Analytical design framework for metasurface projection optics

Beam steering and pattern/image projection have recently emerged as promising applications for optical metasurfaces, potentially bringing significant benefits to fields such as automotive and consumer electronics. To date, designs of metasurfaces for these applications have resorted to iterative numerical optimization. In this paper, we derive analytical solutions to enable computationally efficient design of flat optics systems for optical beam steering and pattern projection. For a single-layer metasurface, we show that a quadratic phase profile yields optimal beam quality. Doublet metasurfaces offer additional control over the beam forming characteristics, and as an example, we demonstrate on-demand distortion correction following analytically derived designs.