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Flat lenses with focal length tunability can enable the development of highly integrated imaging systems. This work explores machine learning to inverse design a multifocal multilevel diffractive lens (MMDL) by wavelength multiplexing. The MMDL output is multiplexed in three color channels, red (650 nm), green (550 nm), and blue (450 nm), to achieve varied focal lengths of 4 mm, 20 mm, and 40 mm at these three color channels, respectively. The focal lengths of the MMDL scale significantly with the wavelength in contrast to conventional diffractive lenses. The MMDL consists of concentric rings with equal widths and varied heights. The machine learning method is utilized to optimize the height of each concentric ring to obtain the desired phase distribution so as to achieve varied focal lengths multiplexed by wavelengths. The designed MMDL is fabricated through a direct-write laser lithography system with gray-scale exposure. The demonstrated singlet lens is miniature and polarization insensitive, and thus can potentially be applied in integrated optical imaging systems to achieve zooming functions.

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.

In this paper, we discuss flat programmable multi-level diffractive lenses (PMDL) enabled by phase change materials working in the near-infrared and visible ranges. The high real part refractive index contrast (Δn ∼ 0.6) of Sb 2 S 3 between amorphous and crystalline states, and extremely low losses in the near-infrared, enable the PMDL to effectively shift the lens focus when the phase of the material is altered between its crystalline and amorphous states. In the visible band, although losses can become significant as the wavelength is reduced, the lenses can still provide good performance as a result of their relatively small thickness (∼ 1.5λ to 3λ). The PMDL consists of Sb 2 S 3 concentric rings with equal width and varying heights embedded in a glass substrate. The height of each concentric ring was optimized by a modified direct binary search algorithm. The proposed designs show the possibility of realizing programmable lenses at design wavelengths from the near-infrared (850 nm) up to the blue (450 nm) through engineering PMDLs with Sb 2 S 3 . Operation at these short wavelengths, to the best of our knowledge, has not been studied so far in reconfigurable lenses with phase-change materials. Therefore, our results open a wider range of applications for phase-change materials, and show the prospect of Sb 2 S 3 for such applications. The proposed lenses are polarization insensitive and can have the potential to be applied in dual-functionality devices, optical imaging, and biomedical science.

In this work, a systematic photoluminescence (PL) study on three series of gallium oxide/aluminum gallium oxide films and bulk single crystals is performed including comparing doping, epitaxial substrates, and aluminum concentration. It is observed that blue/green emission intensity strongly correlates with extended structural defects rather than the point defects frequently assumed. Bulk crystals or Si-doped films homoepitaxially grown on (010) β-Ga 2 O 3 yield an intense dominant UV emission, while samples with extended structural defects, such as gallium oxide films grown on either (-201) β-Ga 2 O 3 or sapphire, as well as thick aluminum gallium oxide films grown on either (010) β-Ga 2 O 3 or sapphire, all show a very broad PL spectrum with intense dominant blue/green emission. PL differences between samples and the possible causes of these differences are analyzed. This work expands previous reports that have so far attributed blue and green emissions to point defects and shows that in the case of thin films, extended defects might have a prominent role in emission properties., (© 2022. The Author(s).)