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.

翻译：光学超振荡能够实现超越衍射极限的远场超分辨率成像。然而，由于缺乏更先进的设计方法以及设计自由度有限，现有用于空间超分辨率成像系统的超振荡透镜在性能上仍面临关键限制。本文提出一种光学超振荡衍射神经网络（SODNN），该网络能够以超越现有方法的优异性能，实现突破衍射极限的超分辨空间分辨率成像。SODNN通过利用衍射层实现光学互连，并采用成像样本或生物传感器实现非线性，从而调制入射光场以在三维空间中产生光学超振荡效应，并生成超分辨聚焦光斑。通过在入射波长尺寸$\lambda$下采用三维光场约束优化衍射层，我们在远场距离超过400$\lambda$的范围内实现了半高全宽为0.407$\lambda$的超振荡光斑，且视场内无旁瓣，景深超过10$\lambda$。此外，SODNN实现了多波长多焦点光斑阵列，有效避免了色差问题。我们的研究工作将推动智能光学仪器的发展，促进成像、传感、感知等领域的应用。