Principal Component Analysis for Nanophotonic Structures: Theory and Applications

Abstract

Recent progress in nanophotonic circuits and metasurfaces has created high-dimensional design spaces that are difficult for traditional optimization tools to navigate. This review positions Principal Component Analysis (PCA) within that landscape, clarifying where linear dimensionality reduction remains state-of-the-art and where nonlinear latent-space models are required. For moderate-dimensional geometric design spaces and relatively smooth spectral responses, PCA and its sparse, probabilistic, and incremental/online variants can achieve substantial application-specific reductions in simulation cost or data dimensionality while maintaining low reconstruction or task-level errors. The magnitude of these gains depends on the application, comparison baseline, sampling strategy, and number of principal components retained. This is illustrated by global mapping of vertical grating couplers, fabrication-aware analysis of cascaded Mach–Zehnder filters, and fibre-based colour sensing. In contrast, for freeform metasurfaces and high-Q resonators, linear PCA may struggle to capture nonlinear spectral responses and resonance shifts. Consequently, this leads to high reconstruction errors and motivates the use of other dimensionality reduction methods. We organize PCA’s role into four domains–inverse-design acceleration, machine-learning preprocessing, global design-space mapping, and fabrication-aware yield analysis–and highlight landmark applications such as design-space mapping, PCA-compressed stochastic filter analysis, and PCA-augmented THz metasurface networks. Comparative discussion with Linear Discriminant Analysis, manifold-learning approaches, and deep generative models emphasizes the central trade-off between computational efficiency, interpretability, and fidelity to nonlinear electromagnetic physics, providing practical guidance on when PCA is sufficient and when richer latent-space techniques are needed.