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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.

This work discusses the design and fabrication of a dual-plane terahertz (THz) hologram and an extended-depth-of-focus THz diffractive lens. The dual-plane THz hologram consists of 50 × 50 diffractive optical elements with identical element pixel size 1×1 mm, and the extended-depth-of-focus THz diffractive lens is designed with 25 concentric rings with identical ring width of 1 mm, resulting in same device dimension 50 mm × 50 mm. The height of the hologram pixels and concentric rings of the diffractive lens are optimized by nonlinear optimization algorithms with scalar diffraction theory based on Ray-Sommerfeld diffraction equation. Finite-Difference Time-Domain (FDTD) simulation results agree with optimization results obtained from the scalar diffraction theory for both the THz hologram and the THz diffractive lens. The demonstrated experimental results show that the proposed THz hologram and THz diffractive lens can generate the desired diffraction patterns. These diffractive structures have the potential to be applied in areas such as THz imaging, data storage, and displays.

This paper discusses the terahertz electromagnetic response of metallic gratings on anisotropic dielectric substrates. The metallic gratings consist of parallel gold stripes. Utilizing numerical simulations, we observe that it is possible to excite a series of resonant modes in these structures. These modes are affected differently by the different indices on the anisotropic substrate. An analytical model is discussed to show that modes associated with transmission peaks are due to the excitation of (a) Fabry–Pérot modes with polarization along the grating and/or (b) waveguide modes with polarization perpendicular to the grating. It is observed that the resonance associated with the TM_1,1mode is a narrow linewidth resonance which, in some particular circumstances, becomes nearly independent of substrate thickness. Therefore, from the spectral position of this resonance, it is possible to extract the out-of-plane component of the substrate refractive index with very small uncertainty. Based on this observation, we demonstrate the refractive index characterization of several lossless semiconductor substrates through frequency-domain polarized terahertz transmission measurements in the frequency range of 0.2–0.6 THz at normal incidence. The reliability of the technique is demonstrated on well-known materials, such as high-resistivity silicon and sapphire substrates. This technique is also applied for the characterization of a Fe-doped β-Ga₂O₃single-crystal substrate.

Diffractive optical neural networks have shown promising advantages over electronic circuits for accelerating modern machine learning (ML) algorithms. However, it is challenging to achieve fully programmable all‐optical implementation and rapid hardware deployment. Here, a large‐scale, cost‐effective, complex‐valued, and reconfigurable diffractive all‐optical neural networks system in the visible range is demonstrated based on cascaded transmissive twisted nematic liquid crystal spatial light modulators. The employment of categorical reparameterization technique creates a physics‐aware training framework for the fast and accurate deployment of computer‐trained models onto optical hardware. Such a full stack of hardware and software enables not only the experimental demonstration of classifying handwritten digits in standard datasets, but also theoretical analysis and experimental verification of physics‐aware adversarial attacks onto the system, which are generated from a complex‐valued gradient‐based algorithm. The detailed adversarial robustness comparison with conventional multiple layer perceptrons and convolutional neural networks features a distinct statistical adversarial property in diffractive optical neural networks. The developed full stack of software and hardware provides new opportunities of employing diffractive optics in a variety of ML tasks and in the research on optical adversarial ML.