Adjoint‐Designed Mosaic Optical Fourier Surfaces for Short‐Distance Red‐Green‐Blue Color Mixing From Spatially Separated Emitters

Short‐distance color mixing from spatially separated red, green, and blue (RGB) emitters is challenging in compact display optics. Here, we demonstrate an adjoint‐designed, fabrication‐constrained mosaic optical Fourier surface (OFS) for RGB homogenization at a 5 mm observation distance. A 3 mm 3 mm aperture comprises 225 sinusoidal tiles with independently optimized period, orientation, and depth. The numerical demonstration uses a publicly documented 3030 RGB package as a reproducible separated‐emitter proxy for compact micro‐LED backlight applications, rather than a sub‐100‐ pixel. A differentiable finite‐source model is followed by direct full‐vector rigorous coupled‐wave analysis (RCWA) of 102,756 local conditions. The optimized OFS reduces from 0.03039 to 0.01429. Replacing 13,766 kernels from 30 high‐risk tiles with ultrafine RCWA or independent finite‐difference time‐domain results gives 0.014293 and 0.014266, with 99.95% and 99.74% dominant‐order agreement. Complementary reduced‐supercell RCWA and full‐size two‐tile FDTD checks directly bound inter‐tile coupling, while first‐order fabrication and material perturbations remain below . The validated library spans 0.90–5.80 periods, 0–350 nm depths, and , linking inverse design, electromagnetic validation, and scalable holographic manufacturing.