  Optical super-oscillation enables far-field super-resolution imaging beyond
diffraction limits. However, the existing super-oscillatory lens for the
spatial super-resolution imaging system still confronts critical limitations in
performance due to the lack of a more advanced design method and the limited
design degree of freedom. Here, we propose an optical super-oscillatory
diffractive neural network, i.e., SODNN, that can achieve super-resolved
spatial resolution for imaging beyond the diffraction limit with superior
performance over existing methods. SODNN is constructed by utilizing
diffractive layers to implement optical interconnections and imaging samples or
biological sensors to implement nonlinearity, which modulates the incident
optical field to create optical super-oscillation effects in 3D space and
generate the super-resolved focal spots. By optimizing diffractive layers with
3D optical field constraints under an incident wavelength size of $\lambda$, we
achieved a super-oscillatory spot with a full width at half maximum of
0.407$\lambda$ in the far field distance over 400$\lambda$ without side-lobes
over the field of view, having a long depth of field over 10$\lambda$.
Furthermore, the SODNN implements a multi-wavelength and multi-focus spot array
that effectively avoids chromatic aberrations. Our research work will inspire
the development of intelligent optical instruments to facilitate the
applications of imaging, sensing, perception, etc.
