Two-photon nanolithography of sub-micrometer thickness microlenses designed by NPCC assisted Rayleigh Sommerfeld...

Recent development of artificial neural networks (ANNs) and inverse design methods have demonstrated their prospective significance for planar diffractive lens design, with a plethora of optical lenses designed for wavelengths ranging from visible to Thz wavelengths. However, previous research to design planner diffractive lenses only considers the maximum intensity in the focus area or its derivatives as the optimization function, leaving the intensity outside the focus area unconsidered. We proposed and investigated a two-dimensional (2D) physics-driven ANN method assisted by the negative Pearson correlation coefficient (NPCC) to design microlenses with varied focusing distances, which takes the entire 2D intensity distribution at the focus plane as an optimization function. Taking advantage of 3D two-photon nanolithographic technology, sub-micrometer thickness microlenses with varied focusing lengths are designed and fabricated, achieving an average focusing efficiency of around 35%, and an average focusing spot size of about 1 µm. Furthermore, a microlens array (19 by 19 microlenses with a total size of 4 mm²) with a curved focusing plane was fabricated and integrated into a CMOS sensor, achieving direct object imaging under incoherent white light illumination. Our results demonstrate that the NPCC is a very useful optimization function for designing planar diffractive lenses, and the use of NPCC in ANNs is of great potential for the future design of functional diffractive optical elements in optics and nanophotonics.