# Metasurface-Based Polarimeters
## 1 Introduction  
The state of polarization (SOP) is an inherent property of light and carries crucial information about the composition and structure of materials interrogated with light [1]. However, the SOP is rather cumbersome to probe experimentally, owing to the fact that it is uncorrelated with the intensity and frequency of light, thereby resulting in the loss of information on the relative phase between orthogonal vector components in conventional detection schemes. Hence, polarimeters, which enable direct measurement of the SOP, are greatly desired in many areas of science and technology, including astronomy [2], medical diagnostics [3], and remote sensing [4]. Despite all scientific and technological potential, polarimeters are still very challenging to develop as SOP characterization requires conventionally six intensity measurements to determine the Stokes parameters [5]. Typically, the SOP is probed by utilizing a set of discrete polarizers and wave-plates consecutively placed in front of a detector. By measuring the light flux transmitting through these polarization components, the Stokes parameters that uniquely define the SOP can be determined. Polarimeters based on conventional discrete optical components amount to bulky, expensive, and complicated optical systems that are not compatible with the general trend of integration and miniaturization in photonics and plasmonics.  
Metasurfaces are thin planar arrays of resonant subwavelength elements arranged in a periodic or aperiodic (even random) manner which modifies boundary conditions for impinging optical waves in order to realize specific wave shaping. In recent years, metasurfaces have attracted progressively increasing attention and have become a rapidly growing field of research, due to their remarkable abilityin manipulating electromagnetic (EM) waves, their versatility, and their ease of on-chip fabrication and integration [6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24]. Such metasurfaces can mimic bulk optics since they are capable of engineering the phase front of reflected and/or refracted optical waves at will. Many ultra-compact flat optical components have been accordingly demonstrated, such as beam steerers [6; 25; 26; 27; 28; 29], surface wave couplers [30; 31; 32; 33; 34; 35], focusing lenses [36; 37; 38; 39; 40; 41; 42; 43], optical holograms [44; 45; 46; 47; 48; 49], and waveplates [50; 51; 52; 53; 54].  
Metasurfaces, therefore represent an opportunity for polarimetry to overcome the bulky and expensive architectures of conventional volume optics. In this review, we highlight the recent progress in metasurface-based polarimeters during the past few years and attempt to provide our perspective on this specific branch of applications. The rest of this paper is organized in the following sections. In Section 2, we briefly explain generalized Snell's law, followed by the Pancharatnam-Berry phase (PB-phase), and the Stokes parameters. Section 3 is devoted to the metasurface-based polarimeters, including general polarimeters, spectropolarimeters, orbital angular momentum (OAM) spectropolarimeters, and photodetector integrated polarimeters. Finally, we summarize and provide perspective for future developments in Section 4.