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Optical monitoring of the position and alignment of objects with a precision of only a few nanometres is key in applications such as smart manufacturing and force sensing. Traditional optical nanometrology requires precise nanostructure fabrication, multibeam interference or complex postprocessing algorithms, sometimes hampering wider adoption of this technology. Here we show a simplified, yet robust, approach to achieve nanometric metrology down to 2 nm resolution that eliminates the need for any reference signal for interferometric measurements. We insert an erbium-doped quartz crystal absorber into a single Fabry-Pérot cavity with a length of 3 cm and then induce exceptional points by matching the optical loss with the intercavity coupling. We experimentally achieve a displacement response enhancement of 86 times compared with lossless methods, and theoretically argue that an enhancement of over 450 times, corresponding to subnanometre resolution, may be achievable. We also show a fivefold enhancement in the signal-to-noise ratio, thus demonstrating that non-Hermitian sensors can lead to improved performances over the Hermitian counterpart., (© 2024. The Author(s), under exclusive licence to Springer Nature Limited.)

Light encodes multidimensional information, such as intensity, polarization, and spectrum. Traditional extraction of this light information requires discrete optical components by subdividing the detection area into many "one-to-one" functional pixels. The broadband photodetection of high-dimensional optical information with a single integrated on-chip detector is highly sought after, yet it poses significant challenges. In this study, we employ a metasurface-assisted graphene photodetector, enabling to simultaneously detect and differentiate various polarization states and wavelengths of broadband light (1-8 μm) at the wavelength prediction accuracy of 0.5 μm. The bipolar polarizability empowered by this design allows to decouple multidimensional information (encompassing polarization and wavelength), which can be achieved by encoding vectorial photocurrents with varying polarities and amplitudes. Furthermore, cooperative multiport metasurfaces are adopted and boosted by machine learning techniques. It enables precise spin-wavelength differentiation over an extremely broad wavelength range (1-8 μm). Our innovation offers a recipe for highly compact and high-dimensional spectral-polarization co-detection., (© 2024. The Author(s).)

High-order diffraction (HOD) from optical microstructures is undesirable in many applications because of the accompanying ghosting patterns and loss of efficiency. In contrast to suppressing HOD with subwavelength structures that challenge the fabrication of large-scale devices, managing HOD is less developed due to the lack of an efficient method for independently manipulating HOD. Here, we report independent manipulation of HODs, which are unexploited for subdiffraction-limit focusing in diffractive lenses, through an analytical formula that correlates the diffraction order and the width of each zone. The large spatial frequencies offered by the HODs enable our lenses to reduce the lateral focal size down to 0.44 λ even without any subwavelength feature (indispensable in most high-NA diffractive lenses), facilitating large-scale manufacture. Experimentally, we demonstrate high-order lens-based confocal imaging with a center-to-center dry resolution of 190 nm, the highest among visible-light confocal microscopies, and laser-ablation lithography with achieved direct-writing resolution of 400 nm (0.385 λ)., (© 2024. The Author(s).)

Anisotropic optical crystals can exhibit a hyperbolic response within the Reststrahlen band (RB) and support directional polaritonic propagations when interacting with light. Most of the reported low-symmetry optical crystals showcase the evolution from hyperbolic to elliptic dispersion topologies, largely owing to their adjacent RBs being either overlapped or separated. Here, we report an exceptional Reststrahlen point (ERP) in rare-earth oxyorthosilicate Y 2 SiO 5 , at which two neighboring RBs almost kiss each other. Consequently, we observe the direct hyperbolic-to-hyperbolic topological transition: the hyperbolic branches close and reopen along with the rotating transverse axis (TA). At such ERP, the TA merges to the direction orthogonal to its proximate phonon mode, mainly due to the interplay between these two non-orthogonal phonon modes. We also find that even with the existence of only one single RB, the TA can rotate in-plane. Our findings are prevalent in isostructural rare-earth oxyorthosilicates, such as Lu 2 SiO 5 . The universally underlying physics of ERP and its corresponding special class of rare-earth oxyorthosilicates may offer playgrounds for continuously tuning phonon polariton propagation direction, and broadband controlling light dispersion of polaritonic nanodevices., (© 2024. The Author(s).)

Caustics occur in diverse physical systems, spanning the nano-scale in electron microscopy to astronomical-scale in gravitational lensing. As envelopes of rays, optical caustics result in sharp edges or extended networks. Caustics in structured light, characterized by complex-amplitude distributions, have innovated numerous applications including particle manipulation, high-resolution imaging techniques, and optical communication. However, these applications have encountered limitations due to a major challenge in engineering caustic fields with customizable propagation trajectories and in-plane intensity profiles. Here, we introduce the "compensation phase" via 3D-printed metasurfaces to shape caustic fields with curved trajectories in free space. The in-plane caustic patterns can be preserved or morphed from one structure to another during propagation. Large-scale fabrication of these metasurfaces is enabled by the fast-prototyping and cost-effective two-photon polymerization lithography. Our optical elements with the ultra-thin profile and sub-millimeter extension offer a compact solution to generating caustic structured light for beam shaping, high-resolution microscopy, and light-matter-interaction studies., (© 2024. The Author(s).)

The dynamic control of electromagnetic waves is a persistent pursuit in modern industrial development. The state-of-the-art dynamic devices suffer from limitations such as narrow bandwidth, limited modulation range, and expensive features. To address these issues, we fuse origami techniques with metamaterial design to achieve ultra-wideband and large-depth reflection modulation. Through a folding process, our proposed metamaterial achieves over 10-dB modulation depth over 4.96 - 38.8 GHz, with a fractional bandwidth of 155% and tolerance to incident angles and polarizations. Its ultra-wideband and large-depth reflection modulation performance is verified through experiments and analyzed through multipole decomposition theory. To enhance its practical applicability, transparent conductive films are introduced to the metamaterial, achieving high optical transparency (>87%) from visible to near-infrared light while maintaining cost-effectiveness. Benefiting from lightweight, foldability, and low-cost properties, our design shows promise for extensive satellite communication and optical window mobile communication management., (© 2024. The Author(s).)

Ultrasonic imaging is crucial in the fields of biomedical engineering for its deep penetration capabilities and non-ionizing nature. However, traditional techniques heavily rely on impedance differences within objects, resulting in poor contrast when imaging acoustically transparent targets. Here, we propose a compact spatial differentiator for underwater isotropic edge-enhanced imaging, which enhances the imaging contrast without the need for contrast agents or external physical fields. This design incorporates an amplitude meta-grating for linear transmission along the radial direction, combined with a phase meta-grating that utilizes focus and spiral phases with a first-order topological charge. Through theoretical analysis, numerical simulations, and experimental validation, we substantiate the effectiveness of our technique in distinguishing amplitude objects with isotropic edge enhancements. Importantly, this method also enables the accurate detection of both phase objects and artificial biological models. This breakthrough creates new opportunities for applications in medical diagnosis and nondestructive testing., (© 2024. The Author(s).)

Extensive investigations on the moiré magic angle in twisted bilayer graphene have unlocked the emerging field-twistronics. Recently, its optics analogue, namely opto-twistronics, further expands the potential universal applicability of twistronics. However, since heat diffusion neither possesses the dispersion like photons nor carries the band structure as electrons, the real magic angle in electrons or photons is ill-defined for heat diffusion, making it elusive to understand or design any thermal analogue of magic angle. Here, we introduce and experimentally validate the twisted thermotics in a twisted diffusion system by judiciously tailoring thermal coupling, in which twisting an analog thermal magic angle would result in the function switching from cloaking to concentration. Our work provides insights for the tunable heat diffusion control, and opens up an unexpected branch for twistronics -- twisted thermotics, paving the way towards field manipulation in twisted configurations including but not limited to fluids., (© 2024. The Author(s).)

Metasurfaces have exhibited unprecedented degree of freedom in manipulating electromagnetic (EM) waves and thus provide fantastic front-end interfaces for smart systems. Here we show a framework for perception enhancement based on vision-driven metasurface. Human's eye movements are matched with microwave radiations to extend the humans' perception spectrum. By this means, our eyes can "sense" visual information and invisible microwave information. Several experimental demonstrations are given for specific implementations, including a physiological-signal-monitoring system, an "X-ray-glasses" system, a "glimpse-and-forget" tracking system and a speech reception system for deaf people. Both the simulation and experiment results verify evident advantages in perception enhancement effects and improving information acquisition efficiency. This framework can be readily integrated into healthcare systems to monitor physiological signals and to offer assistance for people with disabilities. This work provides an alternative framework for perception enhancement and may find wide applications in healthcare, wearable devices, search-and-rescue and others., (© 2024. The Author(s).)

High quantum efficiency and wide-band detection capability are the major thrusts of infrared sensing technology. However, bulk materials with high efficiency have consistently encountered challenges in integration and operational complexity. Meanwhile, two-dimensional (2D) semimetal materials with unique zero-bandgap structures are constrained by the bottleneck of intrinsic quantum efficiency. Here, we report a near-mid infrared ultra-miniaturized graphene photodetector with configurable 2D potential well. The 2D potential well constructed by dielectric structures can spatially (laterally and vertically) produce a strong trapping force on the photogenerated carriers in graphene and inhibit their recombination, thereby improving the external quantum efficiency (EQE) and photogain of the device with wavelength-immunity, which enable a high responsivity of 0.2 A/W-38 A/W across a broad infrared detection band from 1.55 to 11 µm. Thereafter, a room-temperature detectivity approaching 1 × 10 9  cm Hz 1/2 W -1 is obtained under blackbody radiation. Furthermore, a synergistic effect of electric and light field in the 2D potential well enables high-efficiency polarization-sensitive detection at tunable wavelengths. Our strategy opens up alternative possibilities for easy fabrication, high-performance and multifunctional infrared photodetectors., (© 2024. The Author(s).)

Photogating effect is the dominant mechanism of most high-responsivity two-dimensional (2D) material photodetectors. However, the ultrahigh responsivities in those devices are intrinsically at the cost of very slow response speed. In this work, we report a WSe 2 /Ta 2 NiSe 5 heterostructure detector whose photodetection gain and response speed can be enhanced simultaneously, overcoming the trade-off between responsivity and speed. We reveal that photogating-assisted tunneling synergistically allows photocarrier multiplication and carrier acceleration through tunneling under an electrical field. The photogating effect in our device features low-power consumption (in the order of nW) and shows a dependence on the polarization states of incident light, which can be further tuned by source-drain voltages, allowing for wavelength discrimination with just a two-electrode planar structure. Our findings offer more opportunities for the long-sought next-generation photodetectors with high responsivity, fast speed, polarization detection, and multi-color sensing, simultaneously., (© 2024. The Author(s).)

Singularities ubiquitously exist in different fields and play a pivotal role in probing the fundamental laws of physics and developing highly sensitive sensors. Nevertheless, achieving higher-order (≥3) singularities, which exhibit superior performance, typically necessitates meticulous tuning of multiple (≥3) coupled degrees of freedom or additional introduction of nonlinear potential energies. Here we propose theoretically and confirm using mechanics experiments, the existence of an unexplored cusp singularity in the phase-tracked (PhT) steady states of a pair of coherently coupled mechanical modes without the need for multiple (≥3) coupled modes or nonlinear potential energies. By manipulating the PhT singularities in an electrostatically tunable micromechanical system, we demonstrate an enhanced cubic-root response to frequency perturbations. This study introduces a new phase-tracking method for studying interacting systems and sheds new light on building and engineering advanced singular devices with simple and well-controllable elements, with potential applications in precision metrology, portable nonreciprocal devices, and on-chip mechanical computing., (© 2023. The Author(s).)

Dispersion decomposes compound light into its monochromatic components, which is detrimental to broadband imaging but advantageous for spectroscopic applications. Metasurfaces provide a unique path to modulate the dispersion by adjusting structural parameters on a two-dimensional plane. However, conventional linear phase compensation does not adequately match the meta-unit's dispersion characteristics with required complex dispersion, hindering at-will dispersion engineering over a very wide bandwidth particularly. Here, we propose an asymptotic phase compensation strategy for ultra-broadband dispersion-controlled metalenses. Metasurfaces with extraordinarily high aspect ratio nanostructures have been fabricated for arbitrary dispersion control in ultra-broad bandwidth, and we experimentally demonstrate the single-layer achromatic metalenses in the visible to infrared spectrum (400 nm~1000 nm, NA = 0.164). Our proposed scheme provides a comprehensive theoretical framework for single-layer meta-optics, allowing for arbitrary dispersion manipulation without bandwidth restrictions. This development is expected to have significant applications in ultra-broadband imaging and chromatography detection, among others., (© 2023. Springer Nature Limited.)

We introduce a new paradigm for generating high-purity vortex beams with metasurfaces. By applying optical neural networks to a system of cascaded phase-only metasurfaces, we demonstrate the efficient generation of high-quality Laguerre-Gaussian (LG) vortex modes. Our approach is based on two metasurfaces where one metasurface redistributes the intensity profile of light in accord with Rayleigh-Sommerfeld diffraction rules, and then the second metasurface matches the required phases for the vortex beams. Consequently, we generate high-purity LG p,l optical modes with record-high Laguerre polynomial orders p = 10 and l = 200, and with the purity in p, l and relative conversion efficiency as 96.71%, 85.47%, and 70.48%, respectively. Our engineered cascaded metasurfaces suppress greatly the backward reflection with a ratio exceeding -17 dB. Such higher-order optical vortices with multiple orthogonal states can revolutionize next-generation optical information processing., (© 2023. Springer Nature Limited.)

The study of magneto-optical absorption has stimulated diverse energy-technology-related explorations, showing potential in breaking the current theoretical efficiency limits of energy devices compared with reciprocal counterparts. However, experimentally realizing strong infrared non-reciprocal absorption remains an open challenge, and existing proposals of non-reciprocal absorbers are restricted to a narrow working waveband. Here we observe highly asymmetric absorption spectra over a broad mid-infrared band (nearly 10 μm) using doped InAs multilayers with gradient epsilon-near-zero frequencies. We reveal that the magnetized epsilon-near-zero behaviours and material loss play important roles in achieving strongly non-reciprocal absorption under a moderate external magnetic field using a thin epsilon-near-zero film (<λ/40, λ is the wavelength). Our approach enables flexible control over the working frequencies and non-reciprocal bandwidths by designing magnetized InAs films with different doping concentrations. The proposed principles can also be generalized to other III-V semiconductors, magnetized metals, topological Weyl semimetals, magnetized zero-index metamaterials and metasurfaces., (© 2023. The Author(s), under exclusive licence to Springer Nature Limited.)

Planar diffractive lenses (PDLs) with optimized but disordered structures can focus light beyond the diffraction limit. However, these disordered structures have inevitably destroyed wide-field imaging capability, limiting their applications in microscopy. Here, we introduce information entropy S to evaluate the disorder of an objective chip by using the probability of its structural deviation from standard Fresnel zone plates. Inspired by the theory of entropy change, we predict an equilibrium point [Formula: see text] to balance wide-field imaging (theoretically evaluated by the Strehl ratio) and subdiffraction-limit focusing. To verify this, a [Formula: see text] objective chip with a record-long focal length of 1 mm is designed with [Formula: see text], which is the nearest to the equilibrium point among all reported PDLs. Consequently, our fabricated chip can focus light with subdiffraction-limit size of 0.44 λ and image fine details with spatial frequencies up to 4000 lp/mm experimentally. These unprecedented performances enable ultracompact reflective confocal microscopy for superresolution imaging., (© 2023. Springer Nature Limited.)

Tuning the composition of perovskites to approach the ideal bandgap raises the single-junction Shockley-Queisser efficiency limit of solar cells. The rapid development of narrow-bandgap formamidinium lead triiodide-based perovskites has brought perovskite single-junction solar cell efficiencies up to 26.1%. However, such compositional engineering route has reached the limit of the Goldschmidt tolerance factor. Here, we experimentally demonstrate a resonant perovskite solar cell that produces giant light absorption at the perovskite band edge with tiny absorption coefficients. We design multiple guide-mode resonances by momentum matching of waveguided modes and free-space light via Brillouin-zone folding, thus achieving an 18-nm band edge extension and 1.5 mA/cm 2 improvement of the current. The external quantum efficiency spectrum reaches a plateau of above 93% across the spectral range of ~500 to 800 nm. This resonant nanophotonics strategy translates to a maximum EQE-integrated current of 26.0 mA/cm 2 which is comparable to that of the champion single-crystal perovskite solar cell with a thickness of ~20 μm. Our findings break the ray-optics limit and open a new door to improve the efficiency of single-junction perovskite solar cells further when compositional engineering or other carrier managements are close to their limits., (© 2023. Springer Nature Limited.)

Circularly polarized light sources with free-space directional emission play a key role in chiroptics 1 , spintronics 2 , valleytronics 3 and asymmetric photocatalysis 4 . However, conventional approaches fail to simultaneously realize pure circular polarization, high directionality and large emission angles in a compact emitter. Metal-halide perovskite semiconductors are promising light emitters 5-8 , but the absence of an intrinsic spin-locking mechanism results in poor emission chirality. Further, device integration has undermined the efficiency and directionality of perovskite chiral emitters. Here we realize compact spin-valley-locked perovskite emitting metasurfaces where spin-dependent geometric phases are imparted into bound states in the continuum via Brillouin zone folding, and thus, photons with different spins are selectively addressed to opposite valleys. Employing this approach, chiral purity of 0.91 and emission angle of 41.0° are simultaneously achieved, with a beam divergence angle of 1.6°. With this approach, we envisage the realization of chiral light-emitting diodes, as well as the on-chip generation of entangled photon pairs., (© 2023. The Author(s), under exclusive licence to Springer Nature Limited.)

Exceptional points (EPs) arising in non-Hermitian systems have led to a variety of intriguing wave phenomena, and have been attracting increased interest in various physical platforms. In this Review, we highlight the latest fundamental advances in the context of EPs in various nanoscale systems, and overview the theoretical progress related to EPs, including higher-order EPs, bulk Fermi arcs and Weyl exceptional rings. We peek into EP-associated emerging technologies, in particular focusing on the influence of noise for sensing near EPs, improving the efficiency in asymmetric transmission based on EPs, optical isolators in nonlinear EP systems and novel concepts to implement EPs in topological photonics. We also discuss the constraints and limitations of the applications relying on EPs, and offer parting thoughts about promising ways to tackle them for advanced nanophotonic applications., (© 2023. Springer Nature Limited.)

Photonic crystals (PhCs) are a kind of artificial structures that can mold the flow of light at will. Polaritonic crystals (PoCs) made from polaritonic media offer a promising route to controlling nano-light at the subwavelength scale. Conventional bulk PhCs and recent van der Waals PoCs mainly show highly symmetric excitation of Bloch modes that closely rely on lattice orders. Here, we experimentally demonstrate a type of hyperbolic PoCs with configurable and low-symmetry deep-subwavelength Bloch modes that are robust against lattice rearrangement in certain directions. This is achieved by periodically perforating a natural crystal α-MoO 3 that hosts in-plane hyperbolic phonon polaritons. The mode excitation and symmetry are controlled by the momentum matching between reciprocal lattice vectors and hyperbolic dispersions. We show that the Bloch modes and Bragg resonances of hyperbolic PoCs can be tuned through lattice scales and orientations while exhibiting robust properties immune to lattice rearrangement in the hyperbolic forbidden directions. Our findings provide insights into the physics of hyperbolic PoCs and expand the categories of PhCs, with potential applications in waveguiding, energy transfer, biosensing and quantum nano-optics., (© 2023. Crown.)

The quantized bulk quadrupole moment has so far revealed a non-trivial boundary state with lower-dimensional topological edge states and in-gap zero-dimensional corner modes. In contrast to photonic implementations, state-of-the-art strategies for topological thermal metamaterials struggle to achieve such higher-order hierarchical features. This is due to the absence of quantized bulk quadrupole moments in thermal diffusion fundamentally prohibiting possible band topology expansions. Here, we report a recipe for generating quantized bulk quadrupole moments in fluid heat transport and observe the quadrupole topological phases in non-Hermitian thermal systems. Our experiments show that both the real- and imaginary-valued bands exhibit the hierarchical features of bulk, gapped edge and in-gap corner states-in stark contrast to the higher-order states observed only on real-valued bands in classical wave fields. Our findings open up unique possibilities for diffusive metamaterial engineering and establish a playground for multipolar topological physics., (© 2023. The Author(s).)

Differential interference contrast (DIC) microscopy allows high-contrast, low-phototoxicity, and label-free imaging of transparent biological objects, and has been applied in the field of cellular morphology, cell segmentation, particle tracking, optical measurement and others. Commercial DIC microscopy based on Nomarski or Wollaston prism resorts to the interference of two polarized waves with a lateral differential offset (shear) and axial phase shift (bias). However, the shear generated by these prisms is limited to the rectilinear direction, unfortunately resulting in anisotropic contrast imaging. Here we propose an ultracompact metasurface-assisted isotropic DIC (i-DIC) microscopy based on a grand original pattern of radial shear interferometry, that converts the rectilinear shear into rotationally symmetric along radial direction, enabling single-shot isotropic imaging capabilities. The i-DIC presents a complementary fusion of typical meta-optics, traditional microscopes and integrated optical system, and showcases the promising and synergetic advancements in edge detection, particle motion tracking, and label-free cellular imaging., (© 2023. The Author(s).)

The orbital angular momentum is a fundamental degree of freedom of light wavefronts, currently exploited in applications where information capacity is a key requirement, such as optical communication, super-resolution imaging and high-dimensional quantum computing. However, generating orbital angular momentum beams requires spatio-temporally coherent light sources (lasers or supercontinuum sources), because incoherent light would smear out the doughnut features of orbital angular momentum beams, forming polychromatic or obscured orbital angular momentum beams instead. Here we show generation of coloured orbital angular momentum beams using incoherent white light. Spatio-temporal coherence is achieved by miniaturizing spiral phase plates and integrating them with structural colour filters, three-dimensionally printed at the nanoscale. Our scheme can in principle generate multiple helical eigenstates and combine colour information into orbital angular momentum beams independently. These three-dimensional optical elements encoded with colour and orbital angular momentum information substantially increase the number of combinations for optical anti-counterfeiting and photonic lock-key devices in a pairwise fashion., (© 2023. The Author(s), under exclusive licence to Springer Nature Limited.)

Pyroelectricity originates from spontaneous polarization variation, promising in omnipresent non-static thermodynamic energy harvesting. Particularly, changing spontaneous polarization via out-of-plane uniform heat perturbations has been shown in solar pyroelectrics. However, these approaches present unequivocal inefficiency due to spatially coupled low temperature change and duration along the longitudinal direction. Here we demonstrate unconventional giant polarization ripples in transverse pyroelectrics, without increasing the total energy input, into electricity with an efficiency of 5-fold of conventional longitudinal counterparts. The non-uniform graded temperature variation arises from decoupled heat localization and propagation, leading to anomalous in-plane heat perturbation (29-fold) and enhanced thermal disequilibrium effects. This in turn triggers an augmented polarization ripple, fundamentally enabling unprecedented electricity generation performance. Notably, the device generates a power density of 38 mW m -2 at 1 sun illumination, which is competitive with solar thermoelectrics and ferrophotovoltaics. Our findings provide a viable paradigm, not only for universal practical pyroelectric heat harvesting but for flexible manipulation of transverse heat transfer towards sustainable energy harvesting and management., (© 2023. The Author(s).)

Various optical crystals possess permittivity components of opposite signs along different principal directions in the mid-infrared regime, exhibiting exotic anisotropic phonon resonances. Such materials with hyperbolic polaritons-hybrid light-matter quasiparticles with open isofrequency contours-feature large-momenta optical modes and wave confinement that make them promising for nanophotonic on-chip technologies. So far, hyperbolic polaritons have been observed and characterized in crystals with high symmetry including hexagonal (boron nitride), trigonal (calcite) and orthorhombic (α-MoO 3 or α-V 2 O 5 ) crystals, where they obey certain propagation patterns. However, lower-symmetry materials such as monoclinic crystals were recently demonstrated to offer richer opportunities for polaritonic phenomena. Here, using scanning near-field optical microscopy, we report the direct real-space nanoscale imaging of symmetry-broken hyperbolic phonon polaritons in monoclinic CdWO 4 crystals, and showcase inherently asymmetric polariton excitation and propagation associated with the nanoscale shear phenomena. We also introduce a quantitative theoretical model to describe these polaritons that leads to schemes to enhance crystal asymmetry via the damping loss of phonon modes. Ultimately, our findings show that polaritonic nanophotonics is attainable using natural materials with low symmetry, favouring a versatile and general way to manipulate light at the nanoscale., (© 2022. The Author(s), under exclusive licence to Springer Nature Limited.)

Metasurfaces, artificial 2D structures, have been widely used for the design of various functionalities in optics. Jones matrix, a 2×2 matrix with eight parameters, provides the most complete characterization of the metasurface structures in linear optics, and the number of free parameters (i.e., degrees of freedom, DOFs) in the Jones matrix determines the limit to what functionalities we can realize. Great efforts have been made to continuously expand the number of DOFs, and a maximal number of six has been achieved recently. However, the realization of the ultimate goal with eight DOFs (full free parameters) has been proven as a great challenge so far. Here, we show that by cascading two layer metasurfaces and utilizing the gradient descent optimization algorithm, a spatially varying Jones matrix with eight DOFs is constructed and verified numerically and experimentally in optical frequencies. Such ultimate control unlocks opportunities to design optical functionalities that are unattainable with previously known methodologies and may find wide potential applications in optical fields., (© 2022. The Author(s).)

Valleytronics is a promising candidate to address low-energy signal transport on chip, leveraging the valley pseudospin of electrons as a new degree of freedom to encode, process and store information 1-7 . However, valley-carrier nanocircuitry is still elusive, because it essentially requires valley transport that overcomes three simultaneous challenges: high fidelity, high directionality and room-temperature operation. Here we experimentally demonstrate a nanophotonic circuit that can route valley indices of a WS 2 monolayer unidirectionally via the chirality of photons. Two propagating modes are supported in the gap area of the circuit and interfere with each other to generate beating patterns, which exhibit complementary profiles for circular dipoles of different handedness. Based on the spin-dependent beating patterns, we showcase valley fidelity of chiral photons up to 98%, and the circulation directionality is measured to be 0.44 ± 0.04 at room temperature. The proposed nanocircuit can not only enable the construction of large-scale valleytronic networks but also serve as an interactive interface to integrate valleytronics 3-5 , spintronics 8-10 and integrated photonics 11-13 , opening new possibilities for hybrid spin-valley-photon ecosystems at the nanoscale., (© 2022. The Author(s), under exclusive licence to Springer Nature Limited.)

The reduced symmetry in strong spin-orbit coupling materials such as transition metal ditellurides (TMDTs) gives rise to non-trivial topology, unique spin texture, and large charge-to-spin conversion efficiencies. Bilayer TMDTs are non-centrosymmetric and have unique topological properties compared to monolayer or trilayer, but a controllable way to prepare bilayer MoTe 2 crystal has not been achieved to date. Herein, we achieve the layer-by-layer growth of large-area bilayer and trilayer 1T' MoTe 2 single crystals and centimetre-scale films by a two-stage chemical vapor deposition process. The as-grown bilayer MoTe 2 shows out-of-plane ferroelectric polarization, whereas the monolayer and trilayer crystals are non-polar. In addition, we observed large in-plane nonlinear Hall (NLH) effect for the bilayer and trilayer T d phase MoTe 2 under time reversal-symmetric conditions, while these vanish for thicker layers. For a fixed input current, bilayer T d MoTe 2 produces the largest second harmonic output voltage among the thicker crystals tested. Our work therefore highlights the importance of thickness-dependent Berry curvature effects in TMDTs that are underscored by the ability to grow thickness-precise layers., (© 2022. The Author(s).)

Optical metasurfaces with high quality factors (Q-factors) of chiral resonances can boost substantially light-matter interaction for various applications of chiral response in ultrathin, active, and nonlinear metadevices. However, current approaches lack the flexibility to enhance and tune the chirality and Q-factor simultaneously. Here, we suggest a design of chiral metasurface supporting bound state in the continuum (BIC) and demonstrate experimentally chiroptical responses with ultra-high Q-factors and near-perfect circular dichroism (CD = 0.93) at optical frequencies. We employ the symmetry-reduced meta-atoms with high birefringence supporting winding elliptical eigenstate polarizations with opposite helicity. It provides a convenient way for achieving the maximal planar chirality tuned by either breaking in-plane structure symmetry or changing illumination angle. Beyond linear CD, we also achieved strong near-field enhancement CD and near-unitary nonlinear CD in the same planar chiral metasurface design with circular eigen-polarization. Sharply resonant chirality realized in planar metasurfaces promises various practical applications including chiral lasers and chiral nonlinear filters., (© 2022. The Author(s).)

Recent investigations on non-Hermitian physics have unlocked new possibilities to manipulate wave scattering on lossy materials. Coherent perfect absorption is such an effect that enables all-light control by incorporating a suitable amount of loss. On the other hand, controlling heat transfer with heat may empower a distinct paradigm other than using thermal metamaterials. However, since heat neither propagates nor carries any momentum, almost all concepts in wave scattering are ill-defined for steady-state heat diffusion, making it formidable to understand or utilize any coherent effect. Here, we establish a scattering theory for heat diffusion by introducing an imitated momentum for thermal fields. The thermal analogue of coherent perfect absorption is thus predicted and demonstrated as the perfect absorption of exergy fluxes and undisturbed temperature fields. Unlike its photonic counterpart, thermal coherent perfect absorption can be realized for regular thermal materials, and be generalized for various objects., (© 2022. The Author(s).)

Computational meta-optics brings a twist on the accelerating hardware with the benefits of ultrafast speed, ultra-low power consumption, and parallel information processing in versatile applications. Recent advent of metasurfaces have enabled the full manipulation of electromagnetic waves within subwavelength scales, promising the multifunctional, high-throughput, compact and flat optical processors. In this trend, metasurfaces with nonlocality or multi-layer structures are proposed to perform analog optical computations based on Green's function or Fourier transform, intrinsically constrained by limited operations or large footprints/volume. Here, we showcase a Fourier-based metaprocessor to impart customized highly flexible transfer functions for analog computing upon our single-layer Huygens' metasurface. Basic mathematical operations, including differentiation and cross-correlation, are performed by directly modulating complex wavefronts in spatial Fourier domain, facilitating edge detection and pattern recognition of various image processing. Our work substantiates an ultracompact and powerful kernel processor, which could find important applications for optical analog computing and image processing., (© 2022. The Author(s).)

The reciprocity principle governs the symmetry in transmission of electromagnetic and acoustic waves, as well as the diffusion of heat between two points in space, with important consequences for thermal management and energy harvesting. There has been significant recent interest in materials with time-modulated properties, which have been shown to efficiently break reciprocity for light, sound, and even charge diffusion. However, time modulation may not be a plausible approach to break thermal reciprocity, in contrast to the usual perception. We establish a theoretical framework to accurately describe the behavior of diffusive processes under time modulation, and prove that thermal reciprocity in dynamic materials is generally preserved by the continuity equation, unless some external bias or special material is considered. We then experimentally demonstrate reciprocal heat transfer in a time-modulated device. Our findings correct previous misconceptions regarding reciprocity breaking for thermal diffusion, revealing the generality of symmetry constraints in heat transfer, and clarifying its differences from other transport processes in what concerns the principles of reciprocity and microscopic reversibility., (© 2022. The Author(s).)

Thermal metamaterials have exhibited great potential on manipulating, controlling and processing the flow of heat, and enabled many promising thermal metadevices, including thermal concentrator, rotator, cloak, etc. However, three long-standing challenges remain formidable, i.e., transformation optics-induced anisotropic material parameters, the limited shape adaptability of experimental thermal metadevices, and a priori knowledge of background temperatures and thermal functionalities. Here, we present robustly printable freeform thermal metamaterials to address these long-standing difficulties. This recipe, taking the local thermal conductivity tensors as the input, resorts to topology optimization for the freeform designs of topological functional cells (TFCs), and then directly assembles and prints them. Three freeform thermal metadevices (concentrator, rotator, and cloak) are specifically designed and 3D-printed, and their omnidirectional concentrating, rotating, and cloaking functionalities are demonstrated both numerically and experimentally. Our study paves a powerful and flexible design paradigm toward advanced thermal metamaterials with complex shapes, omnidirectional functionality, background temperature independence, and fast-prototyping capability., (© 2021. The Author(s).)

Thin-film architectures are a staple in a wide range of technologies, such as semiconductor devices, optical coatings, magnetic recording, solar cells and batteries. Despite the industrial success of thin-film technology, mostly due to the easy fabrication and low cost, a fundamental drawback remains: it is challenging to alter the features of the film once fabricated. Here we report a methodology to modify the thickness and sequence of the innermost solid-state thin-film layers. We start with a thin-film stack of amorphous iron oxide and silver. By applying a suitable voltage bias and then reversing it, we can float the silver layer above or below the oxide layer by virtue of the migration of silver atoms. Scanning transmission electron microscopy reveals various sequences and thicknesses of the silver and oxide layers achieved with different experimental conditions. As a proof-of-principle, we show a dynamic change of structural colours of the stack derived from this process. Our results may offer opportunities to dynamically reconfigure thin-film-based functional nanodevices in situ., (© 2021. The Author(s), under exclusive licence to Springer Nature Limited.)

A light field print (LFP) displays three-dimensional (3D) information to the naked-eye observer under ambient white light illumination. Changing perspectives of a 3D image are seen by the observer from varying angles. However, LFPs appear pixelated due to limited resolution and misalignment between their lenses and colour pixels. A promising solution to create high-resolution LFPs is through the use of advanced nanofabrication techniques. Here, we use two-photon polymerization lithography as a one-step nanoscale 3D printer to directly fabricate LFPs out of transparent resin. This approach produces simultaneously high spatial resolution (29-45 µm) and high angular resolution (~1.6°) images with smooth motion parallax across 15 × 15 views. Notably, the smallest colour pixel consists of only a single nanopillar (~300 nm diameter). Our LFP signifies a step towards hyper-realistic 3D images that can be applied in print media and security tags for high-value goods.

The ability of light beams to rotate nano-objects has important applications in optical micromachines and biotechnology. However, due to the diffraction limit, it is challenging to rotate nanoparticles at subwavelength scale. Here, we propose a method to obtain controlled fast orbital rotation (i.e., circumgyration) at deep subwavelength scale, based on the nonlinear optical effect rather than sub-diffraction focusing. We experimentally demonstrate rotation of metallic nanoparticles with orbital radius of 71 nm, to our knowledge, the smallest orbital radius obtained by optical trapping thus far. The circumgyration frequency of particles in water can be more than 1 kHz. In addition, we use a femtosecond pulsed Gaussian beam rather than vortex beams in the experiment. Our study provides paradigms for nanoparticle manipulation beyond the diffraction limit, which will not only push toward possible applications in optically driven nanomachines, but also spur more fascinating research in nano-rheology, micro-fluid mechanics and biological applications at the nanoscale.

Metasurfaces have provided unprecedented freedom for manipulating electromagnetic waves. In metasurface design, massive meta-atoms have to be optimized to produce the desired phase profiles, which is time-consuming and sometimes prohibitive. In this paper, we propose a fast accurate inverse method of designing functional metasurfaces based on transfer learning, which can generate metasurface patterns monolithically from input phase profiles for specific functions. A transfer learning network based on GoogLeNet-Inception-V3 can predict the phases of 2 8×8 meta-atoms with an accuracy of around 90%. This method is validated via functional metasurface design using the trained network. Metasurface patterns are generated monolithically for achieving two typical functionals, 2D focusing and abnormal reflection. Both simulation and experiment verify the high design accuracy. This method provides an inverse design paradigm for fast functional metasurface design, and can be readily used to establish a meta-atom library with full phase span.

The emerging monolayer transition metal dichalcogenides have provided an unprecedented material platform for miniaturized opto-electronic devices with integrated functionalities. Although excitonic light-matter interactions associated with their direct bandgaps have received tremendous research efforts, wavefront engineering is less appreciated due to the suppressed phase accumulation effects resulting from the vanishingly small thicknesses. By introducing loss-assisted singular phase behaviour near the critical coupling point, we demonstrate that integration of monolayer MoS 2 on a planar ZnO/Si substrate, approaching the physical thickness limit of the material, enables a π phase jump. Moreover, highly dispersive extinctions of MoS 2 further empowers broadband phase regulation and enables binary phase-modulated supercritical lenses manifesting constant sub-diffraction-limited focal spots of 0.7 Airy units (AU) from the blue to yellow wavelength range. Our demonstrations downscaling optical elements to atomic thicknesses open new routes for ultra-compact opto-electronic systems harnessing two-dimensional semiconductor platforms with integrated functionalities.

Bulk photovoltaic effect (BPVE), featuring polarization-dependent uniform photoresponse at zero external bias, holds potential for exceeding the Shockley-Queisser limit in the efficiency of existing opto-electronic devices. However, the implementation of BPVE has been limited to the naturally existing materials with broken inversion symmetry, such as ferroelectrics, which suffer low efficiencies. Here, we propose metasurface-mediated graphene photodetectors with cascaded polarization-sensitive photoresponse under uniform illumination, mimicking an artificial BPVE. With the assistance of non-centrosymmetric metallic nanoantennas, the hot photocarriers in graphene gain a momentum upon their excitation and form a shift current which is nonlocal and directional. Thereafter, we demonstrate zero-bias uncooled mid-infrared photodetectors with three orders higher responsivity than conventional BPVE and a noise equivalent power of 0.12 nW Hz -1/2 . Besides, we observe a vectorial photoresponse which allows us to detect the polarization angle of incident light with a single device. Our strategy opens up alternative possibilities for scalable, low-cost, multifunctional infrared photodetectors.

Highly confined and low-loss polaritons are known to propagate isotropically over graphene and hexagonal boron nitride in the plane, leaving limited degrees of freedom in manipulating light at the nanoscale. The emerging family of biaxial van der Waals materials, such as α-MoO 3 and V 2 O 5 , support exotic polariton propagation, as their auxiliary optical axis is in the plane. Here, exploiting this strong in-plane anisotropy, we report edge-tailored hyperbolic polaritons in patterned α-MoO 3 nanocavities via real-space nanoimaging. We find that the angle between the edge orientation and the crystallographic direction significantly affects the optical response, and can serve as a key tuning parameter in tailoring the polaritonic patterns. By shaping α-MoO 3 nanocavities with different geometries, we observe edge-oriented and steerable hyperbolic polaritons as well as forbidden zones where the polaritons detour. The lifetime and figure of merit of the hyperbolic polaritons can be regulated by the edge aspect ratio of nanocavity.

Naturally-occurring thermal materials usually possess specific thermal conductivity (κ), forming a digital set of κ values. Emerging thermal metamaterials have been deployed to realize effective thermal conductivities unattainable in natural materials. However, the effective thermal conductivities of such mixing-based thermal metamaterials are still in digital fashion, i.e., the effective conductivity remains discrete and static. Here, we report an analog thermal material whose effective conductivity can be in-situ tuned from near-zero to near-infinity κ. The proof-of-concept scheme consists of a spinning core made of uncured polydimethylsiloxane (PDMS) and fixed bilayer rings made of silicone grease and steel. Thanks to the spinning PDMS and its induced convective effects, we can mold the heat flow robustly with continuously changing and anisotropic κ. Our work enables a single functional thermal material to meet the challenging demands of flexible thermal manipulation. It also provides platforms to investigate heat transfer in systems with moving components.

Meta-holographic encryption is a potentially important technique for information security. Despite rapid progresses in multi-tasked meta-holograms, the number of information channels available in metasurfaces is limited, making meta-holographic encryption vulnerable to some attacking algorithms. Herein, we demonstrate a re-programmable metasurface that can produce arbitrary holographic images for optical encryption. The encrypted information is divided into two matrices. These two matrices are imposed to the incident light and the metasurface, respectively. While the all-dielectric metasurface is static, the phase matrix of incident light provides additional degrees of freedom to precisely control the eventual functions at will. With a single Si metasurface, arbitrary holographic images and videos have been transported and decrypted. We hope that this work paves a more promising way to optical information encryption and authentication.

Polaritons - coupled excitations of photons and dipolar matter excitations - can propagate along anisotropic metasurfaces with either hyperbolic or elliptical dispersion. At the transition from hyperbolic to elliptical dispersion (corresponding to a topological transition), various intriguing phenomena are found, such as an enhancement of the photonic density of states, polariton canalization and hyperlensing. Here, we investigate theoretically and experimentally the topological transition, the polaritonic coupling and the strong nonlocal response in a uniaxial infrared-phononic metasurface, a grating of hexagonal boron nitride (hBN) nanoribbons. By hyperspectral infrared nanoimaging, we observe a synthetic transverse optical phonon resonance (strong collective near-field coupling of the nanoribbons) in the middle of the hBN Reststrahlen band, yielding a topological transition from hyperbolic to elliptical dispersion. We further visualize and characterize the spatial evolution of a deeply subwavelength canalization mode near the transition frequency, which is a collimated polariton that is the basis for hyperlensing and diffraction-less propagation.

The coherent light source is one of the most important foundations in both optical physics studies and applied photonic devices. However, the whispering gallery microcavity, as a prime platform for novel light sources, has the intrinsically chiral symmetry and severely rules out access to directional light output, all-optical flip-flops, efficient light extraction, etc. Here, we demonstrate a reconfigurable symmetry-broken microlaser in an ultrahigh-Q whispering gallery microcavity with the symmetric structure, in which a chirality of lasing field is empowered spontaneously by the optical nonlinear effect. Experimentally, the ratio of counter-propagating lasing intensities is found to exceed 160:1, and the chirality can be controlled dynamically and all-optically by the bias in the pump direction. This work not only presents a distinct recipe for coherent light sources with robust and reconfigurable performance, but also opens up an unexplored avenue to symmetry-broken physics in optical micro-structures.

The generation of anti-Stokes emission through lanthanide-doped upconversion nanoparticles is of great importance for technological applications in energy harvesting, bioimaging and optical cryptography 1-3 . However, the weak absorption and long radiative lifetimes of upconversion nanoparticles may significantly limit their use in imaging and labelling applications in which a fast spontaneous emission rate is essential 4-6 . Here, we report the direct observation of upconversion superburst with directional, fast and ultrabright luminescence by coupling gap plasmon modes to nanoparticle emitters. Through precise control over the nanoparticle's local density of state, we achieve emission amplification by four to five orders of magnitude and a 166-fold rate increase in spontaneous emission. We also demonstrate that tailoring the mode of the plasmonic cavity permits active control over the colour output of upconversion emission. These findings may benefit the future development of rapid nonlinear image scanning nanoscopy and open up the possibility of constructing high-frequency, single-photon emitters driven by telecommunication wavelengths.

Metasurfaces as artificially nanostructured interfaces hold significant potential for multi-functionality, which may play a pivotal role in the next-generation compact nano-devices. The majority of multi-tasked metasurfaces encode or encrypt multi-information either into the carefully tailored metasurfaces or in pre-set complex incident beam arrays. Here, we propose and demonstrate a multi-momentum transformation metasurface (i.e., meta-transformer), by fully synergizing intrinsic properties of light, e.g., orbital angular momentum (OAM) and linear momentum (LM), with a fixed phase profile imparted by a metasurface. The OAM meta-transformer reconstructs different topologically charged beams into on-axis distinct patterns in the same plane. The LM meta-transformer converts red, green and blue illuminations to the on-axis images of "R", "G" and "B" as well as vivid color holograms, respectively. Thanks to the infinite states of light-metasurface phase combinations, such ultra-compact meta-transformer has potential in information storage, nanophotonics, optical integration and optical encryption.

The coloration of some butterflies, Pachyrhynchus weevils, and many chameleons are notable examples of natural organisms employing photonic crystals to produce colorful patterns. Despite advances in nanotechnology, we still lack the ability to print arbitrary colors and shapes in all three dimensions at this microscopic length scale. Here, we introduce a heat-shrinking method to produce 3D-printed photonic crystals with a 5x reduction in lattice constants, achieving sub-100-nm features with a full range of colors. With these lattice structures as 3D color volumetric elements, we printed 3D microscopic scale objects, including the first multi-color microscopic model of the Eiffel Tower measuring only 39 µm tall with a color pixel size of 1.45 µm. The technology to print 3D structures in color at the microscopic scale promises the direct patterning and integration of spectrally selective devices, such as photonic crystal-based color filters, onto free-form optical elements and curved surfaces.