Transfer learning-enhanced physics-informed neural networks for photonic device simulation with mode modeling method

Modal analysis techniques like eigenmode expansion and coupled mode theory are crucial for device simulation in photonic integrated circuits. Conventional numerical methods are inefficient for finely discretized graded-index structures, as they require repeated eigenmode computations across similar cross-sections. To overcome this, we propose a Transfer Learning–Enhanced Multi-Mode Physics-Informed Neural Network (TL-MmPINN) for efficient eigenmode searching in such structures. The framework starts with a single-mode PINN that jointly learns the eigenvalue-eigenfunction pair for a given waveguide configuration and is fine-tuned for similar structures. Building on this, a multi-branch architecture with orthogonality, nontriviality, and mode-selection constraints enables simultaneous prediction of multiple modes. A transfer-learning pipeline further allows pretrained models to be reused for perturbed waveguides, avoiding the repeated discretization and eigenvalue decomposition required by conventional solvers. Numerical experiments show that TL-MmPINN achieves accuracy comparable to finite-difference eigen-solvers while reducing per-structure training iterations, demonstrating its potential as a reusable and efficient tool for photonic device modeling.