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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.

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.

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.

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 Sb 2 S 3 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 Sb 2 S 3 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 Sb 2 S 3 . 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 Sb 2 S 3 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.

We designed, fabricated, and characterized a flat multi-level diffractive lens comprised of only silicon with d i a m e t e r =15.2 m m , focal l e n g t h =19 m m , numerical aperture of 0.371, and operating over the long-wave infrared (LWIR) s p e c t r u m =8µ m to 14 µm. We experimentally demonstrated a field of view of 46°, depth of focus >5 m m , 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.

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.

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 p i t c h =120µ m ), thickness of 2.6 µm, and diffraction-limited ( S t r e h l r a t i o =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.

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

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.

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.

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.