Super-resolution focusing spots generation using diffractive neural networks

Optical superoscillation enables the generation of far-field super-resolved focusing spots beyond the diffraction limit. However, existing superoscillatory lens designs for spatial super-resolution focusing still face significant performance constraints, primarily due to limited flexibility in design space and the absence of advanced optimization strategies. Here, we propose a superoscillatory diffractive neural network (SODNN) that achieves highperformance spatial super-resolution focusing spots beyond the diffraction limit. The SODNN is constructed using diffractive layers to realize optical interconnections, enabling precise modulation of incident optical fields to generate superoscillatory effects in a three-dimensional (3D) space. By optimizing the diffractive layers under 3D optical field constraints at a central wavelength of λ, the system produces superoscillatory optical spots and needles with a full width at half-maximum (FWHM) of 0.405λ at far-field distances, while maintaining sidelobe-free performance across the entire field of view. Furthermore, our approach allows weak sidelobes with intensities below 10% of the central peak to reduce the FWHM to 0.367λ, demonstrating enhanced resolution through controlled energy leakage of the focusing spots. Moreover, the SODNN framework supports both multiwavelength and continuous-wavelength operations, effectively mitigating chromatic aberrations and achieving a balanced enhancement across all key performance metrics. This work offers a new paradigm for designing intelligent optical systems and paves the way for advanced applications in imaging, sensing, and optical perception.