Surpassing the diffraction limit via a vectorial Debye integral neural network

Breaking the diffraction limit has been a key challenge in optical engineering and super-resolution imaging. In this work, we utilize a vectorial Debye integral neural network to design sub-diffraction focusing fields for high-NA objectives. By training the polarization states of incident light, we flexibly achieve transitions from diffraction-limited focusing to superoscillatory regimes. Through parameter adjustments, we optimize focal spot size, energy efficiency, and sidelobe distribution, achieving a focus with a 0.367λ FWHM and enhanced energy utilization. This method significantly simplifies the design process and demonstrates great potential for advanced optical applications, including super-resolution imaging and 3D field engineering.