General design formalism for highly efficient flat optics for broadband applications

The use of flat diffractive optical elements (DOEs) for broadband applications, e.g. conventional optical systems, requires DOEs that maintain high efficiencies across the required range of wavelengths, angles of incidence, and grating periods. Here we introduce a general framework for how dispersion engineering can be used to design DOEs that fulfill these requirements and use our approach to determine design rules for broadband DOEs. Our analysis shows that the key to making échelette-type gratings (EGs) suitable for broadband optical systems is the development of new optical materials with specific uncommon dispersion properties. Subsequently, we use our framework to design a representative range of prototype EGs, which allows us to link the specifications of an optical system to the requirements on the EGs' materials. Finally, we show that our design rules apply to all DOEs based on propagation delays including GRIN DOEs and metagratings. Our design rules therefore guide the way towards unlocking the full potential of DOEs for different kinds of broadband applications.