Non-imaging metasurface design for collimated beam shaping

Metasurfaces provide a versatile platform for realizing ultrathin flat optics for use in a wide variety of optical applications. The design process involves defining or calculating the phase profile of the metasurface that will yield the desired optical output. Here, we present an inverse design method for determining the phase profile for shaping the intensity profile of a collimated incident beam. The model is based on the concept of optimal transport from non-imaging optics and enables a collimated beam with an arbitrary intensity profile to be redistributed to a desired output intensity profile. We derive the model from the generalized law of refraction and numerically solve the resulting differential equation using a finite-difference scheme. Through a variety of examples, we show that our approach accommodates a range of different input and output intensity profiles, and discuss its feasibility as a design platform for non-imaging optics