Metasurface Freeform Nanophotonics

Unveiling Invariant Optical Properties of Dielectric Meta-Atoms

The phase-shift, transmittance, and polarization properties of meta-atoms are investigated, motivated by their use as building blocks of metasurfaces used in metalenses, holograms, and beam shaping. We studied dielectric nanorod meta-atoms of several geometries, which included cylinders, triangles, squares, hexagons, octagons, and truncated cones. By analyzing light propagation through these meta-atoms for three different wavelengths (632.8, 545, and 50 nm), we show that the phase-shift introduced is independent of their cross-section shape, contrary to the expected behavior. Additionally, we show that the polarization response is independent of the shape and that the transmittance is partially shape-independent. We identify a novel dependence of phase-shift on the effective cross-sectional area of meta-atoms. These meta-atom optical properties are independent of its shape if its geometry has a C3 or larger rotational symmetry. This optical invariance has significant implications for the topological optimization of flat optics.

Metasurface-based varifocal Alvarez lens at microwave frequencies

Lenses with a tunable focus are highly desirable but remain a challenge. Here, we demonstrate a microwave varifocal meta-lens based on the Alvarez lens principle, consisting of two mechanically movable tri-layer metasurface phase plates with reversed cubic spatial profiles. The manufactured multilayer Alvarez meta-lens enables microwave beam collimation/focusing at frequencies centered at 7.5 GHz, and shows one octave focal length tunability when transversely translating the phase plates by 8 cm. The measurements reveal a gain enhancement up to 15 dB, 3-dB beam width down to 3.5∘, and relatively broad 3-dB bandwidth of 3 GHz. These advantageous characteristics, along with its simplicity, compactness, and lightweightness, make the demonstrated flat Alvarez meta-lens suitable for deployment in many microwave systems.

Non-imaging metasurface design for collimated beam shaping

Non-imaging optical lenses can shape the light intensity from incoherent sources to a desired target intensity profile, which is important for applications in lighting, solar light concentration, and optical beam shaping. Their surface curvatures are designed to ensure optimal transfer of energy from the light source to the target. The performance of such lenses is directly linked to their asymmetric freeform surface curvature, which is challenging to manufacture. Metasurfaces can mimic any surface curvature without additional fabrication difficulty by imparting a spatially-dependent phase delay using optical antennas. As a result, metasurfaces are uniquely suited to realize non-imaging optics, but non-imaging design principles have not yet been established for metasurfaces. Here, we take an important step in connecting non-imaging optics and metasurface optics, by presenting a phase-design method for beam shaping based on the concept of optimal transport. We establish a theoretical framework that enables a collimated beam to be redistributed by a metasurface to a desired output intensity profile. The optimal transport formulation leads to metasurface phase profiles that transmit all energy from the incident beam to the output beam, resulting in an efficient beam shaping process. Through a variety of examples, we show that our approach accommodates a diverse range of different input and output intensity profiles. Last but not least, a full field simulation of a metasurface has been done to verify our phase-design framework.

Large field-of-view short-wave infrared metalens for scanning fiber endoscopy

SIGNIFICANCE

The scanning fiber endoscope (SFE), an ultrasmall optical imaging device with a large field-of-view (FOV) for having a clear forward view into the interior of blood vessels, has great potential in the cardiovascular disease diagnosis and surgery assistance, which is one of the key applications for short-wave infrared biomedical imaging. The state-of-the-art SFE system uses a miniaturized refractive spherical lens doublet for beam projection. A metalens is a promising alternative that can be made much thinner and has fewer off-axis aberrations than its refractive counterpart.

AIM

We demonstrate a transmissive metalens working at 1310 nm for a forward viewing endoscope to achieve a shorter device length and better resolution at large field angles.

APPROACH

We optimize the metalens of the SFE system using Zemax, fabricate it using e-beam lithography, characterize its optical performances, and compare them with the simulations.

RESULTS

The SFE system has a resolution of ∼ 140    μ m at the center of field (imaging distance 15 mm), an FOV of ∼ 70    deg , and a depth-of-focus of ∼ 15    mm , which are comparable with a state-of-the-art refractive lens SFE. The use of the metalens reduces the length of the optical track from 1.2 to 0.86 mm. The resolution of our metalens-based SFE drops by less than a factor of 2 at the edge of the FOV, whereas the refractive lens counterpart has a ∼ 3 times resolution degradation.

CONCLUSIONS

These results show the promise of integrating a metalens into an endoscope for device minimization and optical performance improvement.

Highly Tunable Cascaded Metasurfaces for Continuous Two-Dimensional Beam Steering

Cascaded metasurfaces can exhibit powerful dynamic light manipulation by mechanically tuning the far-field interactions in the layers. However, in most current designs, the metasurfaces are separated by gaps smaller than a wavelength to form a total phase profile, representing the direct accumulation of the phase profiles of each layer. Such small gap sizes may not only conflict with the far-field conditions but also pose great difficulties for practical implementations. To overcome this limitation, a design paradigm taking advantage of a ray-tracing scheme that allows the cascaded metasurfaces to operate optimally at easily achievable gap sizes is proposed. Enabled by the relative lateral translation of two cascaded metasurfaces, a continuous two-dimensional (2D) beam-steering device for 1064 nm light is designed as a proof of concept. Simulation results demonstrate tuning ranges of ±45° for biaxial deflection angles within ±3.5 mm biaxial translations, while keeping the divergence of deflected light less than 0.007°. The experimental results agree well with theoretical predictions, and a uniform optical efficiency is observed. The  generializeddesign paradigm can pave a way towards myriad tunable cascaded metasurface devices for various applications, including but not limited to light detection and ranging (LiDAR) and free space optical communication.

Miniature color camera via flat hybrid meta-optics

The race for miniature color cameras using flat meta-optics has rapidly developed the end-to-end design framework using neural networks. Although a large body of work has shown the potential of this methodology, the reported performance is still limited due to fundamental limitations coming from meta-optics, mismatch between simulated and resultant experimental point spread functions, and calibration errors. Here, we use a HIL optics design methodology to solve these limitations and demonstrate a miniature color camera via flat hybrid meta-optics (refractive + meta-mask). The resulting camera achieves high-quality full-color imaging for a 5-mm aperture optics with a focal length of 5 mm. We observed a superior quality of the images captured by the hybrid meta-optical camera compared to a compound multi-lens optics of a mirrorless commercial camera.

Modified metasurface Alvarez lens based on the phase compensation in a microwave band

Alvarez lenses, a kind of passive zoom lenses with reconfigurable focus, have been widely applied in optics but very few at lower frequencies such as in a microwave band, where the phase approximation for Alvarez lenses becomes inaccurate. In this article, we propose a design of a modified Alvarez lens with phase compensation for microwave, which consists of a pair of transmissive metasurfaces with high efficiency. The proposed metasurface consists of miniaturized units with the capability of full 2π phase modulation. We further analyze the phase distribution principle of the Alvarez lens and proposed a phase compensation scheme. The simulation results confirm that the proposed modified Alvarez lens has a very good dynamic focal length with theoretical expectation and can be continuously adjusted from 100 to 200 mm.

Recent Advancement in Optical Metasurface: Fundament to Application

Metasurfaces have gained growing interest in recent years due to their simplicity in manufacturing and lower insertion losses. Meanwhile, they can provide unprecedented control over the spatial distribution of transmitted and reflected optical fields in a compact form. The metasurfaces are a kind of planar array of resonant subwavelength components that, depending on the intended optical wavefronts to be sculpted, can be strictly periodic or quasi-periodic, or even aperiodic. For instance, gradient metasurfaces, a subtype of metasurfaces, are designed to exhibit spatially changing optical responses, which result in spatially varying amplitudes of scattered fields and the associated polarization of these fields. This paper starts off by presenting concepts of anomalous reflection and refraction, followed by a brief discussion on the Pancharatanm-Berry Phase (PB) and Huygens' metasurfaces. As an introduction to wavefront manipulation, we next present their key applications. These include planar metalens, cascaded meta-systems, tunable metasurfaces, spectrometer retroreflectors, vortex beams, and holography. The review concludes with a summary, preceded by a perspective outlining our expectations for potential future research work and applications.

Review of Metasurfaces and Metadevices: Advantages of Different Materials and Fabrications

Flat optics, metasurfaces, metalenses, and related materials promise novel on-demand light modulation within ultrathin layers at wavelength scale, enabling a plethora of next-generation optical devices, also known as metadevices. Metadevices designed with different materials have been proposed and demonstrated for different applications, and the mass production of metadevices is necessary for metadevices to enter the consumer electronics market. However, metadevice manufacturing processes are mainly based on electron beam lithography, which exhibits low productivity and high costs for mass production. Therefore, processes compatible with standard complementary metal–oxide–semiconductor manufacturing techniques that feature high productivity, such as i-line stepper and nanoimprint lithography, have received considerable attention. This paper provides a review of current metasurfaces and metadevices with a focus on materials and manufacturing processes. We also provide an analysis of the relationship between the aspect ratio and efficiency of different materials.

Reconfigurable Metalens with Phase-Change Switching between Beam Acceleration and Rotation for 3D Depth Imaging

Depth imaging is very important for many emerging technologies, such as artificial intelligence, driverless vehicles and facial recognition. However, all these applications demand compact and low-power systems that are beyond the capabilities of most state-of-art depth cameras. Recently, metasurface-based depth imaging that exploits point spread function (PSF) engineering has been demonstrated to be miniaturized and single shot without requiring active illumination or multiple viewpoint exposures. A pair of spatially adjacent metalenses with an extended depth-of-field (EDOF) PSF and a depth-sensitive double-helix PSF (DH-PSF) were used, using the former metalens to reconstruct clear images of each depth and the latter to accurately estimate depth. However, due to these two metalenses being non-coaxial, parallax in capturing scenes is inevitable, which would limit the depth precision and field of view. In this work, a bifunctional reconfigurable metalens for 3D depth imaging was proposed by dynamically switching between EDOF-PSF and DH-PSF. Specifically, a polarization-independent metalens working at 1550 nm with a compact 1 mm2 aperture was realized, which can generate a focused accelerating beam and a focused rotating beam at the phase transition of crystalline and amorphous Ge2Sb2Te5 (GST), respectively. Combined with the deconvolution algorithm, we demonstrated the good capabilities of scene reconstruction and depth imaging using a theoretical simulation and achieved a depth measurement error of only 3.42%.

Millimeter-scale focal length tuning with MEMS-integrated meta-optics employing high-throughput fabrication

Miniature varifocal lenses are crucial for many applications requiring compact optical systems. Here, utilizing electro-mechanically actuated 0.5-mm aperture infrared Alvarez meta-optics, we demonstrate 3.1 mm (200 diopters) focal length tuning with an actuation voltage below 40 V. This constitutes the largest focal length tuning in any low-power electro-mechanically actuated meta-optic, enabled by the high energy density in comb-drive actuators producing large displacements at relatively low voltage. The demonstrated device is produced by a novel nanofabrication process that accommodates meta-optics with a larger aperture and has improved alignment between meta-optics via flip-chip bonding. The whole fabrication process is CMOS compatible and amenable to high-throughput manufacturing.

Knowledge distillation circumvents nonlinearity for optical convolutional neural networks

In recent years, convolutional neural networks (CNNs) have enabled ubiquitous image processing applications. As such, CNNs require fast forward propagation runtime to process high-resolution visual streams in real time. This is still a challenging task even with state-of-the-art graphics and tensor processing units. The bottleneck in computational efficiency primarily occurs in the convolutional layers. Performing convolutions in the Fourier domain is a promising way to accelerate forward propagation since it transforms convolutions into elementwise multiplications, which are considerably faster to compute for large kernels. Furthermore, such computation could be implemented using an optical 4f system with orders of magnitude faster operation. However, a major challenge in using this spectral approach, as well as in an optical implementation of CNNs, is the inclusion of a nonlinearity between each convolutional layer, without which CNN performance drops dramatically. Here, we propose a spectral CNN linear counterpart (SCLC) network architecture and its optical implementation. We propose a hybrid platform with an optical front end to perform a large number of linear operations, followed by an electronic back end. The key contribution is to develop a knowledge distillation (KD) approach to circumvent the need for nonlinear layers between the convolutional layers and successfully train such networks. While the KD approach is known in machine learning as an effective process for network pruning, we adapt the approach to transfer the knowledge from a nonlinear network (teacher) to a linear counterpart (student), where we can exploit the inherent parallelism of light. We show that the KD approach can achieve performance that easily surpasses the standard linear version of a CNN and could approach the performance of the nonlinear network. Our simulations show that the possibility of increasing the resolution of the input image allows our proposed 4f optical linear network to perform more efficiently than a nonlinear network with the same accuracy on two fundamental image processing tasks: (i) object classification and (ii) semantic segmentation.

Helicity-dependent continuous varifocal metalens based on bilayer dielectric metasurfaces

Metasurfaces offer a unique platform to realize flat lenses, reducing the size and complexity of imaging systems and thus enabling new imaging modalities. In this paper, we designed a bilayer helicity-dependent continuous varifocal dielectric metalens in the near-infrared range. The first layer consists of silicon nanopillars and functions as a half-wave plate, providing the helicity-dependent metasurface by combining propagation phase and geometric phase. The second layer consists of phase-change material Sb₂S₃ nanopillars and provides tunable propagation phases. Upon excitation with the circularly polarized waves possessing different helicities, the metalens can generate helicity-dependent longitudinal focal spots. Under the excitation of linear polarized light, the helicity-dependent dual foci are generated. The focal lengths in this metalens can be continuously tuned by the crystallization fraction of Sb₂S₃. The zoom range is achieved from 32.5 µm to 37.2 µm for right circularly polarized waves and from 50.5 µm to 60.9 µm for left circularly polarized waves. The simulated focusing efficiencies are above 75% and 87% for the circularly and linearly polarized waves, respectively. The proposed metalens has potential applications in miniaturized devices, including compact optical communication systems, imaging, and medical devices.

Mechanically reconfigurable multi-functional meta-optics studied at microwave frequencies

Metasurfaces advanced the field of optics by reducing the thickness of optical components and merging multiple functionalities into a single layer device. However, this generally comes with a reduction in performance, especially for multi-functional and broadband applications. Three-dimensional metastructures can provide the necessary degrees of freedom for advanced applications, while maintaining minimal thickness. This work explores mechanically reconfigurable devices that perform focusing, spectral demultiplexing, and polarization sorting based on mechanical configuration. As proof of concept, a rotatable device, a device based on rotating squares, and a shearing-based device are designed with adjoint-based topology optimization, 3D-printed, and measured at microwave frequencies (7.6-11.6 GHz) in an anechoic chamber.

2D beam shaping via 1D spatial light modulator using static phase masks

Many emerging, high-speed, reconfigurable optical systems are limited by routing complexity when producing dynamic, two-dimensional (2D) electric fields. We propose a gradient-based inverse-designed, static phase-mask doublet to generate arbitrary 2D intensity wavefronts using a one-dimensional (1D) intensity spatial light modulator (SLM). We numerically simulate the capability of mapping each point in a 49 element 1D array to a distinct $7 \times 7$ 2D spatial distribution. Our proposed method will significantly relax the routing complexity of electrical control signals, possibly enabling high-speed, sub-wavelength 2D SLMs leveraging new materials and pixel architectures.

Large-area optical metasurface fabrication using nanostencil lithography

We demonstrate a large-area fabrication process for optical metasurfaces utilizing reusable SiN on Si nanostencils. To improve the yield of the nanostencil fabrication, we partially etch the front-side SiN layer to transfer the metasurface pattern from the resist to the nanostencil membrane, preserving the integrity of the membrane during the subsequent potassium hydroxide etch. To enhance the reliability and resolution of metasurface fabrication using the nanostencil, we spin coat a sacrificial layer of resist to precisely determine the gap between the nanostencil and the metasurface substrate for the subsequent liftoff. 1.5 mm diameter PbTe meta-lenses on ${\rm{Ca}}{{\rm{F}}_2}$ fabricated using nanostencils show diffraction-limited focusing and focusing efficiencies of 42% for a 2 mm focal length lens and 53% for a 4 mm focal length lens. The nanostencils can also be cleaned using chemical cleaning methods for reuse.

Metaform optics: Bridging nanophotonics and freeform optics

The demand for high-resolution optical systems with a compact form factor, such as augmented reality displays, sensors, and mobile cameras, requires creating new optical component architectures. Advances in the design and fabrication of freeform optics and metasurfaces make them potential solutions to address the previous needs. Here, we introduce the concept of a metaform-an optical surface that integrates the combined benefits of a freeform optic and a metasurface into a single optical component. We experimentally realized a miniature imager using a metaform mirror. The mirror is fabricated via an enhanced electron beam lithography process on a freeform substrate. The design degrees of freedom enabled by a metaform will support a new generation of optical systems.

Design of achromatic augmented reality visors based on composite metasurfaces

A compact near-eye visor (NEV) system that can guide light from a display to the eye could transform augmented reality (AR) technology. Unfortunately, existing implementations of such an NEV either suffer from small field of view or chromatic aberrations. See-through quality and bulkiness further make the overall performance of the visors unsuitable for a seamless user experience. Metasurfaces are an emerging class of nanophotonic elements that can dramatically reduce the size of optical elements while enhancing functionality. In this paper, we present a design of composite metasurfaces for an ultracompact NEV. We simulate the performance of a proof-of-principle visor corrected for chromatic aberrations while providing a large display field of view (>77^∘ both horizontally and vertically) and good see-through quality [>70% transmission and less than a wavelength root mean-square (RMS) wavefront error over the whole visible wavelength range] as needed for an immersive AR experience.

Demonstration of focal length tuning by rotational varifocal moiré metalens in an ir-A wavelength

This paper reports an experimental demonstration of moiré metalens which shows wide focal length tunability from negative to positive by mutual angle rotation at the wavelength of 900 nm. The moiré metalens was developed using high index contrast transmitarray meta-atoms made of amorphous silicon octagonal pillars, which is designed to have polarization insensitivity and full 2π phase coverage. The fabricated moiré metalens showed focal length tunability at the ranges between ±1.73 - ±5 mm, which corresponds to the optical power ranges between ±578 - ±200 m^-1 at the mutual rotation between ±90 degrees.

Coupling coefficients for dielectric cuboids located in free space

Practical formulas are derived for calculating the far-field radiation pattern and coupling coefficient of a rectangular dielectric resonator (cuboid) with free space as well as mutual coupling coefficients between two cuboids for their different orientations relative to each other. An approach is developed using the coupled mode theory and the perturbation theory for the Maxwell equations. The correctness of obtained formulas is checked against the full-wave numerical simulations performed by the COMSOL Multiphysics electromagnetic solver. In particular, the obtained formulas can be used for revealing optical features of realistic (i.e., consisting of a finite number of resonators) all-dielectric metasurfaces with arbitrary curved shapes.

Metasurface Integrated Monolayer Exciton Polariton

Monolayer transition-metal dichalcogenides (TMDs) are the first truly two-dimensional (2D) semiconductor, providing an excellent platform to investigate light-matter interaction in the 2D limit. The inherently strong excitonic response in monolayer TMDs can be further enhanced by exploiting the temporal confinement of light in nanophotonic structures. Here, we demonstrate a 2D exciton-polariton system by strongly coupling atomically thin tungsten diselenide (WSe₂) monolayer to a silicon nitride (SiN) metasurface. Via energy-momentum spectroscopy of the WSe₂-metasurface system, we observed the characteristic anticrossing of the polariton dispersion both in the reflection and photoluminescence spectrum. A Rabi splitting of 18 meV was observed which matched well with our numerical simulation. Moreover, we showed that the Rabi splitting, the polariton dispersion, and the far-field emission pattern could be tailored with subwavelength-scale engineering of the optical meta-atoms. Our platform thus opens the door for the future development of novel, exotic exciton-polariton devices by advanced meta-optical engineering.

Portable deep learning singlet microscope

Having the least lenses, the significant feature of the singlet imaging system, helps the development of the portable and cost-effective microscopes. A novel method of monochromatic/color singlet microscopy, which is combined with only one aspheric lens and deep learning computational imaging technology, is proposed in this article. The designed singlet aspheric lens is an approximate linear signal system, which means modulation-transfer-function curves on all field-of-views (5 mm diagonally) are almost coincident with each other. The purpose of the designed linear signal system is to further improve the resolution of our microscope by using deep learning algorithm. As a proof of concept, we designed a singlet microscopy based on our method, which weighs only 400 g. The experimental data and results of the sample USAF-1951 target and bio-sample (the Equisetum-arvense Strobile L.S), prove that the performance of the proposed singlet microscope is competitive to a commercial microscope with the 4X/NA0.1 objective lens. We believe that our idea and method would guide to design more cost-effective and powerful singlet imaging system.

Azimuthal multiplexing 3D diffractive optics

Diffractive optics have increasingly caught the attention of the scientific community. Classical diffractive optics are 2D diffractive optical elements (DOEs) and computer-generated holograms (CGHs), which modulate optical waves on a solitary transverse plane. However, potential capabilities are missed by the inherent two-dimensional nature of these devices. Previous work has demonstrated that extending the modulation from planar (2D) to volumetric (3D) enables new functionalities, such as generating space-variant functions, multiplexing in the spatial or spectral domain, or enhancing information capacity. Unfortunately, despite significant progress fueled by recent interest in metasurface diffraction, 3D diffractive optics still remains relatively unexplored. Here, we introduce the concept of azimuthal multiplexing. We propose, design, and demonstrate 3D diffractive optics showing this multiplexing effect. According to this new phenomenon, multiple pages of information are encoded and can be read out across independent channels by rotating one or more diffractive layers with respect to the others. We implement the concept with multilayer diffractive optical elements. An iterative projection optimization algorithm helps solve the inverse design problem. The experimental realization using photolithographically fabricated multilevel phase layers demonstrates the predicted performance. We discuss the limitations and potential of azimuthal multiplexing 3D diffractive optics.

MEMS-actuated metasurface Alvarez lens

Miniature lenses with a tunable focus are essential components for many modern applications involving compact optical systems. While several tunable lenses have been reported with various tuning mechanisms, they often face challenges with respect to power consumption, tuning speed, fabrication cost, or production scalability. In this work, we have adapted the mechanism of an Alvarez lens - a varifocal composite lens in which lateral shifts of two optical elements with cubic phase surfaces give rise to a change in the optical power - to construct a miniature, microelectromechanical system (MEMS)-actuated metasurface Alvarez lens. Implementation based on an electrostatic MEMS generates fast and controllable actuation with low power consumption. The utilization of metasurfaces - ultrathin and subwavelength-patterned diffractive optics - as optical elements greatly reduces the device volume compared to systems using conventional freeform lenses. The entire MEMS Alvarez metalens is fully compatible with modern semiconductor fabrication technologies, granting it the potential to be mass-produced at a low unit cost. In the reported prototype operating at 1550 nm wavelength, a total uniaxial displacement of 6.3 µm was achieved in the Alvarez metalens with a direct-current (DC) voltage application up to 20 V, which modulated the focal position within a total tuning range of 68 µm, producing more than an order of magnitude change in the focal length and a 1460-diopter change in the optical power. The MEMS Alvarez metalens has a robust design that can potentially generate a much larger tuning range without substantially increasing the device volume or energy consumption, making it desirable for a wide range of imaging and display applications.

Controlling three-dimensional optical fields via inverse Mie scattering

Controlling the propagation of optical fields in three dimensions using arrays of discrete dielectric scatterers is an active area of research. These arrays can create optical elements with functionalities unrealizable in conventional optics. Here, we present an inverse design method based on the inverse Mie scattering problem for producing three-dimensional optical field patterns. Using this method, we demonstrate a device that focuses 1.55-μm light into a depth-variant discrete helical pattern. The reported device is fabricated using two-photon lithography and has a footprint of 144 μm by 144 μm, the largest of any inverse-designed photonic structure to date. This inverse design method constitutes an important step toward designer free-space optics, where unique optical elements are produced for user-specified functionalities.

Approach to analysis of all-dielectric free-form antenna systems

The analytical model is proposed for simulation of the near-field and far-field characteristics of an all-dielectric free-form antenna system. The antenna system is constructed of an array of high-refractive-index dielectric resonators. The model relies on the coupled mode theory and the perturbation theory for the Maxwell's equations. The model is validated against numerical simulations performed by the ANSYS HFSS electromagnetic solver and microwave experiments. Three designs of the free-form antenna systems are proposed, studied and experimentally tested. The mechanisms of the multiple beam generation and beam steering are demonstrated.

Optical frontend for a convolutional neural network

The parallelism of optics and the miniaturization of optical components using nanophotonic structures, such as metasurfaces, present a compelling alternative to electronic implementations of convolutional neural networks. The lack of a low-power optical nonlinearity, however, requires slow and energy-inefficient conversions between the electronic and optical domains. Here, we design an architecture that utilizes a single electrical to optical conversion by designing a free-space optical frontend unit that implements the linear operations of the first layer with the subsequent layers realized electronically. Speed and power analysis of the architecture indicates that the hybrid photonic-electronic architecture outperforms a fully electronic architecture for large image sizes and kernels. Benchmarking of the photonic-electronic architecture on a modified version of AlexNet achieves high classification accuracies on images from the Kaggle's Cats and Dogs challenge and MNIST databases.

Role of refractive index in metalens performance

Sub-wavelength diffractive optics, commonly known as metasurfaces, have recently garnered significant attention for their ability to create ultra-thin flat lenses with a high numerical aperture. Several materials with different refractive indices have been used to create metasurface lenses (metalenses). In this paper, we analyze the role of refractive index on the performance of these metalenses. We employ both forward and inverse design methodologies to perform our analysis. We found that, while high-refractive-index materials allow for extreme reduction of the focal length, for moderate focal lengths and numerical aperture (<0.6), there is no appreciable difference in the focal spot size and focusing efficiency for metalenses made of different materials with refractive indices ranging between 1.2 and 3.43 in forward design, and 1.25 and 3.5 in inverse design.

Structural color filters based on an all-dielectric metasurface exploiting silicon-rich silicon nitride nanodisks

An all-dielectric metasurface is deemed to serve a potential platform to demonstrate spectral filters. Silicon-rich silicon nitride (SRN), which contains a relatively large portion of silicon, can exhibit higher refractive indices, when compared to silicon nitride. Meanwhile, the extinction coefficient of SRN is smaller than that of hydrogenated amorphous silicon, leading to reduced absorption loss in the shorter wavelength. SRN is therefore recommended as a scattering element from the perspective of realizing all-dielectric metasurfaces. In this work, we propose and embody a suite of highly efficient structural color filters, capitalizing on a dielectric metasurface that consists of a two-dimensional array of SRN nanodisks that are embedded in a polymeric layer. The SRN nanodisks may support the electric dipole (ED) and magnetic dipole (MD) resonances via Mie scattering, thereby leading to appropriate spectral filtering characteristics. The ED and MD are identified from field profile observation with the assistance of finite-difference time-domain simulations. The manufactured color filters are observed to produce various colors in both transmission and reflection modes throughout the visible band, giving rise to a high transmission of around 90% in the off-resonance region and a reflection ranging up to 60%. A variety of colors can be realized by tuning the resonance by adjusting the structural parameters such as the period, diameter, and height of the SRN nanodisks. The spectral position of resonances might be flexibly tuned by tailoring the polymer surrounding the SRN nanodisks. It is anticipated that the proposed coloring devices will be actively used for color displays, imaging devices, and photorealistic color printing.

A broadband achromatic metalens array for integral imaging in the visible

Integral imaging is a promising three-dimensional (3D) imaging technique that captures and reconstructs light field information. Microlens arrays are usually used for the reconstruction process to display 3D scenes to the viewer. However, the inherent chromatic aberration of the microlens array reduces the viewing quality, and thus, broadband achromatic imaging remains a challenge for integral imaging. Here, we realize a silicon nitride metalens array in the visible region that can be used to reconstruct 3D optical scenes in the achromatic integral imaging for white light. The metalens array contains 60 × 60 polarization-insensitive metalenses with nearly diffraction-limited focusing. The nanoposts in each high-efficiency (measured as 47% on average) metalens are delicately designed with zero effective material dispersion and an effective achromatic refractive index distribution from 430 to 780 nm. In addition, such an achromatic metalens array is composed of only a single silicon nitride layer with an ultrathin thickness of 400 nm, making the array suitable for on-chip hybrid-CMOS integration and the parallel manipulation of optoelectronic information. We expect these findings to provide possibilities for full-color and aberration-free integral imaging, and we envision that the proposed approach may be potentially applicable in the fields of high-power microlithography, high-precision wavefront sensors, virtual/augmented reality and 3D imaging.

Broadband Achromatic Metasurface-Refractive Optics

Existing methods of correcting for chromatic aberrations in optical systems are limited to two approaches: varying the material dispersion in refractive lenses or incorporating grating dispersion via diffractive optical elements. Recently, single-layer broadband achromatic metasurface lenses have been demonstrated but are limited to diameters on the order of 100 μm due to the large required group delays. Here, we circumvent this limitation and design a metacorrector by combining a tunable phase and artificial dispersion to correct spherical and chromatic aberrations in a large spherical plano-convex lens. The tunability results from a variation in light confinement in sub-wavelength waveguides by locally tailoring the effective refractive index. The effectiveness of this approach is further validated by designing a metacorrector, which greatly increases the bandwidth of a state-of-the-art immersion objective (composed of 14 lenses and 7 types of glasses) from violet to near-infrared wavelengths. This concept of hybrid metasurface-refractive optics combines the advantages of both technologies in terms of size, scalability, complexity, and functionality.

Design method of nonsymmetric imaging systems consisting of multiple flat phase elements

Imaging systems consisting of flat phase elements can realize the same functions and applications of conventional geometric optical systems, as well as the ones using aspherical or freeform optics, but can achieve more compactness, lighter-weight and easier-alignment. In addition, it is easy to integrate multiple phase elements into a single flat element. Here we propose a novel design method and realize the design of off-axis nonsymmetric imaging systems consisting of multiple flat phase elements. Compared with other traditional design methods of phase elements, the whole design process starts from an initial system using simple true geometric planes. The phase profiles or functions are generated point-by-point directly based on the given system specifications and configuration. In comparison with other direct or point-by-point design methods of flat phase elements, the rays of multiple fields and pupil positions are employed in the design framework. Closed-form phase functions of multiple flat elements are designed quickly and effectively by connecting and integrating the real three-dimensional space and the phase function space. This method can be taken as a fast phase retrieval method to some degree. To demonstrate the feasibility of the proposed design method, we present a high-performance compact system as design example. The design method and framework depicted in this paper can be applied in many areas, such as virtual reality (VR) and augmented reality (AR), miniature cameras, high-performance telescopy, microscopy, and illumination design.

Two-Photon Microscopy with a Double-Wavelength Metasurface Objective Lens

Two-photon microscopy is a key imaging technique in life sciences due to its superior deep-tissue imaging capabilities. Light-weight and compact two-photon microscopes are of great interest because of their applications for in vivo deep brain imaging. Recently, dielectric metasurfaces have enabled a new category of small and lightweight optical elements, including objective lenses. Here we experimentally demonstrate two-photon microscopy using a double-wavelength metasurface lens. It is specifically designed to focus 820 and 605 nm light, corresponding to the excitation and emission wavelengths of the measured fluorophors, to the same focal distance. The captured two-photon images are qualitatively comparable to the ones taken by a conventional objective lens. Our metasurface lens can enable ultracompact two-photon microscopes with similar performance compared to current systems that are usually based on graded-index-lenses. In addition, further development of tunable metasurface lenses will enable fast axial scanning for volumetric imaging.

MEMS-tunable dielectric metasurface lens

Varifocal lenses, conventionally implemented by changing the axial distance between multiple optical elements, have a wide range of applications in imaging and optical beam scanning. The use of conventional bulky refractive elements makes these varifocal lenses large, slow, and limits their tunability. Metasurfaces, a new category of lithographically defined diffractive devices, enable thin and lightweight optical elements with precisely engineered phase profiles. Here we demonstrate tunable metasurface doublets, based on microelectromechanical systems (MEMS), with more than 60 diopters (about 4%) change in the optical power upon a 1-μm movement of one metasurface, and a scanning frequency that can potentially reach a few kHz. They can also be integrated with a third metasurface to make compact microscopes (~1 mm thick) with a large corrected field of view (~500 μm or 40 degrees) and fast axial scanning for 3D imaging. This paves the way towards MEMS-integrated metasurfaces as a platform for tunable and reconfigurable optics.

Inverse design of optical elements based on arrays of dielectric spheres

Arrays of wavelength scale scatterers are a promising platform for designing optical elements with a compact footprint. The large number of degrees of freedom in this system allows for unique and plentiful functionalities. However, the many variables also create a complex design problem. While intuitive forward design methods work for simple optical elements, they often fail to produce complicated elements, especially those involving multiple elements. We present an inverse design methodology for large arrays of wavelength scale spheres based on both adjoint optimization or sensitivity analysis and generalized multi-sphere Mie theory as a solution to the design problem. We validate our methodology by designing two sets of optical elements with scatterers on sub-wavelength and super-wavelength periodic grids. Both sets consist of a singlet and a doublet lens with one and two layers of spheres respectively designed for 1550 nm. The designed NA is ∼0.33 (∼0.5) for the sub-wavelength (super-wavelength) periodic structure. We find that with the sub-wavelength periodicity, the full width at half-maximum of the focal spot produced by the singlet and doublet is smaller than that produced by an ideal lens with the same geometric parameters. Finally, we simulate a realistic experimental scenario for the doublet, where the spheres are placed on a substrate with the same refractive index. We find the performance is similar, but with lower intensity at the focal spot and larger spot size. The method described here will simplify the design procedure for complicated multi-functional optical elements and or scatterer array-based volume optics based on a specified figure of merit.

Metasurface optics for full-color computational imaging

Conventional imaging systems comprise large and expensive optical components that successively mitigate aberrations. Metasurface optics offers a route to miniaturize imaging systems by replacing bulky components with flat and compact implementations. The diffractive nature of these devices, however, induces severe chromatic aberrations, and current multiwavelength and narrowband achromatic metasurfaces cannot support full visible spectrum imaging (400 to 700 nm). We combine principles of both computational imaging and metasurface optics to build a system with a single metalens of numerical aperture ~0.45, which generates in-focus images under white light illumination. Our metalens exhibits a spectrally invariant point spread function that enables computational reconstruction of captured images with a single digital filter. This work connects computational imaging and metasurface optics and demonstrates the capabilities of combining these disciplines by simultaneously reducing aberrations and downsizing imaging systems using simpler optics.

Design of optical wavelength demultiplexer based on off-axis meta-lens

We propose an off-axis meta-lens-based optical wavelength demultiplexer. The performance of the device initially proposed with four output channels (1527-1596 nm, channel spacing 23 nm) composed of an optical fiber array is analyzed by both scalar diffraction theory and ray tracing method. The results show that the fiber energy coupling efficiency of the demultiplexer could be larger than 89% and the channel bandwidth is about 9 nm. Influences of the two key parameters, focal length f and off-axis angle α, are also investigated. We find that the minimum spectral linewidth of the channel is inversely proportional to the sine of α and nearly independent of f for a meta-lens with large F-number (F>5), while the effective spectral range is negatively (positively) dependent on α (f). These results are significant in guiding us to build small and compact demultiplexing devices for optical telecommunication.

Flat metaform near-eye visor

A near-eye visor is one of the most vital components in a head-mounted display. Currently, freeform optics and waveguides are used to design near-eye visors, but these structures are complex and their field of view is limited when the visor is placed near the eye. In this paper, we propose a flat, freeform near-eye visor that uses a subwavelength patterned metasurface reflector. The visor design imparts a spatial phase profile on a projected display pattern and can be implemented using a micron-scale-thick metasurface. As the resulting metaform visor relies on diffraction, it can preserve a large field of view (77.3° both horizontally and vertically) when placed only 2.5 cm away from the eye. We simulate the metasurface visor to estimate the modulation transfer function, and find that the projected image quality is sufficiently high for human vision. While the design of the metasurface is initially performed via ray optics, using full-wave finite-difference time-domain simulation we validate a scaled version of our visor design.

Tunable metasurfaces via subwavelength phase shifters with uniform amplitude

Metasurfaces with tunable spatial phase functions could benefit numerous applications. Currently, most approaches to tuning rely on mechanical stretching which cannot control phase locally, or by modulating the refractive index to exploit rapid phase changes with the drawback of also modulating amplitude. Here, we propose a method to realize phase modulation at subwavelength length scales while maintaining unity amplitude. Our device is inspired by an asymmetric Fabry-Perot resonator, with pixels comprising a scattering nanopost on top of a distributed Bragg reflector, capable of providing a nearly 2π nonlinear phase shift with less than 2% refractive index modulation. Using the designed pixels, we simulate a tunable metasurface composed of an array of moderately coupled nanopost resonators, realizing axicons, vortex beam generators, and aspherical lenses with both variable focal length and in-plane scanning capability, achieving nearly diffraction-limited performance. The experimental feasibility of the proposed method is also discussed.