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Machine learning can efficiently empower the inverse design of cascaded diffractive optical elements. In this work, we explore the inverse design of a bidirectional focusing diffractive lens in a cascaded configuration through the diffractive optical neural network (DONN) machine learning method. The bidirectional focusing diffractive lens consists of two on-axially cascaded multi-level diffractive lenses. Each lens consists of concentric rings with equal widths and varying heights. The height of each concentric ring is optimized as part of the design algorithm. The diffractive lens has a focal length f + as light propagates in the forward (Z+) direction. As light propagates in the backward (Z-) direction, the focal length changes to f - . The designed lens is fabricated through a two-photon polymerization 3D printing technique. The proposed design is polarization insensitive and miniature and can be readily applied in future functional optical imaging systems.

Multilayer diffractive optical neural networks (DONNs) can perform machine learning (ML) tasks at the speed of light with low energy consumption. Decreasing the number of diffractive layers can reduce inevitable material and diffraction losses to improve system performance, and incorporating compact devices can reduce the system footprint. However, current analytical DONN models cannot accurately describe such physical systems. Here we show the ever-ignored effects of interlayer reflection and interpixel interaction on the deployment performance of DONNs through full-wave electromagnetic simulations and terahertz (THz) experiments. We demonstrate that the drop of handwritten digit classification accuracy due to reflection is negligible with conventional low-index THz polymer materials, while it can be substantial with high-index materials. We further show that one- and few-layer DONN systems can achieve high classification accuracy, but there is a trade-off between accuracy and model-system matching rate because of the fast-varying spatial distribution of optical responses in diffractive masks. Deep DONNs can break down such a trade-off because of reduced mask spatial complexity. Our results suggest that new accurate and trainable DONN models are needed to advance the development and deployment of compact DONN systems for sophisticated ML tasks.

We designed, fabricated, and characterized a flat multi-level diffractive lens comprised of only silicon with d i a m e t e r =15.2 m m , focal l e n g t h =19 m m , numerical aperture of 0.371, and operating over the long-wave infrared (LWIR) s p e c t r u m =8µ m to 14 µm. We experimentally demonstrated a field of view of 46°, depth of focus >5 m m , and wavelength-averaged Strehl ratio of 0.46. All of these metrics were comparable to those of a conventional refractive lens. The active device thickness is only 8 µm, and its weight (including the silicon substrate) is less than 0.2 g.

Compound eyes found in insects provide intriguing sources of biological inspiration for miniaturized imaging systems. Inspired by such insect eye structures, we demonstrate an ultrathin arrayed camera enabled by a flat multi-level diffractive microlens array for super-resolution visible imaging. We experimentally demonstrate that the microlens array can achieve a large fill factor (hexagonal close packing with p i t c h =120µ m ), thickness of 2.6 µm, and diffraction-limited ( S t r e h l r a t i o =0.88) achromatic performance in the visible band (450 to 650 nm). We also demonstrate super-resolution imaging with resolution improvement of ∼1.4 times by computationally merging 1600 images in the array.

In Opt. Lett.44, 5450 (2019)OPLEDP0146-959210.1364/OL.44.005450, there were errors in the author listing and in one figure.

We experimentally demonstrate a ∼1-mm-thick near infrared camera comprised of a multi-level diffractive lens coupled with a conventional monochrome image sensor. We performed careful measurements of the point-spread function, the modulation transfer function, focusing efficiency, aberrations, and the field of view of the camera.