PINN-BPM: An Enhanced Physics-Informed Neural Network Framework of Solving Helmholtz Equation for Light Field Propagation in Optical Fiber

Accurate modeling of light field propagation dynamics in waveguide is crucial for the design and application of high-performance photonics devices. The beam propagation method (BPM) that solves the slowly varying field Helmholtz equation (SVHE) has been widely used by the research community for such modelling, typically combined with numerical method. However, the efficiency and accuracy of numerical BPM heavily rely on stable discretization scheme and high grid resolution, meanwhile accompanied by the sacrifice of solution integrity. Inspired by the physics-informed neural network (PINN), we propose the training priority-embedded PINN-BPM specifically for tackling light field propagation dynamics, which combines the efficient automatic differentiation and powerful representation ability of neural network with the regularization of SVHE, providing a promising alternative to avoid limitations of numerical methods. For scenarios of light field propagation, the dynamic complexity and scale of the propagation dimension often exhibits greater than those of the initial state. To this end, the PINN-BPM incorporates several training priorities, including the residual-based sampling, self-adaptive weights, and causal weights, to realize adaptive optimization attention during the training process, yielding the benefits of enhanced training efficiency and accuracy. We comprehensively investigate the feasibility and performance of PINN-BPM in the scenario of optical fiber, and obtain satisfactory modeling accuracies and generalization abilities, demonstrating the promising potential of the PINN-BPM in comprehending, characterizing, and modeling the light propagation dynamics.