Effective medium metasurfaces using nanoimprinting of the refractive index: design, performance, and predictive tolerance analysis

Production of flat optics incorporating subwavelength features, particularly at visible frequencies, remains a significant challenge. Here, we establish a framework for the design of effective medium metasurfaces (EMM), relying on nanoimprinting of mesoporous silicon to realize a patterned refractive index n(x,y) corresponding to an arbitrary transmitted phase profile phi (x,y). The method is used to design the stamp profile required to produce a Fresnel lens and the theoretical performance of the metalens is examined using the finite-difference time-domain method. Additionally, we demonstrate neural network aided Monte Carlo analysis as a method to model the effects of metasurface fabrications errors on EMM performance and process yield.