End-to-End Differentiable Design of Geometric Waveguide Displays

By Dr. Noopur JainReviewed by Louis CastelJan 23 2026

In a recent article posted to arxiv, researchers report an end-to-end differentiable framework that jointly optimizes geometric waveguide (GWG) mirror coatings and non-sequential light transport, improving throughput and uniformity in a representative AR waveguide design.

Image Credit: Xinnian/Shutterstock.com

Background

Geometric waveguides (GWGs) are an attractive architecture for optical see-through augmented reality (AR) displays because they are compact and lightweight, and they can replicate the exit pupil without bulky optics. Unlike diffractive or holographic waveguides, GWGs use partially reflective mirror arrays (PRMAs) to redirect and extract light using geometric optics, which can preserve spectral content and support high image quality with a large eyebox.

Designing GWGs is difficult for two main reasons: light transport is non-sequential, involving multiple partial reflections and transmissions, and performance depends strongly on polarization-sensitive multilayer thin-film coatings. Traditional simulations often rely on ray splitting, which can drive an exponential increase in ray count and computational cost when modeling non-sequential paths. Many existing workflows also separate geometry and coating optimization, which slows iteration and can miss polarization effects that materially affect final performance.

The Current Study

The authors’ approach centers on end-to-end differentiable simulation. Light propagation is modeled using non-sequential Monte Carlo polarization ray tracing. At each partially reflective mirror, a ray is stochastically reflected or transmitted based on a reflection probability (ω). To preserve energy during polarization ray tracing, the complex amplitude of the sampled path is scaled by the square root of the sampling probability.

To improve stability and sampling efficiency, the method includes a pre-optimization step that initializes reflection probabilities (ω) for each mirror to maximize throughput using geometric ray tracing, before the full polarization-aware optimization. Differentiability is enabled via a reparameterization approach that separates stochastic event sampling from the physical coefficients, supporting stable gradient backpropagation. A memory-saving two-pass intersection strategy limits autodiff graph size, allowing large-scale optimization on a single multi-GPU workstation.

Polarization effects are modeled using a differentiable thin-film solver based on the transfer matrix method (TMM). The solver computes effective complex reflection (req) and transmission (teq) coefficients for multilayer stacks as functions of polarization (s and p), incident angle, and wavelength. Fresnel coefficients for s and p polarizations are applied at each interface, and TMM composes them across the stack. In the reported setup, each PRMA uses a 23-layer Ta2O5/SiO2 stack, yielding more than 1,000 optimizable layer thickness parameters across all mirrors.

The optimization target is a multi-objective loss function, L = Lbright + wf·LFoV + we·Leyebox. Here, Lbright minimizes the negative mean eyebox throughput (I) to maximize brightness, while LFoV and Leyebox use the coefficient of variation (CV) across the field of view and eyebox, respectively, to encourage uniformity. Gradients are backpropagated through the sampled ray paths and the thin-film solver to update layer thickness parameters.

Results and Discussion

On a representative GWG architecture, the end-to-end differentiable optimization improved performance substantially. From random initialization, the system optimized more than 1,000 layer-thickness parameters while handling billions of ray–surface intersections. After optimization, the authors report an approximately 8× increase in eyebox throughput. Uniformity improved as well, with CV across the field of view decreasing by about 11× and CV across the eyebox decreasing by about 17×.

Compared with a sampling-based genetic algorithm baseline, the gradient-based method converged faster and reached a lower loss. The baseline achieved 7.9% throughput despite using six times the wall-clock compute time. The authors also report that several layer thicknesses were driven toward zero during optimization, which they interpret as a form of automated topology optimization for the coating stack.

Conclusion

The work introduces an end-to-end differentiable framework for optimizing geometric waveguide displays by coupling non-sequential polarization ray tracing with polarization-dependent thin-film modeling. By enabling scalable, gradient-based optimization over high-dimensional coating parameters, the approach improved light efficiency and uniformity relative to a sampling-based baseline. The reported layer-pruning behavior suggests a path toward more automated coating design for AR waveguide systems.