Effects of interlayer reflection and interpixel interaction in diffractive optical neural networks.

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.

Machine learning enables the design of a bidirectional focusing diffractive lens.

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.

Multifocal multilevel diffractive lens by wavelength multiplexing.

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.

Visible and near-infrared programmable multi-level diffractive lenses with phase change material Sb2S3.

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 Sb2S3 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 Sb2S3 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 Sb2S3. 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 Sb2S3 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.

Broadband lightweight flat lenses for long-wave infrared imaging.

We experimentally demonstrate imaging in the long-wave infrared (LWIR) spectral band (8 µm to 12 µm) using a single polymer flat lens based upon multilevel diffractive optics. The device thickness is only 10 µm, and chromatic aberrations are corrected over the entire LWIR band with one surface. Due to the drastic reduction in device thickness, we are able to utilize polymers with absorption in the LWIR, allowing for inexpensive manufacturing via imprint lithography. The weight of our lens is less than 100 times those of comparable refractive lenses. We fabricated and characterized 2 different flat lenses. Even with about 25% absorption losses, experiments show that our flat polymer lenses obtain good imaging with field of view of 35° and angular resolution less than 0.013°. The flat lenses were characterized with 2 different commercial LWIR image sensors. Finally, we show that, by using lossless, higher-refractive-index materials like silicon, focusing efficiencies in excess of 70% can be achieved over the entire LWIR band. Our results firmly establish the potential for lightweight, ultrathin, broadband lenses for high-quality imaging in the LWIR band.

Imaging from the visible to the longwave infrared wavelengths via an inverse-designed flat lens.

It is generally assumed that correcting chromatic aberrations in imaging requires multiple optical elements. Here, we show that by allowing the phase in the image plane to be a free parameter, it is possible to correct chromatic variation of focal length over an extremely large bandwidth, from the visible (Vis) to the longwave infrared (LWIR) wavelengths using a single diffractive surface, i.e., a flat lens. Specifically, we designed, fabricated and characterized a flat, multi-level diffractive lens (MDL) with a thickness of ≤ 10µm, diameter of ∼1mm, and focal length of 18mm, which was constant over the operating bandwidth of λ=0.45µm (blue) to 15µm (LWIR). We experimentally characterized the point-spread functions, aberrations and imaging performance of cameras comprised of this MDL and appropriate image sensors for λ=0.45µm to 11µm. We further show using simulations that such extreme achromatic MDLs can be achieved even at high numerical apertures (NA=0.81). By drastically increasing the operating bandwidth and eliminating several refractive lenses, our approach enables thinner, lighter and simpler imaging systems.

Monolithic all-silicon flat lens for broadband LWIR imaging.

We designed, fabricated, and characterized a flat multi-level diffractive lens comprised of only silicon with diameter=15.2mm, focal length=19mm, numerical aperture of 0.371, and operating over the long-wave infrared (LWIR) spectrum=8µm to 14 µm. We experimentally demonstrated a field of view of 46°, depth of focus >5mm, and wavelength-averaged Strehl ratio of 0.46. All of these metrics were comparable to those of a conventional refractive lens. The active device thickness is only 8 µm, and its weight (including the silicon substrate) is less than 0.2 g.

Super-resolution imaging with an achromatic multi-level diffractive microlens array.

Compound eyes found in insects provide intriguing sources of biological inspiration for miniaturized imaging systems. Inspired by such insect eye structures, we demonstrate an ultrathin arrayed camera enabled by a flat multi-level diffractive microlens array for super-resolution visible imaging. We experimentally demonstrate that the microlens array can achieve a large fill factor (hexagonal close packing with pitch=120µm), thickness of 2.6 µm, and diffraction-limited (Strehlratio=0.88) achromatic performance in the visible band (450 to 650 nm). We also demonstrate super-resolution imaging with resolution improvement of ∼1.4 times by computationally merging 1600 images in the array.

Ultra-thin near infrared camera enabled by a flat multi-level diffractive lens: erratum.

In Opt. Lett.44, 5450 (2019)OPLEDP0146-959210.1364/OL.44.005450, there were errors in the author listing and in one figure.

Ultra-thin near infrared camera enabled by a flat multi-level diffractive lens.

We experimentally demonstrate a ∼1-mm-thick near infrared camera comprised of a multi-level diffractive lens coupled with a conventional monochrome image sensor. We performed careful measurements of the point-spread function, the modulation transfer function, focusing efficiency, aberrations, and the field of view of the camera.

Terahertz imaging employing graphene modulator arrays.

In this paper we propose and experimentally demonstrate arrays of graphene electro-absorption modulators as electrically reconfigurable patterns for terahertz cameras. The active element of these modulators consists of only single-atom-thick graphene, achieving a modulation of the THz wave reflectance > 50% with a potential modulation depth approaching 100%. Although the prototype presented here only contains 4x4 pixels, it reveals the possibility of developing reliable low-cost video-rate THz imaging systems employing single detector.

Extraordinary control of terahertz beam reflectance in graphene electro-absorption modulators.

We demonstrate a graphene-based electro-absorption modulator achieving extraordinary control of terahertz reflectance. By concentrating the electric field intensity in an active layer of graphene, an extraordinary modulation depth of 64% is achieved while simultaneously exhibiting low insertion loss (∼2 dB), which is remarkable since the active region of the device is atomically thin. This modulator performance, among the best reported to date, indicates the enormous potential of graphene for terahertz reconfigurable optoelectronic devices.

A new class of electrically tunable metamaterial terahertz modulators.

Switchable metamaterials offer unique solutions for efficiently manipulating electromagnetic waves, particularly for terahertz waves, which has been difficult since naturally occurring materials rarely respond to terahertz frequencies controllably. However, few terahertz modulators demonstrated to date exhibit simultaneously low attenuation and high modulation depth. In this letter we propose a new class of electrically-tunable terahertz metamaterial modulators employing metallic frequency-selective-surfaces (FSS) in conjunction with capacitively-tunable layers of electrons, promising near 100% modulation depth and < 15% attenuation. The fundamental departure in our design from the prior art is tuning enabled by self-gated electron layers that is independent from the metallic FSS. Our proposal is applicable to all possible electrically tunable elements including graphene, Si, MoS(2), oxides etc, thus opening up myriad opportunities for realizing high performance switchable metamaterials over an ultra-wide terahertz frequency range.

Effect of extended defects on photoluminescence of gallium oxide and aluminum gallium oxide epitaxial films.

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) ß-Ga2O3 yield an intense dominant UV emission, while samples with extended structural defects, such as gallium oxide films grown on either (-201) ß-Ga2O3 or sapphire, as well as thick aluminum gallium oxide films grown on either (010) ß-Ga2O3 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.

Terahertz characterization of two-dimensional low-conductive layers enabled by metal gratings.

While terahertz spectroscopy can provide valuable information regarding the charge transport properties in semiconductors, its application for the characterization of low-conductive two-dimensional layers, i.e., σs < < 1 mS, remains elusive. This is primarily due to the low sensitivity of direct transmission measurements to such small sheet conductivity levels. In this work, we discuss harnessing the extraordinary optical transmission through gratings consisting of metallic stripes to characterize such low-conductive two-dimensional layers. We analyze the geometric tradeoffs in these structures and provide physical insights, ultimately leading to general design guidelines for experiments enabling non-contact, non-destructive, highly sensitive characterization of such layers.

Real-time multi-task diffractive deep neural networks via hardware-software co-design.

Deep neural networks (DNNs) have substantial computational requirements, which greatly limit their performance in resource-constrained environments. Recently, there are increasing efforts on optical neural networks and optical computing based DNNs hardware, which bring significant advantages for deep learning systems in terms of their power efficiency, parallelism and computational speed. Among them, free-space diffractive deep neural networks (D2NNs) based on the light diffraction, feature millions of neurons in each layer interconnected with neurons in neighboring layers. However, due to the challenge of implementing reconfigurability, deploying different DNNs algorithms requires re-building and duplicating the physical diffractive systems, which significantly degrades the hardware efficiency in practical application scenarios. Thus, this work proposes a novel hardware-software co-design method that enables first-of-its-like real-time multi-task learning in D22NNs that automatically recognizes which task is being deployed in real-time. Our experimental results demonstrate significant improvements in versatility, hardware efficiency, and also demonstrate and quantify the robustness of proposed multi-task D2NN architecture under wide noise ranges of all system components. In addition, we propose a domain-specific regularization algorithm for training the proposed multi-task architecture, which can be used to flexibly adjust the desired performance for each task.

Impact of fabrication errors and refractive index on multilevel diffractive lens performance.

Multilevel diffractive lenses (MDLs) have emerged as an alternative to both conventional diffractive optical elements (DOEs) and metalenses for applications ranging from imaging to holographic and immersive displays. Recent work has shown that by harnessing structural parametric optimization of DOEs, one can design MDLs to enable multiple functionalities like achromaticity, depth of focus, wide-angle imaging, etc. with great ease in fabrication. Therefore, it becomes critical to understand how fabrication errors still do affect the performance of MDLs and numerically evaluate the trade-off between efficiency and initial parameter selection, right at the onset of designing an MDL, i.e., even before putting it into fabrication. Here, we perform a statistical simulation-based study on MDLs (primarily operating in the THz regime) to analyse the impact of various fabrication imperfections (single and multiple) on the final structure as a function of the number of ring height levels. Furthermore, we also evaluate the performance of these same MDLs with the change in the refractive index of the constitutive material. We use focusing efficiency as the evaluation criterion in our numerical analysis; since it is the most fundamental property that can be used to compare and assess the performance of lenses (and MDLs) in general designed for any application with any specific functionality.

A Computational Design Framework for Efficient, Fabrication Error-Tolerant, Planar THz Diffractive Optical Elements.

We demonstrate ultra-thin (1.5-3λ0), fabrication-error tolerant efficient diffractive terahertz (THz) optical elements designed using a computer-aided optimization-based search algorithm. The basic operation of these components is modeled using scalar diffraction of electromagnetic waves through a pixelated multi-level 3D-printed polymer structure. Through the proposed design framework, we demonstrate the design of various ultrathin planar THz optical elements, namely (i) a high Numerical Aperture (N.A.), broadband aberration rectified spherical lens (0.1 THz-0.3 THz), (ii) a spectral splitter (0.3 THz-0.6 THz) and (iii) an on-axis broadband transmissive hologram (0.3 THz-0.5 THz). Such an all-dielectric computational design-based approach is advantageous against metallic or dielectric metasurfaces from the perspective that it incorporates all the inherent structural advantages associated with a scalar diffraction based approach, such as (i) ease of modeling, (ii) substrate-less facile manufacturing, (iii) planar geometry, (iv) high efficiency along with (v) broadband operation, (vi) area scalability and (vii) fabrication error-tolerance. With scalability and error tolerance being two major bottlenecks of previous design strategies. This work is therefore, a significant step towards the design of THz optical elements by bridging the gap between structural and computational design i.e. through a hybrid design-based approach enabling considerably less computational resources than the previous state of the art. Furthermore, the approach used herein can be expanded to a myriad of optical elements at any wavelength regime.

Manifestation of Kinetic Inductance in Terahertz Plasmon Resonances in Thin-Film Cd3As2.

Three-dimensional (3D) semimetals have been predicted and demonstrated to have a wide variety of interesting properties associated with their linear energy dispersion. In analogy to two-dimensional (2D) Dirac semimetals, such as graphene, Cd3As2 has shown ultrahigh mobility and large Fermi velocity and has been hypothesized to support plasmons at terahertz frequencies. In this work, we experimentally demonstrate synthesis of high-quality large-area Cd3As2 thin films through thermal evaporation as well as the experimental realization of plasmonic structures consisting of periodic arrays of Cd3As2 stripes. These arrays exhibit sharp resonances at terahertz frequencies with associated quality factors ( Q) as high as ∼3.7 (at 0.82 THz). Such spectrally narrow resonances can be understood on the basis of a long momentum scattering time, which in our films can approach ∼1 ps at room temperature. Moreover, we demonstrate an ultrafast tunable response through excitation of photoinduced carriers in optical pump/terahertz probe experiments. Our results evidence that the intrinsic 3D nature of Cd3As2 might provide for a very robust platform for terahertz plasmonic applications. Moreover, the long momentum scattering time as well as large kinetic inductance in Cd3As2 also holds enormous potential for the redesign of passive elements such as inductors and hence can have a profound impact in the field of RF integrated circuits.

THz characterization and demonstration of visible-transparent/terahertz-functional electromagnetic structures in ultra-conductive La-doped BaSnO3 Films.

We report on terahertz characterization of La-doped BaSnO3 (BSO) thin-films. BSO is a transparent complex oxide material, which has attracted substantial interest due to its large electrical conductivity and wide bandgap. The complex refractive index of these films is extracted in the 0.3 to 1.5 THz frequency range, which shows a metal-like response across this broad frequency window. The large optical conductivity found in these films at terahertz wavelengths makes this material an interesting platform for developing electromagnetic structures having a strong response at terahertz wavelengths, i.e. terahertz-functional, while being transparent at visible and near-IR wavelengths. As an example of such application, we demonstrate a visible-transparent terahertz polarizer.