Ultrathin Ge-YF₃ antireflective coating with 0.5 % reflectivity on high-index substrate for long-wavelength infrared...

Achieving long-wavelength infrared (LWIR) cameras with high sensitivity and shorter exposure times faces challenges due to series reflections from high-refractive index lenses within compact optical systems. However, designing effective antireflective coatings to maximize light throughput in these systems is complicated by the limited range of transparent materials available for the LWIR. This scarcity narrows the degrees of freedom in design, complicating the optimization process for a system that aims to minimize the number of physical layers and address the inherent large refractive mismatch from high-index lenses. In this study, we use discrete-to-continuous optimization to design a subwavelength-thick antireflective multilayer coating on high-refractive index Si substrate for LWIR cameras, where the coating consists of few (e.g., five) alternating stacks of high- and low-refractive-index thin films (e.g., Ge-YF₃, Ge-ZnS, or ZnS-YF₃). Discrete optimization efficiently reveals the configuration of physical layers through binary optimization supported by a machine learning model. Continuous optimization identifies the optimal thickness of each coating layer using the conventional gradient method. As a result, considering the responsivity of a LWIR camera, the discrete-to-continuous strategy finds the optimal design of a 2.3-μm-thick antireflective coating on Si substrate consisting of five physical layers based on the Ge-YF₃ high-low index pair, showing an average reflectance of 0.54 % within the wavelength range of 8-13 μm. Moreover, conventional thin-film deposition (e.g., electron-beam evaporator) techniques successfully realize the designed structure, and Fourier-transform infrared spectroscopy (FTIR) and thermography confirm the high performance of the antireflective function.