Dispersive Sweatt Model for Broadband Lens Design with Metasurfaces

The Sweatt model has been extensively used to design optical systems containing diffractive optical elements (DOEs) because it captures the dispersive characteristics of DOEs. We introduce a new dispersive Sweatt model (DSM) that can describe meta-atom (MA) dispersion, which has material and geometric contributions in addition to diffraction. It uses a wavelength-dependent scalar coefficient to modify the diffractive dispersion and describe the dispersion of a given MA basis. This provides a robust framework to design systems containing metasurface (MS) elements while including their unique dispersive properties in the design optimization. Importantly, the DSM is based on ray optics and enables the design of MS-containing systems using conventional optical design software such as Zemax and Code V. We use the DSM to demonstrate the design of a hybrid refractive/MS achromatic doublet for the midwave infrared (MWIR) band. The design example includes multiple wavelengths and field angles during optimization and demonstrates excellent agreement between the DSM and real hybrid lens performance modeled using wave optics. We discuss the limits of the DSM and present a simple model to predict performance limits due to phase mismatch at Fresnel zone boundaries.