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Permutation matrices form an important computational building block frequently used in various fields including e.g., communications, information security and data processing. Optical implementation of permutation operators with relatively large number of input-output interconnections based on power-efficient, fast, and compact platforms is highly desirable. Here, we present diffractive optical networks engineered through deep learning to all-optically perform permutation operations that can scale to hundreds of thousands of interconnections between an input and an output field-of-view using passive transmissive layers that are individually structured at the wavelength scale. Our findings indicate that the capacity of the diffractive optical network in approximating a given permutation operation increases proportional to the number of diffractive layers and trainable transmission elements in the system. Such deeper diffractive network designs can pose practical challenges in terms of physical alignment and output diffraction efficiency of the system. We addressed these challenges by designing misalignment tolerant diffractive designs that can all-optically perform arbitrarily-selected permutation operations, and experimentally demonstrated, for the first time, a diffractive permutation network that operates at THz part of the spectrum. Diffractive permutation networks might find various applications in e.g., security, image encryption and data processing, along with telecommunications; especially with the carrier frequencies in wireless communications approaching THz-bands, the presented diffractive permutation networks can potentially serve as channel routing and interconnection panels in wireless networks., Comment: 22 Pages, 6 Figures

A unidirectional imager would only permit image formation along one direction, from an input field-of-view (FOV) A to an output FOV B, and in the reverse path, the image formation would be blocked. Here, we report the first demonstration of unidirectional imagers, presenting polarization-insensitive and broadband unidirectional imaging based on successive diffractive layers that are linear and isotropic. These diffractive layers are optimized using deep learning and consist of hundreds of thousands of diffractive phase features, which collectively modulate the incoming fields and project an intensity image of the input onto an output FOV, while blocking the image formation in the reverse direction. After their deep learning-based training, the resulting diffractive layers are fabricated to form a unidirectional imager. As a reciprocal device, the diffractive unidirectional imager has asymmetric mode processing capabilities in the forward and backward directions, where the optical modes from B to A are selectively guided/scattered to miss the output FOV, whereas for the forward direction such modal losses are minimized, yielding an ideal imaging system between the input and output FOVs. Although trained using monochromatic illumination, the diffractive unidirectional imager maintains its functionality over a large spectral band and works under broadband illumination. We experimentally validated this unidirectional imager using terahertz radiation, very well matching our numerical results. Using the same deep learning-based design strategy, we also created a wavelength-selective unidirectional imager, where two unidirectional imaging operations, in reverse directions, are multiplexed through different illumination wavelengths. Diffractive unidirectional imaging using structured materials will have numerous applications in e.g., security, defense, telecommunications and privacy protection., 27 Pages, 10 Figures

We report deep learning-based design of a massively parallel broadband diffractive neural network for all-optically performing a large group of arbitrarily-selected, complex-valued linear transformations between an input and output field-of-view, each with N_i and N_o pixels, respectively. This broadband diffractive processor is composed of N_w wavelength channels, each of which is uniquely assigned to a distinct target transformation. A large set of arbitrarily-selected linear transformations can be individually performed through the same diffractive network at different illumination wavelengths, either simultaneously or sequentially (wavelength scanning). We demonstrate that such a broadband diffractive network, regardless of its material dispersion, can successfully approximate N_w unique complex-valued linear transforms with a negligible error when the number of diffractive neurons (N) in its design matches or exceeds 2 x N_w x N_i x N_o. We further report that the spectral multiplexing capability (N_w) can be increased by increasing N; our numerical analyses confirm these conclusions for N_w > 180, which can be further increased to e.g., ~2000 depending on the upper bound of the approximation error. Massively parallel, wavelength-multiplexed diffractive networks will be useful for designing high-throughput intelligent machine vision systems and hyperspectral processors that can perform statistical inference and analyze objects/scenes with unique spectral properties., 30 Pages, 9 Figures

Diffractive optical networks provide rich opportunities for visual computing tasks since the spatial information of a scene can be directly accessed by a diffractive processor without requiring any digital pre-processing steps. Here we present data class-specific transformations all-optically performed between the input and output fields-of-view (FOVs) of a diffractive network. The visual information of the objects is encoded into the amplitude (A), phase (P), or intensity (I) of the optical field at the input, which is all-optically processed by a data class-specific diffractive network. At the output, an image sensor-array directly measures the transformed patterns, all-optically encrypted using the transformation matrices pre-assigned to different data classes, i.e., a separate matrix for each data class. The original input images can be recovered by applying the correct decryption key (the inverse transformation) corresponding to the matching data class, while applying any other key will lead to loss of information. The class-specificity of these all-optical diffractive transformations creates opportunities where different keys can be distributed to different users; each user can only decode the acquired images of only one data class, serving multiple users in an all-optically encrypted manner. We numerically demonstrated all-optical class-specific transformations covering A-->A, I-->I, and P-->I transformations using various image datasets. We also experimentally validated the feasibility of this framework by fabricating a class-specific I-->I transformation diffractive network using two-photon polymerization and successfully tested it at 1550 nm wavelength. Data class-specific all-optical transformations provide a fast and energy-efficient method for image and data encryption, enhancing data security and privacy., 27 Pages, 9 Figures, 1 Table

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 ~72 times 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 2x2=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., 24 Pages, 9 Figures

We present a telecommunication-compatible frequency-domain terahertz spectroscopy system realized by novel photoconductive antennas without using short-carrier-lifetime photoconductors. Built on a high-mobility InGaAs photoactive layer, these photoconductive antennas are designed with plasmonics-enhanced contact electrodes to achieve highly confined optical generation near the metal/semiconductor surface, which offers ultrafast photocarrier transport and, hence, efficient continuous-wave terahertz operation including both generation and detection. Consequently, using two plasmonic photoconductive antennas as a terahertz source and a terahertz detector, we successfully demonstrate frequency-domain spectroscopy with a dynamic range more than 95 dB and an operation bandwidth of 2.5 THz. Moreover, this novel approach to terahertz antenna design opens up a wide range of new possibilities for many different semiconductors and optical excitation wavelengths to be utilized, therefore bypassing short-carrier-lifetime photoconductors with limited availability.

We present a bias-free photoconductive emitter that uses an array of nanoantennas on an InGaAs layer with a linearly graded Indium composition. The graded InGaAs structure creates a built-in electric field that extends through the entire photoconductive active region, enabling the efficient drift of the photo-generated electrons to the nanoantennas. The nanoantenna geometry is chosen so that surface plasmon waves are excited in response to a 1550 nm optical pump to maximize photo-generated carrier concentration near the nanoantennas, where the built-in electric field strength is maximized. With the combination of the plasmonic enhancement and built-in electric field, high-power terahertz pulses are generated without using any external bias voltage. We demonstrate the generation of terahertz pulses with 860 µW average power at an average optical pump power of 900 mW, exhibiting the highest radiation power compared to previously demonstrated telecommunication-compatible terahertz pulse emitters.

High-resolution synthesis/projection of images over a large field-of-view (FOV) is hindered by the restricted space-bandwidth-product (SBP) of wavefront modulators. We report a deep learning-enabled diffractive display design that is based on a jointly-trained pair of an electronic encoder and a diffractive optical decoder to synthesize/project super-resolved images using low-resolution wavefront modulators. The digital encoder, composed of a trained convolutional neural network (CNN), rapidly pre-processes the high-resolution images of interest so that their spatial information is encoded into low-resolution (LR) modulation patterns, projected via a low SBP wavefront modulator. The diffractive decoder processes this LR encoded information using thin transmissive layers that are structured using deep learning to all-optically synthesize and project super-resolved images at its output FOV. Our results indicate that this diffractive image display can achieve a super-resolution factor of ~4, demonstrating a ~16-fold increase in SBP. We also experimentally validate the success of this diffractive super-resolution display using 3D-printed diffractive decoders that operate at the THz spectrum. This diffractive image decoder can be scaled to operate at visible wavelengths and inspire the design of large FOV and high-resolution displays that are compact, low-power, and computationally efficient., Comment: 26 Pages, 9 Figures

Privacy protection is a growing concern in the digital era, with machine vision techniques widely used throughout public and private settings. Existing methods address this growing problem by, e.g., encrypting camera images or obscuring/blurring the imaged information through digital algorithms. Here, we demonstrate a camera design that performs class-specific imaging of target objects with instantaneous all-optical erasure of other classes of objects. This diffractive camera consists of transmissive surfaces structured using deep learning to perform selective imaging of target classes of objects positioned at its input field-of-view. After their fabrication, the thin diffractive layers collectively perform optical mode filtering to accurately form images of the objects that belong to a target data class or group of classes, while instantaneously erasing objects of the other data classes at the output field-of-view. Using the same framework, we also demonstrate the design of class-specific permutation cameras, where the objects of a target data class are pixel-wise permuted for all-optical class-specific encryption, while the other objects are irreversibly erased from the output image. The success of class-specific diffractive cameras was experimentally demonstrated using terahertz (THz) waves and 3D-printed diffractive layers that selectively imaged only one class of the MNIST handwritten digit dataset, all-optically erasing the other handwritten digits. This diffractive camera design can be scaled to different parts of the electromagnetic spectrum, including, e.g., the visible and infrared wavelengths, to provide transformative opportunities for privacy-preserving digital cameras and task-specific data-efficient imaging., Comment: 31 Pages, 7 Figures

Surface states generally degrade semiconductor device performance by raising the charge injection barrier height, introducing localized trap states, inducing surface leakage current, and altering the electric potential. Therefore, there has been an endless effort to use various surface passivation treatments to suppress the undesirable impacts of the surface states. We show that the giant built-in electric field created by the surface states can be harnessed to enable passive wavelength conversion without utilizing any nonlinear optical phenomena. Photo-excited surface plasmons are coupled to the surface states to generate an electron gas, which is routed to a nanoantenna array through the giant electric field created by the surface states. The induced current on the nanoantennas, which contains mixing product of different optical frequency components, generates radiation at the beat frequencies of the incident photons. We utilize the unprecedented functionalities of plasmon-coupled surface states to demonstrate passive wavelength conversion of nanojoule optical pulses at a 1550 nm center wavelength to terahertz regime with record-high efficiencies that exceed nonlinear optical methods by 4-orders of magnitude. The presented scheme can be used for optical wavelength conversion to different parts of the electromagnetic spectrum ranging from microwave to infrared regimes by using appropriate optical beat frequencies., Comment: Manuscript: 8 pages, 4 figures Supplementary materials: 21 pages, 11 figures

Our Universe is most radiant at terahertz frequencies (0.1–10.0 THz) (ref. 1), providing critical information on the formation of the planets, stars and galaxies, as well as the atmospheric constituents of the planets, their moons, comets and asteroids2–9. The detection of faint fluxes of photons at terahertz frequencies is crucial for many planetary, cosmological and astrophysical studies10–14. For example, understanding the physics and molecular chemistry of the life cycle of stars and their relationship with the interstellar medium in galaxies requires heterodyne detectors with noise temperatures close to the quantum limit15. Near-quantum-limited heterodyne terahertz detection has so far been possible only through the use of cryogenically cooled superconducting mixers as frequency downconverters15–18. Here we introduce a heterodyne terahertz detection scheme that uses plasmonic photomixing for frequency downconversion to offer quantum-level sensitivities at room temperature. Frequency downconversion is achieved by mixing terahertz radiation and a heterodyning optical beam with a terahertz beat frequency in a plasmonics-enhanced semiconductor active region. We demonstrate terahertz detection sensitivities down to three times the quantum limit at room temperature. With a versatile design capable of broadband operation over a 0.1–5.0 THz bandwidth, this plasmonic photomixer has broad applicability to astronomy, cosmology, atmospheric studies, gas sensing and quantum optics. The measurement of faint fluxes of photons from across the Universe requires sensitive terahertz detectors, cooled to minimize noise. By using a photomixer with plasmonics-based semiconductors to downconvert the high frequencies, terahertz detection can be accomplished at room temperature.

Communication at terahertz carrier frequencies is a promising way to satisfy the ever-growing demands for high-speed wireless networks. The studies of terahertz wireless channels have so far been limited to the atmospheric transmission bands below 350 GHz. Availability of high-power transmitters and high-sensitivity receivers at higher frequencies necessitates extending the wireless channel studies to enable higher data-rate communication systems. With a view to assessing communication system design requirements at higher frequencies, we present the channel measurement results for 650-GHz carrier frequencies in comparison with 350 GHz carrier frequencies in a typical indoor environment. To obtain the spatial and temporal characteristics of the channel, the power angle profile and the power delay profile are measured based on new measurement methods. Multiple spatially resolvable paths are observed at both 350- and 650-GHz carrier frequencies. Signal-to-noise ratio of the received signal through the non-line-of-sight (NLoS) paths is sufficiently high to enable robust communication when the direct line-of-sight (LoS) path is blocked due to a moving object. The measurement results are used to calculate the reduction in the 650-GHz channel capacity in comparison with that of the 350-GHz channel for both LoS and NLoS paths. Channel dispersion characterization over a 10-GHz bandwidth shows that the delay spreads for the resolved LoS and NLoS paths are less than 80 ps for both 350- and 650-GHz bands. Therefore, no complicated equalizer is required to compensate for channel dispersion at both 350 and 650-GHz, which greatly simplifies the terahertz transceiver design.

Imaging through diffusers presents a challenging problem with various digital image reconstruction solutions demonstrated to date using computers. We present a computer-free, all-optical image reconstruction method to see through random diffusers at the speed of light. Using deep learning, a set of diffractive surfaces are designed/trained to all-optically reconstruct images of objects that are covered by random phase diffusers. We experimentally demonstrated this concept using coherent THz illumination and all-optically reconstructed objects distorted by unknown, random diffusers, never used during training. Unlike digital methods, all-optical diffractive reconstructions do not require power except for the illumination light. This diffractive solution to see through diffusers can be extended to other wavelengths, and might fuel various applications in biomedical imaging, astronomy, atmospheric sciences, oceanography, security, robotics, among others., Comment: 35 Pages, 7 Figures

The stability of optical beats in a chaotically oscillating laser is compared to that of a free-running continuous-wave laser using a highly efficient plasmonic photomixer. Using a chaotically oscillating laser diode, stable optical beats are observed over an operation current range of 60-90 mA. The optical spectra are stable even with frequent mode hopping. In contrast, optical beats in a free-running continuous-wave laser are not stable compared to those of a chaotically oscillating laser, because of intermittent hopping of the laser modes. The high stability of chaotically oscillating lasers makes these lasers promising candidates for optical pump sources in terahertz time-domain spectroscopy systems.

We present a telecommunication-compatible photoconductive terahertz detector realized without using any short-carrier-lifetime photoconductor. By utilizing plasmonic contact electrodes on a thin layer of high-mobility photoconductor, the presented detector offers a short transit time for the majority of the photocarriers in the absence of a short-carrier-lifetime photoconductor. Consequently, high-sensitivity terahertz detection is achieved with a record-high signal-to-noise ratio of 122 dB over a 3.6 THz bandwidth under an optical probe power of 10 mW. To achieve such a high sensitivity, the device geometry is chosen to maintain a high resistance and low Johnson Nyquist noise. This design approach can be widely applied for terahertz detection using various semiconductors and optical wavelengths, without being limited by the availability of short-carrier-lifetime photoconductors.

We present a technique for high-precision millimeter-wave frequency determination through plasmonic photomixing. Our technique utilizes a plasmonic photomixer pumped by an optical frequency comb with a high-stability millimeter-wave beat frequency. The plasmonic photomixer down-converts the millimeter-wave signal to the radio frequency regime at which high-accuracy frequency counters are available. The precision of this technique is determined by the frequency stability of the optical beat frequency, which can be directly characterized in the presented experimental setup. We demonstrate frequency measurement precision as low as 3.9×10−10 at 95 GHz through plasmonic photomixing without phase-locking the optical frequency comb.

Recent advances in deep learning have been providing non-intuitive solutions to various inverse problems in optics. At the intersection of machine learning and optics, diffractive networks merge wave-optics with deep learning to design task-specific elements to all-optically perform various tasks such as object classification and machine vision. Here, we present a diffractive network, which is used to shape an arbitrary broadband pulse into a desired optical waveform, forming a compact pulse engineering system. We experimentally demonstrate the synthesis of square pulses with different temporal-widths by manufacturing passive diffractive layers that collectively control both the spectral amplitude and the phase of an input terahertz pulse. Our results constitute the first demonstration of direct pulse shaping in terahertz spectrum, where a complex-valued spectral modulation function directly acts on terahertz frequencies. Furthermore, a Lego-like physical transfer learning approach is presented to illustrate pulse-width tunability by replacing part of an existing network with newly trained diffractive layers, demonstrating its modularity. This learning-based diffractive pulse engineering framework can find broad applications in e.g., communications, ultra-fast imaging and spectroscopy., 27 pages, 6 figures

As an optical machine learning framework, Diffractive Deep Neural Networks (D2NN) take advantage of data-driven training methods used in deep learning to devise light-matter interaction in 3D for performing a desired statistical inference task. Multi-layer optical object recognition platforms designed with this diffractive framework have been shown to generalize to unseen image data achieving e.g., >98% blind inference accuracy for hand-written digit classification. The multi-layer structure of diffractive networks offers significant advantages in terms of their diffraction efficiency, inference capability and optical signal contrast. However, the use of multiple diffractive layers also brings practical challenges for the fabrication and alignment of these diffractive systems for accurate optical inference. Here, we introduce and experimentally demonstrate a new training scheme that significantly increases the robustness of diffractive networks against 3D misalignments and fabrication tolerances in the physical implementation of a trained diffractive network. By modeling the undesired layer-to-layer misalignments in 3D as continuous random variables in the optical forward model, diffractive networks are trained to maintain their inference accuracy over a large range of misalignments; we term this diffractive network design as vaccinated D2NN (v-D2NN). We further extend this vaccination strategy to the training of diffractive networks that use differential detectors at the output plane as well as to jointly-trained hybrid (optical-electronic) networks to reveal that all of these diffractive designs improve their resilience to misalignments by taking into account possible 3D fabrication variations and displacements during their training phase., 15 Pages, 6 Figures

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.

3D engineering of matter has opened up new avenues for designing systems that can perform various computational tasks through light-matter interaction. Here, we demonstrate the design of optical networks in the form of multiple diffractive layers that are trained using deep learning to transform and encode the spatial information of objects into the power spectrum of the diffracted light, which are used to perform optical classification of objects with a single-pixel spectroscopic detector. Using a time-domain spectroscopy setup with a plasmonic nanoantenna-based detector, we experimentally validated this machine vision framework at terahertz spectrum to optically classify the images of handwritten digits by detecting the spectral power of the diffracted light at ten distinct wavelengths, each representing one class/digit. We also report the coupling of this spectral encoding achieved through a diffractive optical network with a shallow electronic neural network, separately trained to reconstruct the images of handwritten digits based on solely the spectral information encoded in these ten distinct wavelengths within the diffracted light. These reconstructed images demonstrate task-specific image decompression and can also be cycled back as new inputs to the same diffractive network to improve its optical object classification. This unique machine vision framework merges the power of deep learning with the spatial and spectral processing capabilities of diffractive networks, and can also be extended to other spectral-domain measurement systems to enable new 3D imaging and sensing modalities integrated with spectrally encoded classification tasks performed through diffractive optical networks., Comment: 21 pages, 5 figures, 1 table

We introduce an all-optical Diffractive Deep Neural Network (D2NN) architecture that can learn to implement various functions after deep learning-based design of passive diffractive layers that work collectively. We experimentally demonstrated the success of this framework by creating 3D-printed D2NNs that learned to implement handwritten digit classification and the function of an imaging lens at terahertz spectrum. With the existing plethora of 3D-printing and other lithographic fabrication methods as well as spatial-light-modulators, this all-optical deep learning framework can perform, at the speed of light, various complex functions that computer-based neural networks can implement, and will find applications in all-optical image analysis, feature detection and object classification, also enabling new camera designs and optical components that can learn to perform unique tasks using D2NNs., Comment: 20 pages, 4 figures

We present a heterodyne terahertz spectrometry platform based on plasmonic photomixing, which enables the resolution of narrow spectral signatures of gases over a broad terahertz frequency range. This plasmonic heterodyne spectrometer replaces the terahertz mixer and local oscillator of conventional heterodyne spectrometers with a plasmonic photomixer and a heterodyning optical pump beam, respectively. The heterodyning optical pump beam is formed by two continuous-wave, wavelength-tunable lasers with a broadly tunable terahertz beat frequency. This broadly tunable terahertz beat frequency enables spectrometry over a broad bandwidth, which is not restricted by the bandwidth limitations of conventional terahertz mixers and local oscillators. We use this plasmonic heterodyne spectrometry platform to resolve the spectral signatures of ammonia over a 1-4.5 THz frequency range.

Deep learning has been transformative in many fields, motivating the emergence of various optical computing architectures. Diffractive optical network is a recently introduced optical computing framework that merges wave optics with deep-learning methods to design optical neural networks. Diffraction-based all-optical object recognition systems, designed through this framework and fabricated by 3D printing, have been reported to recognize hand-written digits and fashion products, demonstrating all-optical inference and generalization to sub-classes of data. These previous diffractive approaches employed monochromatic coherent light as the illumination source. Here, we report a broadband diffractive optical neural network design that simultaneously processes a continuum of wavelengths generated by a temporally incoherent broadband source to all-optically perform a specific task learned using deep learning. We experimentally validated the success of this broadband diffractive neural network architecture by designing, fabricating and testing seven different multi-layer, diffractive optical systems that transform the optical wavefront generated by a broadband THz pulse to realize (1) a series of tuneable, single-passband and dual-passband spectral filters and (2) spatially controlled wavelength de-multiplexing. Merging the native or engineered dispersion of various material systems with a deep-learning-based design strategy, broadband diffractive neural networks help us engineer the light–matter interaction in 3D, diverging from intuitive and analytical design methods to create task-specific optical components that can all-optically perform deterministic tasks or statistical inference for optical machine learning., Optical computing: Harnessing a rainbow with diffractive neural networks An optical machine learning framework termed Diffractive Deep Neural Networks has been expanded to compute a variety of desired tasks through broadband light and simultaneous processing of a wide and continuous range of wavelengths. Aydogan Ozcan and colleagues at the University of California, Los Angeles, USA, incorporated the wavelength-dependent nature of light–matter interaction occurring at multiple layers of a diffractive network to learn and extract input information at increasing levels of complexity. Simultaneously analyzing and processing light across many wavelengths present unique opportunities to enhance the inference and generalization capabilities of diffractive optical networks to perform machine learning tasks, e.g. all-optical object recognition, as well as to design deterministic and task-specific optical components, expanding the optical design space beyond human intuition.

We present a photoconductive terahertz detector that employs a plasmonic nanocavity to offer high-sensitivity and broadband operation when used in a terahertz time-domain spectroscopy system even at very low optical pump power levels. By employing a plasmonic nanocavity, all of the photocarriers are generated within a 100 nm distance from the photoconductor contact electrodes, enabling a short transport time for almost all of the photogenerated carriers. As a result, the photoconductive detector maintains high quantum efficiency and ultrafast operation simultaneously, enabling high-sensitivity and broadband operation at very low optical pump power levels. We utilize a photoconductive detector based on a plasmonic nanocavity optimized for operation at a 770 nm optical wavelength in a terahertz time-domain spectroscopy system and demonstrate a 100 dB signal-to-noise ratio and a 0.1–6 THz noise-equivalent bandwidth at a record-low average optical pump power of 0.1 mW, compared to the state-of-the-art photoconductive terahertz detectors. The extremely low optical power budget of the demonstrated photoconductive detector makes this detector attractive for multi-pixel terahertz imaging systems.

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 telecommunication-compatible, bias-free photoconductive terahertz source with arrays of plasmonic nano-antennas. We demonstrate pulsed terahertz radiation with powers up to 72 $\mu\mathrm{W}$ ., enabling time-domain terahertz spectroscopy over a 3 THz bandwidth with a 100 dB dynamic range.

We report a self-triggered asynchronous optical sampling terahertz spectroscopy system based on a single bidirectional mode-locked fiber laser and plasmonics-enhanced photoconductive nanoantennas. The fiber laser generates two optical mutually coherent pulse trains with a stable repetition rate difference, enabling time-domain terahertz spectroscopy without using any mechanical delay line, stabilization electronics, or external trigger. The resolved terahertz spectra over a 0.1–2 THz frequency range and a 30-second measurement time show more than a 70-dB dynamic range, revealing water absorption lines matching the HITRAN database, through a light-weight and compact spectroscopy setup.

We present a photoconductive terahertz detector operating at the 1 µm wavelength range at which high-power and compact Ytterbium-doped femtosecond fiber lasers are available. The detector utilizes an array of plasmonic nanoantennas to provide sub-picosecond transit time for the majority of photo-generated carriers to enable high-sensitivity terahertz detection without using a short-carrier-lifetime substrate. By using a high-mobility semiconductor substrate and preventing photocarrier recombination, the presented detector offers significantly higher sensitivity levels compared with previously demonstrated broadband photoconductive terahertz detectors operating at the 1 µm wavelength range. We demonstrate pulsed terahertz detection over a 4 THz bandwidth with a record-high signal-to-noise ratio of 95 dB at an average terahertz radiation power of 6.8 µW, when using an optical pump power of 30 mW.