Jones matrix holography with metasurfaces

Non-convex optimization for inverse problem solving in computer-generated holography

Computer-generated holography is a promising technique that modulates user-defined wavefronts with digital holograms. Computing appropriate holograms with faithful reconstructions is not only a problem closely related to the fundamental basis of holography but also a long-standing challenge for researchers in general fields of optics. Finding the exact solution of a desired hologram to reconstruct an accurate target object constitutes an ill-posed inverse problem. The general practice of single-diffraction computation for synthesizing holograms can only provide an approximate answer, which is subject to limitations in numerical implementation. Various non-convex optimization algorithms are thus designed to seek an optimal solution by introducing different constraints, frameworks, and initializations. Herein, we overview the optimization algorithms applied to computer-generated holography, incorporating principles of hologram synthesis based on alternative projections and gradient descent methods. This is aimed to provide an underlying basis for optimized hologram generation, as well as insights into the cutting-edge developments of this rapidly evolving field for potential applications in virtual reality, augmented reality, head-up display, data encryption, laser fabrication, and metasurface design.

Full-Dimensional Geometric-Phase Spatial Light Metamodulation

Full-dimensional spatial light modulation requires simultaneous, arbitrary, and independent manipulation of the spatial phase, amplitude, and polarization. This is crucial for leveraging the complete physical dimension resources of light. However, full-dimensional metamodulation can be challenging due to the need for multiple independent control factors. To address this challenge, here we propose parallel-tasking metasurfaces to enable full-dimensional spatial light metamodulation based fully on the geometric-phase concept. Indeed, the meta-atoms are divided into several subphases, each of which serves as an independent control factor to manipulate light phase, amplitude, and polarization through geometric phase, interference, and orthogonal polarization superposition, respectively. Therefore, the macroscopic group of meta-atoms leads to metasurfaces that can achieve broadband full-dimensional spatial light metamodulation, as demonstrated by various types of structured light generation. This approach paves the way to future wide applications of light manipulation enabled by full-dimensional spatial light metamodulation.

Cylindrical Vector Beam Holography without Preservation of OAM Modes

Orbital angular momentum (OAM) multiplexed holograms have attracted a great deal of attention recently due to their physically unbounded set of orthogonal helical modes. However, preserving the OAM property in each pixel hinders fine sampling of the target image in principle and requires a fundamental filtering aperture array in the detector plane. Here, we demonstrate the concept of metasurface-based vectorial holography with cylindrical vector beams (CVBs), whose unlimited polarization orders and unique polarization distributions can be used to boost information storage capacity. Although CVBs are composed of OAM modes, the holographic images do not preserve the OAM modes in our design, enabling fine sampling of the target image in a quasi-continuous way like traditional computer-generated holograms. Moreover, the images can be directly observed by passing them through a polarizer without the need for a fundamental mode filter array. We anticipate that our method may pave the way for high-capacity holographic devices.

Poincaré sphere trajectory encoding metasurfaces based on generalized Malus' law

As a fundamental property of light, polarization serves as an excellent information encoding carrier, playing significant roles in many optical applications, including liquid crystal displays, polarization imaging, optical computation and encryption. However, conventional polarization information encoding schemes based on Malus' law usually consider 1D polarization projections on a linear basis, implying that their encoding flexibility is largely limited. Here, we propose a Poincaré sphere (PS) trajectory encoding approach with metasurfaces that leverages a generalized form of Malus' law governing universal 2D projections between arbitrary elliptical polarization pairs spanning the entire PS. Arbitrary polarization encodings are realized by engineering PS trajectories governed by either arbitrary analytic functions or aligned modulation grids of interest, leading to versatile polarization image transformation functionalities, including histogram stretching, thresholding and image encryption within non-orthogonal PS loci. Our work significantly expands the encoding dimensionality of polarization information, unveiling new opportunities for metasurfaces in polarization optics for both quantum and classical regimes.

Full Stokes polarimetry based on an inverse-designed multi-foci metalens

In the realm of metasurface-based polarimetry, well-known for its remarkable compactness and integration capabilities, previous attempts have been hindered by limitations such as the restricted choices of target polarization states and the inefficient focusing of light. To address these problems, this study introduces and harnesses a novel, to our knowledge, forward-solving model, grounded in the equivalence principle and dyadic Green's function, to inversely optimize the vectorial focusing patterns of metalenses. Leveraging this methodology, we develop and experimentally validate a single multi-foci metalens-based polarimeter, capable of simultaneously separating and concentrating four distinct elliptical polarization states at a wavelength of 10.6 µm. Rigorous experimental evaluations, involving the assessment of 18 scalar polarized beams, reveal an average error of 5.92% and a high contrast ratio of 0.92, which demonstrates the efficacy of the polarimeter. The results underscore the potential of our system in diverse sectors, including military defense, healthcare, and autonomous vehicle technology.

Universal Polarization Transformations: Spatial Programming of Polarization Scattering Matrices Using a Deep Learning-Designed Diffractive Polarization Transformer

Controlled synthesis of optical fields having nonuniform polarization distributions presents a challenging task. Here, a universal polarization transformer is demonstrated that can synthesize a large set of arbitrarily-selected, complex-valued polarization scattering matrices between the polarization states at different positions within its input and output field-of-views (FOVs). This framework comprises 2D arrays of linear polarizers positioned between isotropic diffractive layers, each containing tens of thousands of diffractive features with optimizable transmission coefficients. After its deep learning-based training, this diffractive polarization transformer can successfully implement Ni No = 10 000 different spatially-encoded polarization scattering matrices with negligible error, where Ni and No represent the number of pixels in the input and output FOVs, respectively. This universal polarization transformation framework is experimentally validated in the terahertz spectrum by fabricating wire-grid polarizers and integrating them with 3D-printed diffractive layers to form a physical polarization transformer. Through this set-up, an all-optical polarization permutation operation of spatially-varying polarization fields is demonstrated, and distinct spatially-encoded polarization scattering matrices are simultaneously implemented between the input and output FOVs of a compact diffractive processor. This framework opens up new avenues for developing novel devices for universal polarization control and may find applications in, e.g., remote sensing, medical imaging, security, material inspection, and machine vision.

Single-shot measurement of the Jones matrix for anisotropic media using four-channel digital polarization holography

Dynamic measurement of the Jones matrix is crucial in investigating polarization light fields, which have wide applications in biophysics, chemistry, and mineralogy. However, acquiring the four elements of the Jones matrix instantly is difficult, hindering the characterization of random media and transient processes. In this study, we propose a single-shot measurement method of the Jones matrix for anisotropic media called "four-channel digital polarization holography" (FC-DPH). The FC-DPH system is created by a slightly off-axis superposition of reference light waves, which are modulated by a spatial light modulator (SLM), and signal light waves that pass through a Ronchi grating. The SLM enables flexible adjustment of the spatial carrier frequency, which can be adapted to different anisotropic media. The four elements of the Jones matrix can be obtained from the interferogram through the inverse Fourier transform. Optical experiments on anisotropic objects validate the feasibility and accuracy of the proposed method.

Bi-Chiral Nanostructures Featuring Dynamic Optical Rotatory Dispersion for Polychromatic Light Multiplexing

Chiral nanostructures featuring the unique optical activity have attracted broad interests from scientists. The typical polarization rotation of transmitted light is usually wavelength dependent, namely the optical rotatory dispersion. However, its dynamic tunability and intriguing collaboration with other optical degrees of freedom, especially the highly desired spatial phase, remain elusive. Herein, a bi-chiral liquid crystalline nanostructure is proposed to induce an effect called reflective optical rotatory dispersion. Thanks to the independent manipulation of opposite-handed self-assembled helices, spin-decoupled geometric phases are induced simultaneously. These naturally unite multi-dimensions of light and versatile stimuli-responsiveness of soft matter. Dynamic holography driven by heat and electric field is demonstrated with a fast response. For polychromatic light, the hybrid multiplexed holographic painting is exhibited with fruitful tunable colors. This study extends the ingenious construction of soft chiral superstructures, presents an open-ended strategy for on-demand light control, and enlightens advanced applications of display, optical computing, and communication.

Underwater active polarization descattering based on a single polarized image

Active polarization imaging techniques have tremendous potential for a variety of underwater applications. However, multiple polarization images as input are necessary for almost all methods, thereby limiting the range of applicable scenarios. In this paper, via taking full advantage of the polarization feature of target reflective light, the cross-polarized backscatter image is reconstructed via introducing an exponential function for the first time, only based on mapping relations of co-polarized image. Compared with rotating the polarizer, the result performs a more uniform and continuous distribution of grayscale. Furthermore, the relationship of degree of polarization (DOP) between the whole scene and backscattered light is established. This leads to an accurate estimation of backscattered noise and high-contrast restored images. Besides, single-input greatly simplifies the experimental process and upgrades efficiency. Experimental results demonstrate the advancement of the proposed method for objects with high polarization under various turbidities.

Ultra-broadband holography in visible and infrared regions with full-polarization nondispersive response

Holography is promising to fully record and reconstruct the fundamental properties of light, while the limitations of working bandwidth, allowed polarization states, and dispersive response impede further advances in the integration level and functionality. Here, we propose an ultra-broadband holography based on twisted nematic liquid crystals (TNLCs), which can efficiently work in both the visible and infrared regions with a working spectrum of over 1000 nm. The underlying physics is that the electric field vector of light through TNLCs can be parallelly manipulated in the broad spectral range, thus enabling to build the ultra-broadband TNLC hologram by dynamic photopatterning. Furthermore, by introducing a simple nematic liquid crystal (NLC) element, the cascaded device allows for an excellent nondispersive polarization-maintaining performance that can adapt to full-polarization incidence. We expect our proposed methodology of holography may inspire new avenues for usages in polarization imaging, augmented/virtual reality display, and optical encryption.

Advances in Meta-Optics and Metasurfaces: Fundamentals and Applications

Meta-optics based on metasurfaces that interact strongly with light has been an active area of research in recent years. The development of meta-optics has always been driven by human's pursuits of the ultimate miniaturization of optical elements, on-demand design and control of light beams, and processing hidden modalities of light. Underpinned by meta-optical physics, meta-optical devices have produced potentially disruptive applications in light manipulation and ultra-light optics. Among them, optical metalens are most fundamental and prominent meta-devices, owing to their powerful abilities in advanced imaging and image processing, and their novel functionalities in light manipulation. This review focuses on recent advances in the fundamentals and applications of the field defined by excavating new optical physics and breaking the limitations of light manipulation. In addition, we have deeply explored the metalenses and metalens-based devices with novel functionalities, and their applications in computational imaging and image processing. We also provide an outlook on this active field in the end.

Angular momentum holography via a minimalist metasurface for optical nested encryption

Metasurfaces can perform high-performance multi-functional integration by manipulating the abundant physical dimensions of light, demonstrating great potential in high-capacity information technologies. The orbital angular momentum (OAM) and spin angular momentum (SAM) dimensions have been respectively explored as the independent carrier for information multiplexing. However, fully managing these two intrinsic properties in information multiplexing remains elusive. Here, we propose the concept of angular momentum (AM) holography which can fully synergize these two fundamental dimensions to act as the information carrier, via a single-layer, non-interleaved metasurface. The underlying mechanism relies on independently controlling the two spin eigenstates and arbitrary overlaying them in each operation channel, thereby spatially modulating the resulting waveform at will. As a proof of concept, we demonstrate an AM meta-hologram allowing the reconstruction of two sets of holographic images, i.e., the spin-orbital locked and the spin-superimposed ones. Remarkably, leveraging the designed dual-functional AM meta-hologram, we demonstrate a novel optical nested encryption scheme, which is able to achieve parallel information transmission with ultra-high capacity and security. Our work opens a new avenue for optionally manipulating the AM, holding promising applications in the fields of optical communication, information security and quantum science.

Evaluation and characterization of imaging polarimetry through metasurface polarization gratings

Metasurfaces are a new class of diffractive optical elements with subwavelength elements whose behavior can be lithographically tailored. By leveraging form birefringence, metasurfaces can serve as multifunctional freespace polarization optics. Metasurface gratings are novel, to the best of our knowledge, polarimetric components that integrate multiple polarization analyzers into a single optical element enabling the realization of compact imaging polarimeters. The promise of metasurfaces as a new polarization building block is contingent on the calibration of metagrating-based optical systems. A prototype metasurface full Stokes imaging polarimeter is compared to a benchtop reference instrument using an established linear Stokes test for 670, 532, and 460 nm gratings. We propose a complementary full Stokes accuracy test and demonstrate it using the 532 nm grating. This work presents methods and practical considerations involved in producing accurate polarization data from a metasurface-based Stokes imaging polarimeter and informs their use in polarimetric systems more generally.

Disorder-Induced Topological State Transition in the Optical Skyrmion Family

Skyrmions endowed with topological protection have been extensively investigated in various platforms including magnetics, ferroelectrics, and liquid crystals, stimulating applications such as memories, logic devices, and neuromorphic computing. While the optical counterpart has been proposed and realized recently, the study of optical skyrmions is still in its infancy. Among the unexplored questions, the investigation of the topology induced robustness against disorder is of substantial importance on both fundamental and practical sides but remains elusive. In this Letter, we manage to generate optical skyrmions numerically in real space with different topological features at will, providing a unique platform to investigate the robustness of various optical skyrmions. A disorder-induced topological state transition is observed for the first time in a family of optical skyrmions composed of six classes with different skyrmion numbers. Intriguingly, the optical skyrmions produced from a vectorial hologram are exceptionally robust against scattering from a random medium, shedding light on topological photonic devices for the generation and manipulation of robust states for applications including imaging and communication.

Spin-decoupling of vertical cavity surface-emitting lasers with complete phase modulation using on-chip integrated Jones matrix metasurfaces

Polarization response of artificially structured nano-antennas can be exploited to design innovative optical components, also dubbed "vectorial metasurfaces", for the modulation of phase, amplitude, and polarization with subwavelength spatial resolution. Recent efforts in conceiving Jones matrix formalism led to the advancement of vectorial metasurfaces to independently manipulate any arbitrary phase function of orthogonal polarization states. Here, we are taking advantages of this formalism to design and experimentally validate the performance of CMOS compatible Jones matrix metasurfaces monolithically integrated with standard VCSELs for on-chip spin-decoupling and phase shaping. Our approach enables accessing the optical spin states of VCSELs in an ultra-compact way with previously unattainable phase controllability. By exploiting spin states as a new degree of freedom for laser wavefront engineering, our platform is capable of operating and reading-out the spin-momentum of lasers associated with injected spin carriers, which would potentially play a pivotal role for the development of emerging spin-optoelectronic devices.

Visibility enhancement of underwater images based on polarization common-mode rejection of a highly polarized target signal

Underwater active polarization imaging is promising due to its effect of significantly descattering. Polarization-difference is commonly used to filter out backscattered noise. However, the polarization common-mode rejection of target signal has rarely been utilized. In this paper, via taking full advantage of this feature of Stokes vectors S₂ which ably avoids interference from target light, the spatial variation of the degree of polarization of backscattered light is accurately estimated, and the whole scene intensity distribution of background is reconstructed by Gaussian surface fitting based on least square. Meanwhile, the underwater image quality measure is applied as optimization feedback, through iterative computations, not only sufficiently suppresses backscattered noise but also better highlights the details of the target. Experimental results demonstrate the effectiveness of the proposed method for highly polarized target in strongly scattering water.

Universal Metasurfaces for Complete Linear Control of Coherent Light Transmission

Recent advances in metasurfaces and optical nanostructures have enabled complex control of incident light with optically thin devices. However, it has thus far been unclear whether it is possible to achieve complete linear control of coherent light transmission, that is, independent control of polarization, amplitude, and phase for both input polarization states, with just a single, thin nanostructure array. Here, it is proved possible, and a universal metasurface is proposed, a bilayer array of high-index elliptic cylinders that possesses a complete degree of optical freedom with fully designable chirality and anisotropy. The completeness of achievable light control is mathematically shown with corresponding Jones matrices, new types of 3D holographic schemes that were formerly impossible are experimentally demonstrated, and a systematic way of realizing any input-state-sensitive vector linear optical device is presented. The results unlock previously inaccessible degrees of freedom in light transmission control.

An All-Dielectric Metasurface Polarimeter

The polarization state of light is a key parameter in many imaging systems. For example, it can image mechanical stress and other physical properties that are not seen with conventional imaging and can also play a central role in quantum sensing. However, polarization is more difficult to image, and polarimetry typically involves several independent measurements with moving parts in the measurement device. Metasurfaces with interleaved designs have demonstrated sensitivity to either linear or circular/elliptical polarization states. Here, we present an all-dielectric meta-polarimeter for direct measurement of any arbitrary polarization state from a single-unit-cell design. By engineering a completely asymmetric design, we obtained a metasurface that can excite eigenmodes of the nanoresonators, thus displaying a unique diffraction pattern for not only any linear polarization state but all elliptical polarization states (and handedness) as well. The unique diffraction patterns are quantified into Stokes parameters with a resolution of 5° and with a polarization state fidelity of up to 99 ± 1%. This holds promise for applications in polarization imaging and quantum state tomography.

Nonseparable Polarization Wavefront Transformation

In this Letter, we investigate a new class of polarization wave front transformations which exhibit nonconventional far field interference behavior. We show that these can be realized by double-layer metasurfaces, which overcome the intrinsic limitations of single-layer metasurfaces. Holograms that encode four or more distinct patterns in nonorthogonal polarization states are theoretically demonstrated. This Letter clarifies and expands the possibilities enabled by a broad range of technologies which can spatially modulate light's polarization state and, for metasurfaces specifically, rigorously establishes when double-layer metasurfaces are-and are not-required.

Compound Meta-Optics for Complete and Loss-Less Field Control

Optical metasurfaces offer a compact platform for manipulation of the amplitude, phase, and polarization state of light. Independent control over these properties, however, is hindered by the symmetric transmission matrix associated with single-layer metasurfaces. Here, we utilize multilayer birefringent meta-optics to realize high-efficiency, independent control over the amplitude, phase, and polarization state of light. High-efficiency control is enabled by redistributing the wavefront between cascaded metasurfaces, while end-to-end inverse design is used to realize independent complex-valued functions for orthogonal polarization states. Based on this platform, we demonstrate spatial mode division multiplexing, optical mode conversion, and universal vectorial holograms, all with diffraction efficiencies over 80%. This meta-optic platform expands the design space of flat optics and could lead to advances in optical communications, quantum entanglement, and information encryption.

An Ultra-Broadband High Efficiency Polarization Beam Splitter for High Spectral Resolution Polarimetric Imaging in the Near Infrared

A broadband, high efficiency polarized beam splitter (PBS) metagrating based on integrated resonant units (IRUs) to enable simultaneous polarization analysis, spectral dispersion, and spatial imaging in the near infrared (NIR) is developed. A PBS metagrating with a diameter of 60 mm is the key technology component of the high-resolution multiple-species atmospheric profiler in the NIR (HiMAP-NIR), which is a spaceborne instrument concept crafted to be a core payload of NASA's new generation Earth System Observatory. HiMAP-NIR will enable the aerosol profiling in Earth's planetary boundary layer (from surface to2 km altitude) by simultaneously measuring four spatial-spectral-polarimetric images from 680 to 780 nm. Through detailed optimization of hybridized resonant modes in IRUs, the PBS metagrating shows a diffraction efficiency of 70% (or better) for all four linear-polarized incident light, and polarization contrasts between orthogonal states are 0.996 (or better) from 680 to 780 nm. It meets the stringent performance required by the HiMAP-NIR exploiting a new paradigm for the broad applications of metasurfaces.

Three-channel metasurface based on simultaneous and independent control of near and far field under a single line light source

Metasurface based on independent and simultaneous control of near field and far field has significant potential for use in multichannel optics platform devices. However, the previous studies cannot satisfy independent and simultaneous control of near field and far field under a single line source, which made a significant challenge to multichannel optical platforms working in a compact environment. To manipulate effectively and freely the amplitude and phase of transmission under line source, Marius' law and Propagation phase was introduced on all-dielectric encoding metasurfaces meta-atoms. The Marius' law and Propagation phase can control the size and rotation angle of meta-atoms to encode grayscale amplitude images and holographic phase images. Finite-difference time-domain simulation results reveal that dual channel metasurface under a single line source achieves the same display effect as the dual channel metasurface under multiple light sources, which proves the feasibility of our studies. Moreover, under different angles of the line source, we encode the near-field binary image by using the degeneracy rotation angle of meta-atoms. Finally, a three-channel metasurface was obtained without affecting the display of the previous two-channel metasurface. As a result, the independent control amplitude, phase, and polarization of the incident light wave were achieved. The proposed metasurface could be applied in creating a multi-channel metasurface optical platform in a compact environment, which has application potential in image displays, optical storage, optical anti-counterfeiting, and information encryption technology.

Nonlinear vectorial holography with quad-atom metasurfaces

Vectorial optical holography represents a solution to control the polarization and amplitude distribution of light in the Fourier space. While vectorial optical holography has been experimentally demonstrated in the linear optical regime, its nonlinear counterpart, which can provide extra degrees of freedom of light-field manipulation through the frequency conversion processes, remains unexplored. Here, we experimentally demonstrate the nonlinear vectorial holography through the second harmonic generation process on a quad-atom plasmonic metasurface. The quad-atom metasurface consists of gold meta-atoms with threefold rotational symmetry. Based on the concept of nonlinear geometric phase, we can simultaneously manipulate the phase and amplitude of the left and right circularly polarized second harmonic waves generated from the quad-atom metasurface. By superposing the two orthogonal polarization components, the quad-atom metasurface can produce nonlinear holographic images with vectorial polarization distributions. The proposed metasurface platform may have important applications in vectorial polarization nonlinear optical source, high-capacity optical information storage, and optical encryption.

Tunable structured light with flat optics

Flat optics has emerged as a key player in the area of structured light and its applications, owing to its subwavelength resolution, ease of integration, and compact footprint. Although its first generation has revolutionized conventional lenses and enabled anomalous refraction, new classes of meta-optics can now shape light and dark features of an optical field with an unprecedented level of complexity and multifunctionality. Here, we review these efforts with a focus on metasurfaces that use different properties of input light-angle of incidence and direction, polarization, phase distribution, wavelength, and nonlinear behavior-as optical knobs for tuning the output response. We discuss ongoing advances in this area as well as future challenges and prospects. These recent developments indicate that optically tunable flat optics is poised to advance adaptive camera systems, microscopes, holograms, and portable and wearable devices and may suggest new possibilities in optical communications and sensing.

Imaging polarimetry through metasurface polarization gratings

Metasurfaces-subwavelength arrays of phase-shifting elements-present new possibilities for polarization optics and polarimetry. In particular, a periodic, polarization-sensitive metasurface diffraction grating can enable full-Stokes imaging polarimetry with a single polarization-sensitive component. In this work, we show that a suitably-designed metasurface grating can serve as a polarimetric "attachment" to an existing intensity-only imaging system, converting it into one capable of full-Stokes imaging polarimetry. Design rules and tradeoffs governing this adaptation are described and demonstrated using a machine vision imaging system as an example.

Near unity transmission and full phase control with asymmetric Huygens' dielectric metasurfaces for holographic projections

Huygens' metasurfaces are transparent arrays of nanostructures that enable phase-front manipulation. This is achieved by simultaneous excitation of electric dipole (ED) and magnetic dipole (MD) resonances with equal amplitudes and phases in the constituent meta-atoms. In usual designs, the size changes of the meta-atoms, necessary to map the phase front, can detune the overlapping of ED and MD resonances, decreasing the transmission and limiting the operating bandwidth. In this report, we demonstrate that ED and MD resonances can be almost perfectly tuned together over a large wavelength range, keeping their spectral overlap, in a silicon metasurface by using anisotropic meta-atoms. In particular, we show near-unity transmission (>95% in simulations) and 2π phase control in a wavelength range from 760 to 815 nm using cuboidal nanoantennas. Using this concept, we also experimentally demonstrate clear reconstruction from holograms of a single metasurface spanning the near infrared and the whole visible spectral range.

Towards compact and snapshot channeled Mueller matrix imaging

A polarization transformation can be fully described by a 4 × 4 matrix, known as the Mueller matrix. To fully image an object's polarization response, one needs to compute the Mueller matrix at each pixel of the image. Standard divison-of-time Mueller matrix imaging, because of its sequential nature, is ill-suited to applications requiring immediate and real-time imaging and is also bulky owing to multiple moving parts. In this work, we propose a new method for compact, snapshot Mueller matrix imaging, based on structured polarization illumination, and division-of-focal plane imaging, which can, in a single-shot, fully capture the Mueller matrix information of a band-limited signal.