Full-vectorial physics-informed neural operator for forward and inverse waveguide modeling

Abstract In this work, we tailor Physics-Informed Neural Operators for full-vectorial modal analysis of optical waveguides. We develop a two-headed neural operator, conditioned on coordinate inputs alongside spatial material profiles and operational parameters. This enables a unified framework that simultaneously predicts the effective indices and the corresponding electromagnetic field distributions while preserving the discretization invariance of neural operators. To ensure stable training, we employ a normalized eigenvalue prediction strategy, enforced by construction and complemented by a short-lived biasing term, yielding accurate and robust predictions. Moreover, the differentiable nature of the proposed framework naturally supports inverse design, allowing figures of merit like dispersion to be exactly calculated and optimized. The forward model achieves 1–2% relative errors compared against analytic solutions and standard numerical benchmarks, while offering up to a 29-fold speedup when evaluated on a GPU. This high forward-model accuracy also translates to notable agreement in the dispersion curves compared to the numerical references, capturing both magnitude and spectral trends across the considered parameter ranges.