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Abstract The ability to design and dynamically control chiroptical responses in solid-state matter at a wafer scale enables new opportunities in various areas. Here, we present a full stack of computer-aided designs and experimental implementations of a dynamically programmable, unified, scalable chiroptical heterostructure containing wafer-scale twisted aligned one-dimensional carbon nanotubes and non-volatile phase change materials. We develop a software infrastructure based on high-performance machine learning frameworks, including differentiable programming and derivative-free optimization, to efficiently optimize the tunability of both reciprocal and nonreciprocal circular dichroism responses, which are experimentally validated. Further, we demonstrate the heterostructure scalability regarding stacking layers and the dual roles of aligned carbon nanotubes - the layer to produce chiroptical responses and the Joule heating electrode to electrically program phase change materials. This heterostructure platform is versatile and expandable to a library of one-dimensional nanomaterials, phase change materials, and electro-optic materials for exploring novel chiral phenomena and photonic and optoelectronic devices. 

Abstract Solving partial differential equations (PDEs) is the cornerstone of scientific research and development. Data-driven machine learning (ML) approaches are emerging to accelerate time-consuming and computation-intensive numerical simulations of PDEs. Although optical systems offer high-throughput and energy-efficient ML hardware, their demonstration for solving PDEs is limited. Here, we present an optical neural engine (ONE) architecture combining diffractive optical neural networks for Fourier space processing and optical crossbar structures for real space processing to solve time-dependent and time-independent PDEs in diverse disciplines, including Darcy flow equation, the magnetostatic Poisson’s equation in demagnetization, the Navier-Stokes equation in incompressible fluid, Maxwell’s equations in nanophotonic metasurfaces, and coupled PDEs in a multiphysics system. We numerically and experimentally demonstrate the capability of the ONE architecture, which not only leverages the advantages of high-performance dual-space processing for outperforming traditional PDE solvers and being comparable with state-of-the-art ML models but also can be implemented using optical computing hardware with unique features of low-energy and highly parallel constant-time processing irrespective of model scales and real-time reconfigurability for tackling multiple tasks with the same architecture. The demonstrated architecture offers a versatile and powerful platform for large-scale scientific and engineering computations. 

Creating artificial matter with controllable chirality in a simple and scalable manner brings new opportunities to diverse areas. Here we show two such methods based on controlled vacuum filtration - twist stacking and mechanical rotation - for fabricating wafer-scale chiral architectures of ordered carbon nanotubes (CNTs) with tunable and large circular dichroism (CD). By controlling the stacking angle and handedness in the twist-stacking approach, we maximize the CD response and achieve a high deep-ultraviolet ellipticity of 40 ± 1 mdeg nm⁻¹. Our theoretical simulations using the transfer matrix method reproduce the experimentally observed CD spectra and further predict that an optimized film of twist-stacked CNTs can exhibit an ellipticity as high as 150 mdeg nm⁻¹, corresponding to agfactor of 0.22. Furthermore, the mechanical rotation method not only accelerates the fabrication of twisted structures but also produces both chiralities simultaneously in a single sample, in a single run, and in a controllable manner. The created wafer-scale objects represent an alternative type of synthetic chiral matter consisting of ordered quantum wires whose macroscopic properties are governed by nanoscopic electronic signatures and can be used to explore chiral phenomena and develop chiral photonic and optoelectronic devices. 

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. 

Abstract 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.