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Abstract Diffractive deep neural networks (D2NNs) are composed of successive transmissive layers optimized using supervised deep learning to all-optically implement various computational tasks between an input and output field-of-view. Here, we present a pyramid-structured diffractive optical network design (which we term P-D2NN), optimized specifically for unidirectional image magnification and demagnification. In this design, the diffractive layers are pyramidally scaled in alignment with the direction of the image magnification or demagnification. This P-D2NN design creates high-fidelity magnified or demagnified images in only one direction, while inhibiting the image formation in the opposite direction—achieving the desired unidirectional imaging operation using a much smaller number of diffractive degrees of freedom within the optical processor volume. Furthermore, the P-D2NN design maintains its unidirectional image magnification/demagnification functionality across a large band of illumination wavelengths despite being trained with a single wavelength. We also designed a wavelength-multiplexed P-D2NN, where a unidirectional magnifier and a unidirectional demagnifier operate simultaneously in opposite directions, at two distinct illumination wavelengths. Furthermore, we demonstrate that by cascading multiple unidirectional P-D2NN modules, we can achieve higher magnification factors. The efficacy of the P-D2NN architecture was also validated experimentally using terahertz illumination, successfully matching our numerical simulations. P-D2NN offers a physics-inspired strategy for designing task-specific visual processors.

Abstract Optical phase conjugation (OPC) is a nonlinear technique used for counteracting wavefront distortions, with applications ranging from imaging to beam focusing. Here, we present a diffractive wavefront processor to approximate all-optical phase conjugation. Leveraging deep learning, a set of diffractive layers was optimized to all-optically process an arbitrary phase-aberrated input field, producing an output field with a phase distribution that is the conjugate of the input wave. We experimentally validated this wavefront processor by 3D-fabricating diffractive layers and performing OPC on phase distortions never seen during training. Employing terahertz radiation, our diffractive processor successfully performed OPC through a shallow volume that axially spans tens of wavelengths. We also created a diffractive phase-conjugate mirror by combining deep learning-optimized diffractive layers with a standard mirror. Given its compact, passive and multi-wavelength nature, this diffractive wavefront processor can be used for various applications, e.g., turbidity suppression and aberration correction across different spectral bands.

Abstract Complex field imaging, which captures both the amplitude and phase information of input optical fields or objects, can offer rich structural insights into samples, such as their absorption and refractive index distributions. However, conventional image sensors are intensity-based and inherently lack the capability to directly measure the phase distribution of a field. This limitation can be overcome using interferometric or holographic methods, often supplemented by iterative phase retrieval algorithms, leading to a considerable increase in hardware complexity and computational demand. Here, we present a complex field imager design that enables snapshot imaging of both the amplitude and quantitative phase information of input fields using an intensity-based sensor array without any digital processing. Our design utilizes successive deep learning-optimized diffractive surfaces that are structured to collectively modulate the input complex field, forming two independent imaging channels that perform amplitude-to-amplitude and phase-to-intensity transformations between the input and output planes within a compact optical design, axially spanning ~100 wavelengths. The intensity distributions of the output fields at these two channels on the sensor plane directly correspond to the amplitude and quantitative phase profiles of the input complex field, eliminating the need for any digital image reconstruction algorithms. We experimentally validated the efficacy of our complex field diffractive imager designs through 3D-printed prototypes operating at the terahertz spectrum, with the output amplitude and phase channel images closely aligning with our numerical simulations. We envision that this complex field imager will have various applications in security, biomedical imaging, sensing and material science, among others.

Abstract Nonlinear optical processing of ambient natural light is highly desired for computational imaging and sensing. Strong optical nonlinear response under weak broadband incoherent light is essential for this purpose. By merging 2D transparent phototransistors (TPTs) with liquid crystal (LC) modulators, we create an optoelectronic neuron array that allows self-amplitude modulation of spatially incoherent light, achieving a large nonlinear contrast over a broad spectrum at orders-of-magnitude lower intensity than achievable in most optical nonlinear materials. We fabricated a 10,000-pixel array of optoelectronic neurons, and experimentally demonstrated an intelligent imaging system that instantly attenuates intense glares while retaining the weaker-intensity objects captured by a cellphone camera. This intelligent glare-reduction is important for various imaging applications, including autonomous driving, machine vision, and security cameras. The rapid nonlinear processing of incoherent broadband light might also find applications in optical computing, where nonlinear activation functions for ambient light conditions are highly sought.

Abstract Image denoising, one of the essential inverse problems, targets to remove noise/artifacts from input images. In general, digital image denoising algorithms, executed on computers, present latency due to several iterations implemented in, e.g., graphics processing units (GPUs). While deep learning-enabled methods can operate non-iteratively, they also introduce latency and impose a significant computational burden, leading to increased power consumption. Here, we introduce an analog diffractive image denoiser to all-optically and non-iteratively clean various forms of noise and artifacts from input images – implemented at the speed of light propagation within a thin diffractive visual processor that axially spans

Abstract Free-space optical communication becomes challenging when an occlusion blocks the light path. Here, we demonstrate a direct communication scheme, passing optical information around a fully opaque, arbitrarily shaped occlusion that partially or entirely occludes the transmitter’s field-of-view. In this scheme, an electronic neural network encoder and a passive, all-optical diffractive network-based decoder are jointly trained using deep learning to transfer the optical information of interest around the opaque occlusion of an arbitrary shape. Following its training, the encoder-decoder pair can communicate any arbitrary optical information around opaque occlusions, where the information decoding occurs at the speed of light propagation through passive light-matter interactions, with resilience against various unknown changes in the occlusion shape and size. We also validate this framework experimentally in the terahertz spectrum using a 3D-printed diffractive decoder. Scalable for operation in any wavelength regime, this scheme could be particularly useful in emerging high data-rate free-space communication systems.

Abstract Terahertz waves offer advantages for nondestructive detection of hidden objects/defects in materials, as they can penetrate most optically-opaque materials. However, existing terahertz inspection systems face throughput and accuracy restrictions due to their limited imaging speed and resolution. Furthermore, machine-vision-based systems using large-pixel-count imaging encounter bottlenecks due to their data storage, transmission and processing requirements. Here, we report a diffractive sensor that rapidly detects hidden defects/objects within a 3D sample using a single-pixel terahertz detector, eliminating sample scanning or image formation/processing. Leveraging deep-learning-optimized diffractive layers, this diffractive sensor can all-optically probe the 3D structural information of samples by outputting a spectrum, directly indicating the presence/absence of hidden structures or defects. We experimentally validated this framework using a single-pixel terahertz time-domain spectroscopy set-up and 3D-printed diffractive layers, successfully detecting unknown hidden defects inside silicon samples. This technique is valuable for applications including security screening, biomedical sensing and industrial quality control.

Abstract Many exciting terahertz imaging applications, such as non-destructive evaluation, biomedical diagnosis, and security screening, have been historically limited in practical usage due to the raster-scanning requirement of imaging systems, which impose very low imaging speeds. However, recent advancements in terahertz imaging systems have greatly increased the imaging throughput and brought the promising potential of terahertz radiation from research laboratories closer to real-world applications. Here, we review the development of terahertz imaging technologies from both hardware and computational imaging perspectives. We introduce and compare different types of hardware enabling frequency-domain and time-domain imaging using various thermal, photon, and field image sensor arrays. We discuss how different imaging hardware and computational imaging algorithms provide opportunities for capturing time-of-flight, spectroscopic, phase, and intensity image data at high throughputs. Furthermore, the new prospects and challenges for the development of future high-throughput terahertz imaging systems are briefly introduced.

Abstract Multispectral imaging has been used for numerous applications in e.g., environmental monitoring, aerospace, defense, and biomedicine. Here, we present a diffractive optical network-based multispectral imaging system trained using deep learning to create a virtual spectral filter array at the output image field-of-view. This diffractive multispectral imager performs spatially-coherent imaging over a large spectrum, and at the same time, routes a pre-determined set of spectral channels onto an array of pixels at the output plane, converting a monochrome focal-plane array or image sensor into a multispectral imaging device without any spectral filters or image recovery algorithms. Furthermore, the spectral responsivity of this diffractive multispectral imager is not sensitive to input polarization states. Through numerical simulations, we present different diffractive network designs that achieve snapshot multispectral imaging with 4, 9 and 16 unique spectral bands within the visible spectrum, based on passive spatially-structured diffractive surfaces, with a compact design that axially spans ~72λ m , where λ m is the mean wavelength of the spectral band of interest. Moreover, we experimentally demonstrate a diffractive multispectral imager based on a 3D-printed diffractive network that creates at its output image plane a spatially repeating virtual spectral filter array with 2 × 2 = 4 unique bands at terahertz spectrum. Due to their compact form factor and computation-free, power-efficient and polarization-insensitive forward operation, diffractive multispectral imagers can be transformative for various imaging and sensing applications and be used at different parts of the electromagnetic spectrum where high-density and wide-area multispectral pixel arrays are not widely available.

Abstract Classification of an object behind a random and unknown scattering medium sets a challenging task for computational imaging and machine vision fields. Recent deep learning-based approaches demonstrated the classification of objects using diffuser-distorted patterns collected by an image sensor. These methods demand relatively large-scale computing using deep neural networks running on digital computers. Here, we present an all-optical processor to directly classify unknown objects through unknown, random phase diffusers using broadband illumination detected with a single pixel. A set of transmissive diffractive layers, optimized using deep learning, forms a physical network that all-optically maps the spatial information of an input object behind a random diffuser into the power spectrum of the output light detected through a single pixel at the output plane of the diffractive network. We numerically demonstrated the accuracy of this framework using broadband radiation to classify unknown handwritten digits through random new diffusers, never used during the training phase, and achieved a blind testing accuracy of 87.74 ± 1.12%. We also experimentally validated our single-pixel broadband diffractive network by classifying handwritten digits “0” and “1” through a random diffuser using terahertz waves and a 3D-printed diffractive network. This single-pixel all-optical object classification system through random diffusers is based on passive diffractive layers that process broadband input light and can operate at any part of the electromagnetic spectrum by simply scaling the diffractive features proportional to the wavelength range of interest. These results have various potential applications in, e.g., biomedical imaging, security, robotics, and autonomous driving.

High-spectral-purity frequency-agile room-temperature THz sources are foundational elements for imaging, sensing, metrology, and communications. Here a parametric oscillator-photomixer chip with coherent 2.8-octave tunable THz radiation is achieved.

Semiconductor surface states often stand in the way of device performance, but here, the authors take advantage of them for wavelength conversion. They present a compact, passive conversion device insensitive to optical alignment by using plasmon-coupled surface states that enable the efficient conversion without nonlinear phenomena.

Diffractive networks have recently been discussed as an all-optical analogue for performing neural network operations. The authors present a method using deep learning-designed 3D-printed diffractive surfaces to engineer temporal waveforms and perform pulse shaping in the terahertz regime.

Strong terahertz (THz) emission from the methylammonium lead iodide (MAPbI3) perovskite semiconductors has been observed following above-bandgap photoexcitation, yet local THz responses of crystalline microstructures are absent. We implement laser THz emission microscope (LTEM), yet-to-be applied to the perovskite semiconductors, as a novel and complementary tool to evaluate the electronic and grain heterogeneity of MAPbI3 thin films. Two MAPbI3 samples with different grain sizes are studied. Using this approach, we show that the one with a larger grain size gives more uniform THz radiation. More significant spatial THz intensity fluctuation is observed for the sample with a smaller grain size.

Abstract Increases in the frequency and severity of droughts across many regions worldwide necessitate an improved capacity to determine the water status of plants at organ, whole plant, canopy, and regional scales. Noninvasive methods have most potential for simultaneously improving basic water relations research and ground‐, flight‐, and space‐based sensing of water status, with applications in sustainability, food security, and conservation. The most frequently used methods to measure the most salient proxies of plant water status, that is, water mass per leaf area (WMA), relative water content (RWC), and leaf water potential (Ψleaf), require the excision of tissues and laboratory analysis, and have thus been limited to relatively low throughput and small study scales. Applications using electromagnetic radiation in the visible, infrared, and terahertz ranges can resolve the water status of canopies, yet heretofore have typically focused on statistical approaches to estimating RWC for leaves before and after severe dehydration, and few have predicted Ψleaf. Terahertz radiation has great promise to estimate leaf water status across the range of leaf dehydration important for the control of gas exchange and leaf survival. We demonstrate a refined method and physical model to predict WMA, RWC, and Ψleaf from terahertz transmission across a wide range of levels of dehydration for given leaves of three species, as well as across leaves of given species and across multiple species. These findings highlight the powerful potential and the outstanding challenges in applying in vivo terahertz spectrometry as a remote sensor of water status for a range of applications.

Abstract The scope and potential uses of time-domain terahertz imaging and spectroscopy are mainly limited by the low optical-to-terahertz conversion efficiency of photoconductive terahertz sources. State-of-the-art photoconductive sources utilize short-carrier-lifetime semiconductors to recombine carriers that cannot contribute to efficient terahertz generation and cause additional thermal dissipation. Here, we present a novel photoconductive terahertz source that offers a significantly higher efficiency compared with terahertz sources fabricated on short-carrier-lifetime substrates. The key innovative feature of this source is the tight three-dimensional confinement of the optical pump beam around the terahertz nanoantennas that are used as radiating elements. This is achieved by means of a nanocavity formed by plasmonic structures and a distributed Bragg reflector. Consequently, almost all of the photo-generated carriers can be routed to the terahertz nanoantennas within a sub-picosecond time-scale. This results in a very strong, ultrafast current that drives the nanoantennas to produce broadband terahertz radiation. We experimentally demonstrate that this terahertz source can generate 4 mW pulsed terahertz radiation under an optical pump power of 720 mW over the 0.1–4 THz frequency range. This is the highest reported power level for terahertz radiation from a photoconductive terahertz source, representing more than an order of magnitude of enhancement in the optical-to-terahertz conversion efficiency compared with state-of-the-art photoconductive terahertz sources fabricated on short-carrier-lifetime substrates.

We present a polarization-insensitive plasmonic photoconductive terahertz emitter that uses a two-dimensional array of nanoscale cross-shaped apertures as the plasmonic contact electrodes. The geometry of the cross-shaped apertures is set to maximize optical pump absorption in close proximity to the contact electrodes. The two-dimensional symmetry of the cross-shaped apertures offers a polarization-insensitive interaction between the plasmonic contact electrodes and optical pump beam. We experimentally demonstrate a polarization-insensitive terahertz radiation from the presented emitter in response to a femtosecond optical pump beam and similar terahertz radiation powers compared to previously demonstrated polarization-sensitive photoconductive emitters with plasmonic contact electrode gratings at the optimum optical pump polarization.

In nonlinear microresonators driven by continuous-wave (cw) lasers, Turing patterns have been studied in the formalism of the Lugiato-Lefever equation with emphasis on their high coherence and exceptional robustness against perturbations. Destabilization of Turing patterns and the transition to spatiotemporal chaos, however, limit the available energy carried in the Turing rolls and prevent further harvest of their high coherence and robustness to noise. Here, we report a novel scheme to circumvent such destabilization, by incorporating the effect of local mode hybridizations, and we attain globally stable Turing pattern formation in chip-scale nonlinear oscillators with significantly enlarged parameter space, achieving a record-high power-conversion efficiency of 45% and an elevated peak-to-valley contrast of 100. The stationary Turing pattern is discretely tunable across 430 GHz on a THz carrier, with a fractional frequency sideband nonuniformity measured at 7.3×10^{−14}. We demonstrate the simultaneous microwave and optical coherence of the Turing rolls at different evolution stages through ultrafast optical correlation techniques. The free-running Turing-roll coherence, 9 kHz in 200 ms and 160 kHz in 20 minutes, is transferred onto a plasmonic photomixer for one of the highest-power THz coherent generations at room temperature, with 1.1% optical-to-THz power conversion. Its long-term stability can be further improved by more than 2 orders of magnitude, reaching an Allan deviation of 6×10^{−10} at 100 s, with a simple computer-aided slow feedback control. The demonstrated on-chip coherent high-power Turing-THz system is promising to find applications in astrophysics, medical imaging, and wireless communications.

A photoconductive terahertz emitter based on plasmonic contact electrode gratings is presented and experimentally demonstrated. The nanoscale grating enables ultrafast and high quantum efficiency operation simultaneously, by reducing the photo-generated carrier transport path to the photoconductor contact electrodes. The presented photoconductor eliminates the need for a short-carrier lifetime semiconductor, which limits the efficiency of conventional photoconductive terahertz emitters. Additionally, the photo-absorbing active area of the plasmonic photoconductive terahertz emitter can be increased without a significant increase in the capacitive loading to the terahertz radiating antenna, enabling high quantum-efficiency operation at high pump power levels by preventing the carrier screening effect and thermal breakdown. A plasmonic photoconductive terahertz emitter prototype based on the presented scheme is implemented and integrated with dipole antenna arrays on a semi-insulating In _0.53 Ga _0.47 As substrate. Emitted terahertz radiation is characterized in a terahertz time-domain spectroscopy setup, measuring a terahertz pulse width of 590 fs full-width at half maximum in response to 150 fs pump pulses at 925 nm.