Fig. 1. Training SODNN to optimize the diffractive elements with 3D optical field constraints. (a) Utilizing diffractive modulation layers and free-space propagation to implement the weighted optical interconnections, and imaging samples or biological sensors to implement nonlinearity. SODNN can modulate the multiwavelength incident optical field to create optical superoscillation effects in 3D superoscillatory regions. (b) The conventional methods optimize a 2D focus spot at a specific focusing distance to achieve optical superoscillation with a large sidelobe. (c) The enlarged 3D superoscillatory regions show that SODNN optimizes the 3D optical field in a certain distance range to achieve superoscillation without the sidelobe.

Fig. 2. Optical superoscillatory spots and optical needle design of SODNN. The FWHM (a) and the output (b) of superoscillatory spots at the designed focal length and distributions offsetting the designed focal length with the collimated input optical field. (c) The optical superoscillatory needle within a DoF of 6μm with uniform light intensity and consistent FWHM. (d) The 3D distributions of the output optical superoscillatory needle. (e) The output of the slices of the optical superoscillatory needle.

Fig. 3. Multiwavelength and multifocus SODNNs. (a) The superoscillatory spots under red, green, and blue light channels with the FWHM of 259, 221, and 199 nm, respectively. (b) The 3×5 superoscillatory spot arrays under red, green, and blue light channels with the FWHM of 267, 222, and 199 nm, respectively. (c) The superoscillatory spots of the T-H-U pattern with the FWHM of 274 nm and the superoscillatory spots of the heart-shaped pattern with the FWHM of 262 nm.

Fig. 4. Characterization of SODNN. (a) Schematic of the experimental setup. (b), (c) Imaging results of the resolution testing chart by commercial Olympus objective and SODNN. (d) The diffractive modulation layer of single-layer SODNNs for a single-focus (left) and 2×2 multifocus (middle) with the layer profile characterized by scanning electron microscope, i.e., SEM (right). (e) The numerical analysis results (left) and experimental results (middle) of the single-focus SODNN. (f) The numerical analysis results (left) and experimental results (middle) of the 2×2 multifocus SODNN.

Fig. 5. Performance analysis of SODNN. The FWHM of the output spot with respect to the modulation element number (a), the layer number (b), (c), and the modulation element size (d).

Fig. 6. Reconfigurable SODNN for superoscillatory imaging. The superoscillatory spot can raster scan over the field for imaging by dynamically programming the modulation coefficients of diffractive elements.

Fig. 7. Integrating SODNN with optical fiber. (a) Schematic diagram of the endoscope designed by integrating SODNN and optical fiber. (b) The imaging function is realized by utilizing the intensity of reflected light produced by different transmittance structures, such as the metal structure producing a strong reflection (c) and the glass forming a weak reflection on the hypothetical observation plane (d).