Designing and simulating large-diameter metalenses in the long-wave infrared (LWIR) range poses significant challenges due to the cost of computation resources involved. To address this challenge, we propose a scalable 3D FDTD inverse design approach that utilizes axial symmetry to enable the development of integrated meta-optics for LWIR. Our approach incorporates discrete axial symmetry and radially and azimuthally-fractured domain decomposition schemes to enable fast and accurate simulation and optimization of large-area, freeform, broadband dispersion-engineered LWIR metalenses. By formulating Maxwells equations in polar coordinates and developing new symmetry reduction and domain decomposition strategies, our approach unlocks new structural freedoms for the design of LWIR metalenses, while leading to a significant reduction in computation costs. Our axially symmetric structures are designed by incorporating the principle of dispersion engineering into our inverse-design software. These dispersion-engineered and inverse-designed structures form the building blocks for a metalens, whose high focusing efficiency can be maintained over a broad bandwidth (8-12 um). Our goal is to being capable of design and simulate an LWIR metalens with a physical aperture area of 5 cm x 5 cm, a numerical aperture of 0.25, and at least 95% average focusing efficiency over the broadband range. We will also verify our design and simulation results with fabricated metasurface prototypes.
