Polarization, the path along which light’s electric field oscillates, is a key property of electromagnetic radiation. In this work, we motivate a mathematical framework—Matrix Fourier optics—that enables a simple description of light’s interaction with diffractive optics that spatially modify polarization. This formalism generalizes a large body of past work in metasurface polarization optics. We show how Matrix Fourier optics allows for the design of arbitrary polarization-analyzing metasurface gratings. These gratings can be used as the single polarization component in a compact full-Stokes polarization camera. We demonstrate practical, real-time polarization photography with this camera, which may find application in machine vision and remote sensing.
Metasurfaces, nanophotonic arrays of phase shifting elements, hold promise for the miniaturization of a variety of bulk optical elements, most notably lenses and imaging systems. Owing to the flexibility with which their constituent elements may be engineered, metasurfaces allow for point-to-point polarization control on a subwavelength scale. For this reason, metasurfaces represent an exciting new platform for polarization optics as well.
I will discuss how this functionality allows for a new perspective on diffractive optics which explicitly acknowledges the vectorial nature of light. This perspective motivates a theory of unitary polarization gratings; I will derive a few key results concerning these gratings. I will discuss and demonstrate how this perspective allows for the design of metasurfaces with new polarization functionalities.
I will describe how, through relatively simple optimization methods, a metasurface producing arbitrarily specified polarization states can be designed. This functionality is equivalent to a traditional diffraction grating with individual waveplate optics on each order; here, all the necessary polarization optics can be integrated into a flat, ultrathin optical element. Moreover, such a metasurface can be used in a reverse configuration as a parallel snapshot polarimeter with no need for additional polarization optics. I present a detailed experimental characterization of this device in the visible spectral region and a comparison of the performance of the metasurface to a commercially available rotating waveplate polarimeter.
Finally, I will discuss the extension of these concepts to compact polarization imaging systems and will provide a broad outlook on metasurfaces in polarization optics, polarization sensing systems, and polarization instrumentation more generally.
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