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.

Ultrathin carpet cloak enabled by infinitely anisotropic medium

Thanks to the pioneering studies conducted on the fields of transformation optics (TO) and metasurfaces, many unprecedented devices such as invisibility cloaks have been recently realized. However, each of these methods has some drawbacks limiting the applicability of the designed devices for real-life scenarios. For instance, TO studies lead to bulky coating layer with the thickness that is comparable to, or even larger than the dimension of the concealed object. In this paper, based on the coordinate transformation, an ultrathin carpet cloak is proposed to hide objects with arbitrary shape and size using a thin anisotropic material, called as infinitely anisotropic medium (IAM). It is shown that unlike the previous metasurface-based carpet cloaks, the proposed IAM hides objects from all viewing incident angles while it is extremely thin compared with the object dimensions. This material also circumvents the conventional transformation optics' complexities and could be easily implemented in practical scenarios. To demonstrate the capability of the proposed carpet cloak, several full-wave simulations are carried out. Finally, as a proof of concept, the IAM is implemented based on the effective medium theory which exhibits good agreement with the results obtained from the theoretical investigations. The introduced material not only constitutes a significant step towards the invisibility cloak but also can greatly promote the practical application of the other TO-based devices.

A new member of the structured light family: optical spatiotemporal vortices

The burgeoning growth of structured light has opened up new possibilities for harnessing the spatiotemporal coupling effects in light. Optical spatiotemporal vortices, as a subset of spatiotemporal light, have emerged as a focal point of recent research, owing to their distinctive characteristics and vast range for application. This unique structured light will endow photons with a new degree of freedom, promising to revolutionize researchers' understanding of photonics. Conducting thorough research on optical spatiotemporal vortices will establish a solid foundation for the development of innovative physical mechanisms and advanced applications in photonics.

Transformation-Optics-Designed Plasmonic Singularities for Efficient Photocatalytic Hydrogen Evolution at Metal/Semiconductor Interfaces

Inspired by transformation optics, we propose a new concept for plasmonic photocatalysis by creating a novel hybrid nanostructure with a plasmonic singularity. Our geometry enables broad and strong spectral light harvesting at the active site of a nearby semiconductor where the chemical reaction occurs. A proof-of-concept nanostructure comprising Cu₂ZnSnS₄ (CZTS) and Au-Au dimer (t-CZTS@Au-Au) is fabricated via a colloidal strategy combining templating and seeded growth. On the basis of numerical and experimental results of different related hybrid nanostructures, we show that both the sharpness of the singular feature and the relative position to the reactive site play a pivotal role in optimizing photocatalytic activity. Compared with bare CZTS, the hybrid nanostructure (t-CZTS@Au-Au) exhibits an enhancement of the photocatalytic hydrogen evolution rate by up to ∼9 times. The insights gained from this work might be beneficial for designing efficient composite plasmonic photocatalysts for diverse photocatalytic reactions.

Light People: Prof. Sir John Pendry, father of metamaterials, spoke about the future of meta

When consulting with the Marconi company in 1995, Prof. Sir John Pendry uncovered exotic structures that gave negative permittivity and negative permeability, respectively. In 1999, Prof. Pendry introduced split ring resonators (SRRs), and later in 2000, Prof. David Smith and Prof. Sheldon Schultz experimentally showed that periodic array of SRRs and continuous wires previously proposed by Prof. Pendry could exhibit simultaneously negative values of effective permeability and permittivity at the same frequency. Shortly after, Prof. Pendry revealed that a slab of material with simultaneous negative permittivity and permeability could challenge the Abbé diffraction limit on traditional lenses and focus all Fourier components of a point object onto a perfect image, leading to a "perfect lens". The vision of a perfect lens attracted extensive research interest and opened a new field which was later widely known as metamaterials. Now two decades on, the explosion of metamaterials has revolutionized numerous researches in physics, materials science, chemistry, and engineering. To shed light on the research direction of metamaterials, Light: Science & Applications invited Sir John Pendry, father and living legend of metamaterials, to speak about the future of metamaterials. The original interview can be accessed in Supplementary video.

On Transformation Form-Invariance in Thermal Convection

Over the past two decades, effective control of physical fields, such as light fields or acoustics fields, has greatly benefited from transforming media. One of these rapidly growing research areas is transformation thermotics, especially embodied in the thermal conductive and radiative modes. On the other hand, transformation media in thermal convection has seldom been studied due to the complicated governing equations involving both fluid motion and heat transfer terms. The difficulty lies in the robustness of form invariance in the Navier-Stokes equations or their simplified forms under coordinate transformations, which determines whether the transformation operations can be executed on thermal convection to simultaneously regulate the flow and thermal fields. In this work, we show that thermal convection in two-dimensional Hele-Shaw cells keeps form-invariance, while its counterpart in general creeping flows or general laminar flows does not. This conclusion is numerically verified by checking the performances of invisible devices made of transformation media in convective environments. We further exploit multilayered structures constituted of isotropic homogeneous natural materials to realize the anisotropic inhomogeneous properties required for transformation media. Our results clarify the long-term confusion about the validation of the transformation method in thermal convection and provide a rigorous foundation and classical paradigm on inspiring various fascinating metadevices in both thermal and flow fields.

Quasioptics for increasing the beam efficiency of wireless power transfer systems

The highest beam efficiency in a wireless power transfer (WPT) system that uses focusing components was 51%, using a [Formula: see text] diameter reflector for a transfer distance of [Formula: see text]. We have beaten that record, and present here a system that surpasses it by 25%. Using the quasioptical framework for reducing spillover losses in WPT, we present a double-reflector system that achieved a higher beam efficiency than the state-of-the-art. The transmitting and receiving antennas were 3D-printed conical smooth-walled horn antennas, specially designed for this purpose. The theoretical analysis enabled the design of a [Formula: see text] system, whose energy focus location has been experimentally verified. Then, the complete system was experimented upon, enabling a high beam transfer efficiency of 63.75%. Additionally, the advantage of using quasioptics in radiative wireless power transfer applications is discussed, as well as the sensitivity of its systems. Finally, a comparison with the state-of-the-art is done by the proposal of new figures-of-merit, relating the systems' physical dimensions and beam efficiency. This research is a paradigm shift by presenting a promising path for future WPT research through quasioptics, whose high efficiencies may enable commercial applications of this technology for solving power supply issues in our society.

Optical clearing of the mouse skull

High spatial resolution imaging of the mouse brain through the intact skull is challenging because of the skull-induced aberration and scattering. The research group of Dan Zhu from Huazhong University of Science and Technology has developed a skull-clearing technique that provides a long-term (~ weeks), stable, transparent window for high resolution optical imaging over a large field of view.

A multichannel optical computing architecture for advanced machine vision

Endowed with the superior computing speed and energy efficiency, optical neural networks (ONNs) have attracted ever-growing attention in recent years. Existing optical computing architectures are mainly single-channel due to the lack of advanced optical connection and interaction operators, solving simple tasks such as hand-written digit classification, saliency detection, etc. The limited computing capacity and scalability of single-channel ONNs restrict the optical implementation of advanced machine vision. Herein, we develop Monet: a multichannel optical neural network architecture for a universal multiple-input multiple-channel optical computing based on a novel projection-interference-prediction framework where the inter- and intra- channel connections are mapped to optical interference and diffraction. In our Monet, optical interference patterns are generated by projecting and interfering the multichannel inputs in a shared domain. These patterns encoding the correspondences together with feature embeddings are iteratively produced through the projection-interference process to predict the final output optically. For the first time, Monet validates that multichannel processing properties can be optically implemented with high-efficiency, enabling real-world intelligent multichannel-processing tasks solved via optical computing, including 3D/motion detections. Extensive experiments on different scenarios demonstrate the effectiveness of Monet in handling advanced machine vision tasks with comparative accuracy as the electronic counterparts yet achieving a ten-fold improvement in computing efficiency. For intelligent computing, the trends of dealing with real-world advanced tasks are irreversible. Breaking the capacity and scalability limitations of single-channel ONN and further exploring the multichannel processing potential of wave optics, we anticipate that the proposed technique will accelerate the development of more powerful optical AI as critical support for modern advanced machine vision.

Bound vortex light in an emulated topological defect in photonic lattices

Topology have prevailed in a variety of branches of physics. And topological defects in cosmology are speculated akin to dislocation or disclination in solids or liquid crystals. With the development of classical and quantum simulation, such speculative topological defects are well-emulated in a variety of condensed matter systems. Especially, the underlying theoretical foundations can be extensively applied to realize novel optical applications. Here, with the aid of transformation optics, we experimentally demonstrated bound vortex light on optical chips by simulating gauge fields of topological linear defects in cosmology through position-dependent coupling coefficients in a deformed photonic graphene. Furthermore, these types of photonic lattices inspired by topological linear defects can simultaneously generate and transport optical vortices, and even can control the orbital angular momentum of photons on integrated optical chips.

Polarization multiplexed diffractive computing: all-optical implementation of a group of linear transformations through a polarization-encoded diffractive network

Research on optical computing has recently attracted significant attention due to the transformative advances in machine learning. Among different approaches, diffractive optical networks composed of spatially-engineered transmissive surfaces have been demonstrated for all-optical statistical inference and performing arbitrary linear transformations using passive, free-space optical layers. Here, we introduce a polarization-multiplexed diffractive processor to all-optically perform multiple, arbitrarily-selected linear transformations through a single diffractive network trained using deep learning. In this framework, an array of pre-selected linear polarizers is positioned between trainable transmissive diffractive materials that are isotropic, and different target linear transformations (complex-valued) are uniquely assigned to different combinations of input/output polarization states. The transmission layers of this polarization-multiplexed diffractive network are trained and optimized via deep learning and error-backpropagation by using thousands of examples of the input/output fields corresponding to each one of the complex-valued linear transformations assigned to different input/output polarization combinations. Our results and analysis reveal that a single diffractive network can successfully approximate and all-optically implement a group of arbitrarily-selected target transformations with a negligible error when the number of trainable diffractive features/neurons (N) approaches [Formula: see text], where N_i and N_o represent the number of pixels at the input and output fields-of-view, respectively, and N_p refers to the number of unique linear transformations assigned to different input/output polarization combinations. This polarization-multiplexed all-optical diffractive processor can find various applications in optical computing and polarization-based machine vision tasks.

Classification and reconstruction of spatially overlapping phase images using diffractive optical networks

Diffractive optical networks unify wave optics and deep learning to all-optically compute a given machine learning or computational imaging task as the light propagates from the input to the output plane. Here, we report the design of diffractive optical networks for the classification and reconstruction of spatially overlapping, phase-encoded objects. When two different phase-only objects spatially overlap, the individual object functions are perturbed since their phase patterns are summed up. The retrieval of the underlying phase images from solely the overlapping phase distribution presents a challenging problem, the solution of which is generally not unique. We show that through a task-specific training process, passive diffractive optical networks composed of successive transmissive layers can all-optically and simultaneously classify two different randomly-selected, spatially overlapping phase images at the input. After trained with ~ 550 million unique combinations of phase-encoded handwritten digits from the MNIST dataset, our blind testing results reveal that the diffractive optical network achieves an accuracy of > 85.8% for all-optical classification of two overlapping phase images of new handwritten digits. In addition to all-optical classification of overlapping phase objects, we also demonstrate the reconstruction of these phase images based on a shallow electronic neural network that uses the highly compressed output of the diffractive optical network as its input (with e.g., ~ 20-65 times less number of pixels) to rapidly reconstruct both of the phase images, despite their spatial overlap and related phase ambiguity. The presented phase image classification and reconstruction framework might find applications in e.g., computational imaging, microscopy and quantitative phase imaging fields.

Light chaotic dynamics in the transformation from curved to flat surfaces

Exploring light dynamics and chaos on curved surfaces is one of the new challenges met in modern cosmology. To address this question and investigate chaotic dynamics of light on three-dimensional curved surfaces, we consider their connection under a conformal transformation with flat billiards with spatially varying refractive index. Through this connection, we demonstrate that these two systems share the same dynamics; the complexity of the problem simplifies, and well-known tools originating from chaos analysis in planar billiards can be used to explore chaotic dynamics on curved space. We discover that the degree of chaos is fully controlled by a single curvature-related geometrical parameter, providing a degree of freedom in chaos engineering, as well as potentialities to design nonuniform table billiards/cavities/resonators.

Light propagation on a two-dimensional curved surface embedded in a three-dimensional space has attracted increasing attention as an analog model of four-dimensional curved spacetime in the laboratory. Despite recent developments in modern cosmology on the dynamics and evolution of the universe, investigation of nonlinear dynamics of light on non-Euclidean geometry is still scarce, with fundamental questions, such as the effect of curvature on deterministic chaos, challenging to address. Here, we study classical and wave chaotic dynamics on a family of surfaces of revolution by considering its equivalent conformally transformed flat billiard, with nonuniform distribution of the refractive index. We prove rigorously that these two systems share the same dynamics. By exploring the Poincaré surface of section, the Lyapunov exponent, and the statistics of eigenmodes and eigenfrequency spectrum in the transformed inhomogeneous table billiard, we find that the degree of chaos is fully controlled by a single, curvature-related geometric parameter of the curved surface. A simple interpretation of our findings in transformed billiards, the “fictitious force,” allows us to extend our prediction to other classes of curved surfaces. This powerful analogy between two a priori unrelated systems not only brings forward an approach to control the degree of chaos, but also provides potentialities for further studies and applications in various fields, such as billiards design, optical fibers, or laser microcavities.

Hyperbolic optics and superlensing in room-temperature KTN from self-induced k-space topological transitions

A hyperbolic medium will transfer super-resolved optical waveforms with no distortion, support negative refraction, superlensing, and harbor nontrivial topological photonic phases. Evidence of hyperbolic effects is found in periodic and resonant systems for weakly diffracting beams, in metasurfaces, and even naturally in layered systems. At present, an actual hyperbolic propagation requires the use of metamaterials, a solution that is accompanied by constraints on wavelength, geometry, and considerable losses. We show how nonlinearity can transform a bulk KTN perovskite into a broadband 3D hyperbolic substance for visible light, manifesting negative refraction and superlensing at room-temperature. The phenomenon is a consequence of giant electro-optic response to the electric field generated by the thermal diffusion of photogenerated charges. Results open new scenarios in the exploration of enhanced light-matter interaction and in the design of broadband photonic devices.

Transformation Metamaterials

Based on the form-invariance of Maxwell's equations under coordinate transformations, mathematically smooth deformation of space can be physically equivalent to inhomogeneous and anisotropic electromagnetic (EM) medium (called a transformation medium). It provides a geometric recipe to control EM waves at will. A series of examples of achieving transformation media by artificially structured units from conventional materials is summarized here. Such concepts are firstly implemented for EM waves, and then extended to other wave dynamics, such as elastic waves, acoustic waves, surface water waves, and even stationary fields. These shall be cataloged as transformation metamaterials. In addition, it might be conceptually attractive and practically useful to control diverse waves for multi-physics designs.

Revealing topology with transformation optics

Symmetry deepens our insight into a physical system and its interplay with topology enables the discovery of topological phases. Symmetry analysis is conventionally performed either in the physical space of interest, or in the corresponding reciprocal space. Here we borrow the concept of virtual space from transformation optics to demonstrate how a certain class of symmetries can be visualised in a transformed, spectrally related coordinate space, illuminating the underlying topological transitions. By projecting a plasmonic system in a higher-dimensional virtual space onto a lower-dimensional system in real space, we show how transformation optics allows us to construct a topologically non-trivial system by inspecting its modes in the virtual space. Interestingly, we find that the topological invariant can be controlled via the singularities in the conformal mapping, enabling the intuitive engineering of edge states. The confluence of transformation optics and topology here can be generalized to other wave realms beyond photonics.

Optical meta-waveguides for integrated photonics and beyond

The growing maturity of nanofabrication has ushered massive sophisticated optical structures available on a photonic chip. The integration of subwavelength-structured metasurfaces and metamaterials on the canonical building block of optical waveguides is gradually reshaping the landscape of photonic integrated circuits, giving rise to numerous meta-waveguides with unprecedented strength in controlling guided electromagnetic waves. Here, we review recent advances in meta-structured waveguides that synergize various functional subwavelength photonic architectures with diverse waveguide platforms, such as dielectric or plasmonic waveguides and optical fibers. Foundational results and representative applications are comprehensively summarized. Brief physical models with explicit design tutorials, either physical intuition-based design methods or computer algorithms-based inverse designs, are cataloged as well. We highlight how meta-optics can infuse new degrees of freedom to waveguide-based devices and systems, by enhancing light-matter interaction strength to drastically boost device performance, or offering a versatile designer media for manipulating light in nanoscale to enable novel functionalities. We further discuss current challenges and outline emerging opportunities of this vibrant field for various applications in photonic integrated circuits, biomedical sensing, artificial intelligence and beyond.

All-optical synthesis of an arbitrary linear transformation using diffractive surfaces

Spatially-engineered diffractive surfaces have emerged as a powerful framework to control light-matter interactions for statistical inference and the design of task-specific optical components. Here, we report the design of diffractive surfaces to all-optically perform arbitrary complex-valued linear transformations between an input (N_i) and output (N_o), where N_i and N_o represent the number of pixels at the input and output fields-of-view (FOVs), respectively. First, we consider a single diffractive surface and use a matrix pseudoinverse-based method to determine the complex-valued transmission coefficients of the diffractive features/neurons to all-optically perform a desired/target linear transformation. In addition to this data-free design approach, we also consider a deep learning-based design method to optimize the transmission coefficients of diffractive surfaces by using examples of input/output fields corresponding to the target transformation. We compared the all-optical transformation errors and diffraction efficiencies achieved using data-free designs as well as data-driven (deep learning-based) diffractive designs to all-optically perform (i) arbitrarily-chosen complex-valued transformations including unitary, nonunitary, and noninvertible transforms, (ii) 2D discrete Fourier transformation, (iii) arbitrary 2D permutation operations, and (iv) high-pass filtered coherent imaging. Our analyses reveal that if the total number (N) of spatially-engineered diffractive features/neurons is ≥N_i × N_o, both design methods succeed in all-optical implementation of the target transformation, achieving negligible error. However, compared to data-free designs, deep learning-based diffractive designs are found to achieve significantly larger diffraction efficiencies for a given N and their all-optical transformations are more accurate for N < N_i × N_o. These conclusions are generally applicable to various optical processors that employ spatially-engineered diffractive surfaces.

Full-duplex reflective beamsteering metasurface featuring magnetless nonreciprocal amplification

Nonreciprocal radiation refers to electromagnetic wave radiation in which a structure provides different responses under the change of the direction of the incident field. Modern wireless telecommunication systems demand versatile apparatuses which are capable of full-duplex nonreciprocal wave processing and amplification, especially in the reflective state. To realize such a functionality, we propose an architecture in which a chain of series cascaded radiating patches are integrated with nonreciprocal phase shifters, providing an original and efficient apparatus for full-duplex reflective beamsteering. Such an ultrathin reflective metasurface can provide directive and diverse radiation beams, large wave amplification, steerable beams by simply changing the bias of the gradient active nonmagnetic nonreciprocal phase shifters, and is immune to undesired time harmonics. Having accomplished all these functionalities in the reflective state, the metasurface represents a conspicuous apparatus for efficient, controllable and programmable wave engineering.

Ultrathin Conformal Magnetic Invisible Cloak for Irregular Objects

Magnetic invisible cloaking has been previously demonstrated but only limited to objects with rotational geometries either in spherical or cylindrical shapes, for which the classic analytical bilayer scheme could be strictly applied to design the hiding coat. In this work, we show that a quasi-static cloaking effect could be achieved for irregular objects, e.g., metals with sharp edges, using a numerical optimization scheme. In the quasi-static limit, it is unambiguously proved that the disturbance of the irregular geometries could be well compensated by the inhomogeneous distribution of the soft ferromagnetic (FM) layer either in permeability values or in shapes under the framework of a bilayer cloak. An FM mesh coat with a constant thickness of 0.5 mm was successfully engineered to meet the specific requirements. Experimentally, good cloaking performance with a field disturbance of less than 0.5% has been achieved for a 2 × 2 × 5 cm³ brass bar in a wide frequency range from ∼10 to 250 kHz. A commercial metal scanner was also applied to verify the practical potential. The general strategy to hide almost arbitrary objects was discussed in the end. In principle, the numerical conformal coat engineered by the composite material proposed here could be broadly extended for objects with various geometries.

Programmable nonreciprocal meta-prism

Optical prisms are made of glass and map temporal frequencies into spatial frequencies by decomposing incident white light into its constituent colors and refract them into different directions. Conventional prisms suffer from their volumetric bulky and heavy structure and their material parameters are dictated by the Lorentz reciprocity theorem. Considering various applications of prisms in wave engineering and their growing applications in the invisible spectrum and antenna applications, there is a demand for compact apparatuses that are capable of providing prism functionality in a reconfigurable manner, with a nonreciprocal/reciprocal response. Here, we propose a nonreciprocal metasurface-based prism constituted of an array of phase- and amplitude-gradient frequency-dependent spatially variant radiating super-cells. In conventional optical prisms, nonreciprocal devices and metamaterials, the spatial decomposition and nonreciprocity functions are fixed and noneditable. Here, we present a programmable metasurface integrated with amplifiers to realize controllable nonreciprocal spatial decomposition, where each frequency component of the incident polychromatic wave can be transmitted under an arbitrary and programmable angle of transmission with a desired transmission gain. Such a polychromatic metasurface prism is constituted of frequency-dependent spatially variant transistor-based phase shifters and amplifiers for the spatial decomposition of the wave components. Interesting features include three-dimensional prism functionality with programmable angles of refraction, power amplification, and directive and diverse radiation beams. Furthermore, the metasurface prism can be digitally controlled via a field- programmable gate array (FPGA), making the metasurface a suitable solution for radars, holography applications, and wireless telecommunication systems.

High-performance quasi-2D perovskite light-emitting diodes: from materials to devices

Quasi-two-dimensional (quasi-2D) perovskites have attracted extraordinary attention due to their superior semiconducting properties and have emerged as one of the most promising materials for next-generation light-emitting diodes (LEDs). The outstanding optical properties originate from their structural characteristics. In particular, the inherent quantum-well structure endows them with a large exciton binding energy due to the strong dielectric- and quantum-confinement effects; the corresponding energy transfer among different n-value species thus results in high photoluminescence quantum yields (PLQYs), particularly at low excitation intensities. The review herein presents an overview of the inherent properties of quasi-2D perovskite materials, the corresponding energy transfer and spectral tunability methodologies for thin films, as well as their application in high-performance LEDs. We then summarize the challenges and potential research directions towards developing high-performance and stable quasi-2D PeLEDs. The review thus provides a systematic and timely summary for the community to deepen the understanding of quasi-2D perovskite materials and resulting LED devices.

Ultrahigh numerical aperture meta-fibre for flexible optical trapping

Strong focusing on diffraction-limited spots is essential for many photonic applications and is particularly relevant for optical trapping; however, all currently used approaches fail to simultaneously provide flexible transportation of light, straightforward implementation, compatibility with waveguide circuitry, and strong focusing. Here, we demonstrate the design and 3D nanoprinting of an ultrahigh numerical aperture meta-fibre for highly flexible optical trapping. Taking into account the peculiarities of the fibre environment, we implemented an ultrathin meta-lens on the facet of a modified single-mode optical fibre via direct laser writing, leading to a diffraction-limited focal spot with a record-high numerical aperture of up to NA ≈ 0.9. The unique capabilities of this flexible, cost-effective, bio- and fibre-circuitry-compatible meta-fibre device were demonstrated by optically trapping microbeads and bacteria for the first time with only one single-mode fibre in combination with diffractive optics. Our study highlights the relevance of the unexplored but exciting field of meta-fibre optics to a multitude of fields, such as bioanalytics, quantum technology and life sciences.

All-optical information-processing capacity of diffractive surfaces

The precise engineering of materials and surfaces has been at the heart of some of the recent advances in optics and photonics. These advances related to the engineering of materials with new functionalities have also opened up exciting avenues for designing trainable surfaces that can perform computation and machine-learning tasks through light-matter interactions and diffraction. Here, we analyze the information-processing capacity of coherent optical networks formed by diffractive surfaces that are trained to perform an all-optical computational task between a given input and output field-of-view. We show that the dimensionality of the all-optical solution space covering the complex-valued transformations between the input and output fields-of-view is linearly proportional to the number of diffractive surfaces within the optical network, up to a limit that is dictated by the extent of the input and output fields-of-view. Deeper diffractive networks that are composed of larger numbers of trainable surfaces can cover a higher-dimensional subspace of the complex-valued linear transformations between a larger input field-of-view and a larger output field-of-view and exhibit depth advantages in terms of their statistical inference, learning, and generalization capabilities for different image classification tasks when compared with a single trainable diffractive surface. These analyses and conclusions are broadly applicable to various forms of diffractive surfaces, including, e.g., plasmonic and/or dielectric-based metasurfaces and flat optics, which can be used to form all-optical processors.

Unitary transformation for Poincaré beams on different parts of Poincaré sphere

We construct an experimental setup, consisting of conical refraction transformation in two biaxial cascade crystals and 4f-system, to realize Unitary transformation of light beam and the manipulation of Poincaré beams on the different parts of Poincaré sphere. The spatial structure of the polarization can be controlled by changing the polarization of the incident beam or rotating the angle between these two crystals. The beams with different SoPs covering the full-Poincaré sphere, part-Poincaré sphere and one point on the sphere are generated for the different angles between crystals. The Unitary transformation of light beam is proposed in the experiment with the invariant intensity distribution. Subsequently, the spin angular momentum is derived from the distribution of polarization measured in our experiment. Moreover, the conversion between orbital angular momentum and spin angular momentum of light beam is obtained by changing the angle between crystals. And the conversion progress can also be influenced by the polarization of incident beam. We realized the continuous control of the spatial structure of the angular momentum density, which has potential in the manipulation of optical trapping systems and polarization-multiplexed free-space optical communication.

3D-Printing for Transformation Optics in Electromagnetic High-Frequency Lens Applications

This article presents the design, construction and analysis of a 3D-printed transformed hyperbolic flat lens working on the 30 GHz band. The transformed lens was printed using only one ABS dielectric filament of relative permittivity of 12, varying the infill percentage of each transformed lens section in order to achieve the permittivity values obtained with the transformation optics. The 3D-printed hyperbolic transformed lens exhibits good radiation performance compared to the original canonical lens.

Hybridization of singular plasmons via transformation optics

Surface plasmon resonances of metallic nanostructures offer great opportunities to guide and manipulate light on the nanoscale. In the design of novel plasmonic devices, a central topic is to clarify the intricate relationship between the resonance spectrum and the geometry of the nanostructure. Despite many advances, the design becomes quite challenging when the desired spectrum is highly complex. Here we develop a theoretical model for surface plasmons of interacting nanoparticles to reduce the complexity of the design process significantly. Our model is developed by combining plasmon hybridization theory with transformation optics, which yields an efficient way of simultaneously controlling both global and local features of the resonance spectrum. As an application, we propose a design of metasurface whose absorption spectrum can be controlled over a large class of complex patterns through only a few geometric parameters in an intuitive way. Our approach provides fundamental tools for the effective design of plasmonic metamaterials with on-demand functionality.

A Magnifying Glass for Virtual Imaging of Subwavelength Resolution by Transformation Optics

Traditional magnifying glasses can give magnified virtual images with diffraction-limited resolution, that is, detailed information is lost. Here, a novel magnifying glass by transformation optics, referred to as a "superresolution magnifying glass" (SMG) is designed, which can produce magnified virtual images with a predetermined magnification factor and resolve subwavelength details (i.e., light sources with subwavelength distances can be resolved). Based on theoretical calculations and reductions, a metallic plate structure to produce the reduced SMG in microwave frequencies, which gives good performance verified by both numerical simulations and experimental results, is proposed and realized. The function of SMG is to create a superresolution virtual image, unlike traditional superresolution imaging devices that create real images. The proposed SMG will create a new branch of superresolution imaging technology.

3D Visible-Light Invisibility Cloak

The concept of an invisibility cloak is a fixture of science fiction, fantasy, and the collective imagination. However, a real device that can hide an object from sight in visible light from absolutely any viewpoint would be extremely challenging to build. The main obstacle to creating such a cloak is the coupling of the electromagnetic components of light, which would necessitate the use of complex materials with specific permittivity and permeability tensors. Previous cloaking solutions have involved circumventing this obstacle by functioning either in static (or quasistatic) fields where these electromagnetic components are uncoupled or in diffusive light scattering media where complex materials are not required. In this paper, concealing a large-scale spherical object from human sight from three orthogonal directions is reported. This result is achieved by developing a 3D homogeneous polyhedral transformation and a spatially invariant refractive index discretization that considerably reduce the coupling of the electromagnetic components of visible light. This approach allows for a major simplification in the design of 3D invisibility cloaks, which can now be created at a large scale using homogeneous and isotropic materials.

Directed Thermal Diffusions through Metamaterial Source Illusion with Homogeneous Natural Media

Owing to the utilization of transformation optics, many significant research and development achievements have expanded the applications of illusion devices into thermal fields. However, most of the current studies on relevant thermal illusions used to reshape the thermal fields are dependent of certain pre-designed geometric profiles with complicated conductivity configurations. In this paper, we propose a methodology for designing a new class of thermal source illusion devices for achieving directed thermal diffusions with natural homogeneous media. The employments of the space rotations in the linear transformation processes allow the directed thermal diffusions to be independent of the geometric profiles, and the utilization of natural homogeneous media improve the feasibility. Four schemes, with fewer types of homogeneous media filling the functional regions, are demonstrated in transient states. The expected performances are observed in each scheme. The related performance are analyzed by comparing the thermal distribution characteristics and the illusion effectiveness on the measured lines. The findings obtained in this paper see applications in the development of directed diffusions with minimal thermal loss, used in novel “multi-beam” thermal generation, thermal lenses, solar receivers, and waveguide.

Porous Silicon Gradient Refractive Index Micro-Optics

The emergence and growth of transformation optics over the past decade has revitalized interest in how a gradient refractive index (GRIN) can be used to control light propagation. Two-dimensional demonstrations with lithographically defined silicon (Si) have displayed the power of GRIN optics and also represent a promising opportunity for integrating compact optical elements within Si photonic integrated circuits. Here, we demonstrate the fabrication of three-dimensional Si-based GRIN micro-optics through the shape-defined formation of porous Si (PSi). Conventional microfabrication creates Si square microcolumns (SMCs) that can be electrochemically etched into PSi elements with nanoscale porosity along the shape-defined etching pathway, which imparts the geometry with structural birefringence. Free-space characterization of the transmitted intensity distribution through a homogeneously etched PSi SMC exhibits polarization splitting behavior resembling that of dielectric metasurfaces that require considerably more laborious fabrication. Coupled birefringence/GRIN effects are studied by way of PSi SMCs etched with a linear (increasing from edge to center) GRIN profile. The transmitted intensity distribution shows polarization-selective focusing behavior with one polarization focused to a diffraction-limited spot and the orthogonal polarization focused into two laterally displaced foci. Optical thickness-based analysis readily predicts the experimentally observed phenomena, which strongly match finite-element electromagnetic simulations.

Concealing arbitrary objects remotely with multi-folded transformation optics

An invisibility cloak that can hide an arbitrary object external to the cloak itself has not been devised before. In this Letter, we introduce a novel way to design a remote cloaking device that makes any object located at a certain distance invisible. This is accomplished using multi-folded transformation optics to remotely generate a hidden region around the object that no field can penetrate and that does not disturb the far-field scattering electromagnetic field. As a result, any object in the hidden region can stay in position or move freely within that region and remain invisible. Our idea is further extended in order to design a remote illusion optics that can transform any arbitrary object into another one. Unlike other cloaking methods, this method would require no knowledge of the details of the object itself. The proposed multi-folded transformation optics will be crucial in the design of remote devices in a variety of contexts.

Transformation Optics: A Time- and Frequency-Domain Analysis of Electron-Energy Loss Spectroscopy

Electron energy loss spectroscopy (EELS) and cathodoluminescence (CL) play a pivotal role in many of the cutting edge experiments in plasmonics. EELS and CL experiments are usually supported by numerical simulations, which-though accurate-may not provide as much physical insight as analytical calculations do. Fully analytical solutions to EELS and CL systems in plasmonics are rare and difficult to obtain. This paper aims to narrow this gap by introducing a new method based on transformation optics that allows to calculate the quasistatic frequency- and time-domain response of plasmonic particles under electron beam excitation. We study a nonconcentric annulus (and ellipse in the Supporting Information ) as an example.

Shaping 3D Path of Electromagnetic Waves Using Gradient-Refractive-Index Metamaterials

An all-dielectric semispherical lens with functions in shaping 3D wave-propagation paths is proposed and experimentally verified. When radiation sources are placed in the central region, the lens behaves as a magnifying device to resolve the sources in subwavelength scale; while when the electromagnetic waves impinge on the semispherical lens from outside, they will be guided spirally inward.

Graphene as a Tunable Anisotropic or Isotropic Plasmonic Metasurface

We demonstrate a tunable plasmonic metasurface by considering a graphene sheet subject to a periodically patterned doping level. The unique optical properties of graphene result in electrically tunable plasmons that allow for extreme confinement of electromagnetic energy in the technologically significant regime of THz frequencies. Here, we add an extra degree of freedom by using graphene as a metasurface, proposing to dope it with an electrical gate patterned in the micron or submicron scale. By extracting the effective conductivity of the sheet, we characterize metasurfaces periodically modulated along one or two directions. In the first case, and making use of the analytical insight provided by transformation optics, we show an efficient control of THz radiation for one polarization. In the second case, we demonstrate a metasurface with an isotropic response that is independent of wave polarization and orientation.

A Phase-Shifting Method for Improving the Heating Uniformity of Microwave Processing Materials

Microwave processing of materials has been found to deliver enormous advantages over conventional processing methods in terms of mechanical and physical properties of the materials. However, the non-uniform temperature distribution is the key problem of microwave processing, which is related to the structure of the cavity, and the placement and physical parameters of the material. In this paper, a new microwave cavity structure with a sliding short based on phase-shifting heating is creatively proposed to improve the temperature uniformity. An electronic mathematical model based on the Finite Element Method (FEM) is built to predict the temperature distribution. Meanwhile, a new computational approach based on the theory of transformation optics is first provided to solve the problem of the moving boundary in the model simulation. At first, the experiment is carried out to validate the model, and heating results from the experiment show good agreement with the model’s prediction. Based on the verified model, materials selected among a wide range of dielectric constants are treated by stationary heating and phase-shifting heating. The coefficient of variation (COV) of the temperature and temperature difference has been compared in detail between stationary heating and phase-shifting heating. A significant improvement in heating uniformity can be seen from the temperature distribution for most of the materials. Furthermore, three other materials are also treated at high temperature and the heating uniformity is also improved. Briefly, the strategy of phase-shifting heating plays a significant role in solve the problem of non-uniform heating in microwave-based material processing. A 25%–58% increase in uniformity from adapting the phase-shifting method can be observed for the microwave-processed materials.

Spatially variant periodic structures in electromagnetics

Spatial transforms are a popular technique for designing periodic structures that are macroscopically inhomogeneous. The structures are often required to be anisotropic, provide a magnetic response, and to have extreme values for the constitutive parameters in Maxwell's equations. Metamaterials and photonic crystals are capable of providing these, although sometimes only approximately. The problem still remains about how to generate the geometry of the final lattice when it is functionally graded, or spatially varied. This paper describes a simple numerical technique to spatially vary any periodic structure while minimizing deformations to the unit cells that would weaken or destroy the electromagnetic properties. New developments in this algorithm are disclosed that increase efficiency, improve the quality of the lattices and provide the ability to design aplanatic metasurfaces. The ability to spatially vary a lattice in this manner enables new design paradigms that are not possible using spatial transforms, three of which are discussed here. First, spatially variant self-collimating photonic crystals are shown to flow unguided waves around very tight bends using ordinary materials with low refractive index. Second, multi-mode waveguides in spatially variant band gap materials are shown to guide waves around bends without mixing power between the modes. Third, spatially variant anisotropic materials are shown to sculpt the near-field around electric components. This can be used to improve electromagnetic compatibility between components in close proximity.

On cosmology in the laboratory

In transformation optics, ideas from general relativity have been put to practical use for engineering problems. This article asks the question how this debt can be repaid. In discussing a series of recent laboratory experiments, it shows how insights from wave phenomena shed light on the quantum physics of the event horizon.

Manufacture of electrical and magnetic graded and anisotropic materials for novel manipulations of microwaves

Spatial transformations (ST) provide a design framework to generate a required spatial distribution of electrical and magnetic properties of materials to effect manipulations of electromagnetic waves. To obtain the electromagnetic properties required by these designs, the most common materials approach has involved periodic arrays of metal-containing subwavelength elements. While aspects of ST theory have been confirmed using these structures, they are often disadvantaged by narrowband operation, high losses and difficulties in implementation. An all-dielectric approach involves weaker interactions with applied fields, but may offer more flexibility for practical implementation. This paper investigates manufacturing approaches to produce composite materials that may be conveniently arranged spatially, according to ST-based designs. A key aim is to highlight the limitations and possibilities of various manufacturing approaches, to constrain designs to those that may be achievable. The article focuses on polymer-based nano- and microcomposites in which interactions with microwaves are achieved by loading the polymers with high-permittivity and high-permeability particles, and manufacturing approaches based on spray deposition, extrusion, casting and additive manufacture.

Broadband surface-wave transformation cloak

Guiding surface electromagnetic waves around disorder without disturbing the wave amplitude or phase is in great demand for modern photonic and plasmonic devices, but is fundamentally difficult to realize because light momentum must be conserved in a scattering event. A partial realization has been achieved by exploiting topological electromagnetic surface states, but this approach is limited to narrow-band light transmission and subject to phase disturbances in the presence of disorder. Recent advances in transformation optics apply principles of general relativity to curve the space for light, allowing one to match the momentum and phase of light around any disorder as if that disorder were not there. This feature has been exploited in the development of invisibility cloaks. An ideal invisibility cloak, however, would require the phase velocity of light being guided around the cloaked object to exceed the vacuum speed of light--a feat potentially achievable only over an extremely narrow band. In this work, we theoretically and experimentally show that the bottlenecks encountered in previous studies can be overcome. We introduce a class of cloaks capable of remarkable broadband surface electromagnetic waves guidance around ultrasharp corners and bumps with no perceptible changes in amplitude and phase. These cloaks consist of specifically designed nonmagnetic metamaterials and achieve nearly ideal transmission efficiency over a broadband frequency range from 0(+) to 6 GHz. This work provides strong support for the application of transformation optics to plasmonic circuits and could pave the way toward high-performance, large-scale integrated photonic circuits.

van der Waals interactions at the nanoscale: the effects of nonlocality

Calculated using classical electromagnetism, the van der Waals force increases without limit as two surfaces approach. In reality, the force saturates because the electrons cannot respond to fields of very short wavelength: polarization charges are always smeared out to some degree and in consequence the response is nonlocal. Nonlocality also plays an important role in the optical spectrum and distribution of the modes but introduces complexity into calculations, hindering an analytical solution for interactions at the nanometer scale. Here, taking as an example the case of two touching nanospheres, we show for the first time, to our knowledge, that nonlocality in 3D plasmonic systems can be accurately analyzed using the transformation optics approach. The effects of nonlocality are found to dramatically weaken the field enhancement between the spheres and hence the van der Waals interaction and to modify the spectral shifts of plasmon modes.

Full control and manipulation of heat signatures: cloaking, camouflage and thermal metamaterials

Thermal camouflage and cloaking can transform an actual heat signature into a pre-controlled one. A viable recipe for controlling and manipulating heat signatures using thermal metamaterials to empower cloaking and camouflage in heat conduction is demonstrated. The thermal signature of the object is thus metamorphosed and perceived as multiple targets with different geometries and compositions, with the original object cloaked.

Broadband all-dielectric magnifying lens for far-field high-resolution imaging

A transformation-optics magnifying lens is reported in the microwave frequency, which is made of inhomogeneous but isotropic dielectrics to reach impedance matching. The authors demonstrate the broadband subwavelength imaging performance and magnification factor experimentally from the far-field radiation patterns.

Broadband wide angle lens implemented with dielectric metamaterials

The Luneburg lens is a powerful imaging device, exhibiting aberration free focusing for parallel rays incident from any direction. However, its advantages are offset by a focal surface that is spherical and thus difficult to integrate with standard planar detector and emitter arrays. Using the recently developed technique of transformation optics, it is possible to transform the curved focal surface to a flat plane while maintaining the perfect focusing behavior of the Luneburg over a wide field of view. Here we apply these techniques to a lesser-known refractive Luneburg lens and implement the design with a metamaterial composed of a semi-crystalline distribution of holes drilled in a dielectric. In addition, we investigate the aberrations introduced by various approximations made in the implementation of the lens. The resulting design approach has improved mechanical strength with small aberrations and is ideally suited to implementation at infrared and visible wavelengths.

Broadband Transformation Optics Devices

Recently we have suggested that two-dimensional broadband transformation optics devices based on metamaterial designs may be built using tapered waveguides. Here we review application of this principle to broadband electromagnetic cloaking, trapped rainbow, and novel microscopy devices.