by the intensities of the refracted beams. The limited efficiency is ascribed to the single electric dipole resonance supported by the non-magnetic Au nanorods on top of ITO-coated glass substrate, which sets the upper bound of the coupling efficiency between the two polarizations to be 25% in the limit of negligible absorption [57; 58]. PB-phase GSPM have been demonstrated to increase the efficiency [71]. Figure 2d presents a novel and compact circular dichroism (CD) spectrometer based on PB-phase GSPM, which utilizes PSBE in reflection. Specifically, an array of anisotropic elements is used to achieve different phase gradients in response to LCP and RCP light. Therefore, the spin components of the incident broadband source are reflected in opposite directions, and the reflection angle of each wavelength component is varied according to generalized Snell's law [6]. When a broadband light source is incident on the metasurface, the LCP and RCP spectra are spatially separated and can be recorded simultaneously, which eliminates the need of switching the incident polarization, as shown in Figure 2e. By analyzing the spectra of different spin components, the CD of the light source can be easily obtained, which can serve as an important tool in sensing chiral molecules. Additionally, there is no other hardware required for this type of CD spectrometry. Figure 2: Pancharatnam–Berry (PB) phase metasurfaces for determining the degree of circular polarization. (**a**) Schematic illustration of the phase gradient metasurface.