Rapid Modeling of Photopolymerization in Projection Two-Photon Lithography via an Operator Splitting Finite Difference Method

Abstract

Two-photon lithography (TPL) is an attractive technique for nanoscale additive manufacturing of functional 3D structures due to its ability to print sub-diffraction features with light. Despite its advantages, it has not been widely adopted due to its slow point-by-point writing mechanism. Projection TPL (P-TPL) is a high-throughput variant that overcomes this limitation by enabling the printing of entire 2D layers at once. However, printing the desired 3D structures is challenging due to the lack of fast and accurate process models. Here, we present a fast and accurate physics-based model of P-TPL to predict the printed geometry and the degree of curing. Our model implements a finite difference method enabled by operator splitting to solve the reaction-diffusion rate equations that govern photopolymerization. When compared with finite element simulations, our model is at least a hundred times faster and its predictions lie within 5% of the predictions of the finite element simulations. This rapid modeling capability enabled performing high-fidelity simulations of printing of arbitrarily complex 3D structures for the first time. We demonstrate how these 3D simulations can predict those aspects of the 3D printing behavior that cannot be captured by simulating the printing of individual 2D layers. Thus, our models provide a resource-efficient and knowledge-based predictive capability that can significantly reduce the need for guesswork-based iterations during process planning and optimization.