Physics-informed finite element multi-scale modeling of light propagation using numerical approximation of slowly varying envelope

In this paper, we extend the numerical techniques based on the slow envelope approximation in the finite element method by introducing physical information into the construction of multi-scale basis functions for scenarios where the wave effects matter. Thereby, the proposed method here enables the modeling and simulation of multi-scale optical devices and systems, especially those that involve strong wave effects. Various multi-scale basis function construction techniques have been developed, tailored to different physical scenarios of strong wave effects, to achieve precise and efficient computation. Without loss of generality, the accuracy and efficiency of the method are verified by computing double-slit interference, off-axis reflective systems, and refractive-diffractive hybrid optical systems. These results show that this method can be applied to various scenarios, such as refraction, multiple reflection, and multi-beam diffraction, while it can achieve an order of magnitude improvement in calculation speed compared with the standard finite element method.