End-to-end differentiable design of geometric waveguide displays

Geometric waveguides are a promising architecture for optical see-through augmented reality displays, but their performance is severely bottlenecked by the difficulty of jointly optimizing non-sequential light transport and polarization-dependent multilayer thin-film coatings. Here we present the first end-to-end differentiable optimization framework for geometric waveguide that couples non-sequential Monte Carlo polarization ray tracing with a differentiable transfer-matrix thin-film solver. A differentiable Monte Carlo ray tracer avoids the exponential growth of deterministic ray splitting while enabling gradients backpropagation from eyebox metrics to design parameters. With memory-saving strategies, we optimize more than one thousand layer-thickness parameters and billions of non-sequential ray-surface intersections on a single multi-GPU workstation. Automated layer pruning is achieved by starting from over-parameterized stacks and driving redundant layers to zero thickness under discrete manufacturability constraints, effectively performing topology optimization to discover optimal coating structures. On a representative design, starting from random initialization within thickness bounds, our method increases light efficiency from 4.1\% to 33.5\% and improves eyebox and FoV uniformity by $\sim$17$\times$ and $\sim$11$\times$, respectively. Furthermore, we jointly optimize the waveguide and an image preprocessing network to improve perceived image quality. Our framework not only enables system-level, high-dimensional coating optimization inside the waveguide, but also expands the scope of differentiable optics for next-generation optical design.