Matrix Fourier optics enables a compact full-Stokes polarization camera

RESEARCH ARTICLE SUMMARY ◥ METASURFACES Matrix Fourier optics enables a compact full-Stokes polarization camera Noah A. Rubin, Gabriele D’Aversa, Paul Chevalier, Zhujun Shi, Wei Ting Chen, Federico Capasso* INTRODUCTION: Polarization describes the path along which light’s electric field vector os- cillates. An essential quality of electromagnetic radiation, polarization is often omitted in its mathematical treatment. Nevertheless, polari- zation and its measurement are of interest in almost every area of science, as well as in imag- ingtechnology.Traditional camerasaresensitive to intensity alone, but in a variety of contexts, knowledge of polarization can reveal features thatareotherwise invisible. Determination of the full-Stokes vector—the most complete descrip- tion of light’s polarization—necessitates at least four individual measurements. This results in optical systems that are often bulky, reliant on moving parts, and limited in time resolution. RATIONALE: We introduce a formalism— matrix Fourier optics—for treating polarization in paraxial diffractive optics. This formalism is a powerful generalization of a large body of past work on optical elements in which polari- zation may vary spatially. Moreover, it suggests a path to realizing many polarization devices in parallel using a single optical element. We can then design diffraction gratings whose orders behave as polarizers for an arbitrarily selected set of polarization states, a new class of optical element. The intensity of light on a set of diffrac- ti