Flat optics with dispersion-engineered metasurfaces

Control over the dispersion of the refractive index is essential to the performance of most modern optical systems. These range from laboratory microscopes to optical fibres and even consumer products, such as photography cameras. Conventional methods of engineering optical dispersion are based on altering material composition, but this process is time-consuming and difficult, and the resulting optical performance is often limited to a certain bandwidth. Recent advances in nanofabrication have led to high-quality metasurfaces with the potential to perform at a level comparable to their state-of-the-art refractive counterparts. In this Review, we introduce the underlying physical principles of metasurface optical elements (with a focus on metalenses) and, drawing on various works in the literature, discuss how their constituent nanostructures can be designed with a highly customizable effective index of refraction that incorporates both phase and dispersion engineering. These metasurfaces can serve as an essential component for achromatic optics with unprecedented levels of performance across a broad bandwidth or provide highly customized, engineered chromatic behaviour in instruments such as miniature aberration-corrected spectrometers. We identify some key areas in which these achromatic or dispersion-engineered metasurface optical elements could be useful and highlight some future challenges, as well as promising ways to overcome them.