Fast Free-Form Phase Mask Design for Three-Dimensional Photolithography Using Convergent Born Series

Advancements in three-dimensional (3D) photolithography are crucial for enhancing the performance of devices in applications ranging from energy storage and sensors to microrobotics. Proximity-field nanopatterning (PnP), which utilizes light-shaping phase masks, has emerged as a promising method to boost productivity. This study presents a swift and effective strategy for the design of phase masks tailored to the PnP process. Conventional design methodologies, grounded in basic optical theories, have been constrained by the simplicity and limited contrast of the resulting nanopatterns. Our approach, which merges the use of a frequency-domain electromagnetic solver-termed the convergent Born series-with gradient-based optimization and GPU acceleration, successfully addresses these shortcomings. The proposed solver outperforms CPU-intensive commercial FDTD software in our 2D test case by approximately 30 times, and its computational advantage increases in 3D simulations. This approach facilitates the creation of complex, high-contrast nanostructures within practical timeframes. We validate our method's effectiveness by engineering phase masks to produce distinct hologram patterns, such as single and double helices, thereby underscoring its utility for pioneering nanophotonic devices. Our findings propel the PnP process forward, ushering in novel avenues for the creation of sophisticated 3D nanostructures with superior optical and mechanical features.