Experimental demonstration of a bilayer thermal cloak

Analytical realization of complex thermal meta-devices

Fourier's law dictates that heat flows from warm to cold. Nevertheless, devices can be tailored to cloak obstacles or even reverse the heat flow. Mathematical transformation yields closed-form equations for graded, highly anisotropic thermal metamaterial distributions needed for obtaining such functionalities. For simple geometries, devices can be realized by regular conductor distributions; however, for complex geometries, physical realizations have so far been challenging, and sub-optimal solutions have been obtained by expensive numerical approaches. Here we suggest a straightforward and highly efficient analytical de-homogenization approach that uses optimal multi-rank laminates to provide closed-form solutions for any imaginable thermal manipulation device. We create thermal cloaks, rotators, and concentrators in complex domains with close-to-optimal performance and esthetic elegance. The devices are fabricated using metal 3D printing, and their omnidirectional thermal functionalities are investigated numerically and validated experimentally. The analytical approach enables next-generation free-form thermal meta-devices with efficient synthesis, near-optimal performance, and concise patterns.

Natural tristability of a confined helical filament with anisotropic bending rigidities

We find that whenc 0 R ∼ 0.5 andτ 0 R < 0.11 < c 0 R , confining a helical filament with anisotropic bending rigidities within a cylindrical tube of radius R can create a natural tristable status which is consisted of two low-pitch helices and one high-pitch helix, where a helical filament is referred to as a filament that has both an intrinsic curvature ( c 0 ) and an intrinsic twist rate ( τ 0 ). The formation of the tristable status also requires that the filament has a significant difference between two bending rigidities and a large twisting rigidity. The relative heights of two low-pitch helices in a tristable status are close to zero, and the smaller the intrinsic twisting angle, the smaller the difference between these two heights. Moreover, at a large intrinsic twisting angle, two low-pitch helices display a large energy difference, and the energy difference increases with decreasing τ 0 . Meanwhile, the relative height of the high-pitch helix is always close to that of a straight line. Finally, at some specific intrinsic parameters, the tristable status can include an isoenergic status with two helices of the same energy but distinct pitches.

Observation of parity-time symmetry in diffusive systems

Phase modulation has scarcely been mentioned in diffusive physical systems because the diffusion process does not carry the momentum like waves. Recently, non-Hermitian physics provides a unique perspective for understanding diffusion and shows prospects in thermal phase regulation, exemplified by the discovery of anti-parity-time (APT) symmetry in diffusive systems. However, precise control of thermal phase remains elusive hitherto and can hardly be realized, due to the phase oscillations. Here we construct the PT-symmetric diffusive systems to achieve the complete suppression of thermal phase oscillation. The real coupling of diffusive fields is readily established through a strong convective background, and the decay-rate detuning is enabled by thermal metamaterial design. We observe the phase transition of PT symmetry breaking with the symmetry-determined amplitude and phase regulation of coupled temperature fields. Our work shows the existence of PT symmetry in dissipative energy exchanges and provides unique approaches for harnessing the mass transfer of particles, wave dynamics in strongly scattering systems, and thermal conduction.

Machine Learning Aided Design and Optimization of Thermal Metamaterials

Artificial Intelligence (AI) has advanced material research that were previously intractable, for example, the machine learning (ML) has been able to predict some unprecedented thermal properties. In this review, we first elucidate the methodologies underpinning discriminative and generative models, as well as the paradigm of optimization approaches. Then, we present a series of case studies showcasing the application of machine learning in thermal metamaterial design. Finally, we give a brief discussion on the challenges and opportunities in this fast developing field. In particular, this review provides: (1) Optimization of thermal metamaterials using optimization algorithms to achieve specific target properties. (2) Integration of discriminative models with optimization algorithms to enhance computational efficiency. (3) Generative models for the structural design and optimization of thermal metamaterials.

Achieving Environmentally-Adaptive and Multifunctional Hydrodynamic Metamaterials through Active Control

As hydrodynamic metamaterials continue to develop, the inherent limitations of passive-mode metamaterials become increasingly apparent. First, passive devices are typically designed for specific environments and lack the adaptability to environmental changes. Second, their unique functions often rely on intricate structures, or challenging material properties, or a combination of both. These limitations considerably hinder the potential applications of hydrodynamic metamaterials. In this study, an active-mode hydrodynamic metamaterial is theoretically proposed and experimentally demonstrated by incorporating source-and-sink flow-dipoles into the system, enabling active manipulation of the flow field with various functionalities. By adjusting the magnitude and direction of the flow-dipole moment, this device can easily achieve invisibility, flow shielding, and flow enhancing. Furthermore, it is environmentally adaptive and can maintain proper functions in different environments. It is anticipated that this design will significantly enhance tunability and adaptability of hydrodynamic metamaterials in complex and ever-changing environments.

Twisted moiré conductive thermal metasurface

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.

Deep Learning-Assisted Active Metamaterials with Heat-Enhanced Thermal Transport

Heat management is crucial for state-of-the-art applications such as passive radiative cooling, thermally adjustable wearables, and camouflage systems. Their adaptive versions, to cater to varied requirements, lean on the potential of adaptive metamaterials. Existing efforts, however, feature with highly anisotropic parameters, narrow working-temperature ranges, and the need for manual intervention, which remain long-term and tricky obstacles for the most advanced self-adaptive metamaterials. To surmount these barriers, heat-enhanced thermal diffusion metamaterials powered by deep learning is introduced. Such active metamaterials can automatically sense ambient temperatures and swiftly, as well as continuously, adjust their thermal functions with a high degree of tunability. They maintain robust thermal performance even when external thermal fields change direction, and both simulations and experiments demonstrate exceptional results. Furthermore, two metadevices with on-demand adaptability, performing distinctive features with isotropic materials, wide working temperatures, and spontaneous response are designed. This work offers a framework for the design of intelligent thermal diffusion metamaterials and can be expanded to other diffusion fields, adapting to increasingly complex and dynamic environments.

Omnidirectional thermal-electric signatures of functional illusion device with anisotropic geometry

The omnidirectional thermal-electric signatures induced by the anisotropic functional illusion device and the corresponding camouflage device are reported. We first theoretically derive the anisotropic effective parameters of confocal elliptical bilayer core-shell structure for constructing the functional illusion device. Then, the thermal-electric signatures of the functional illusion device with camouflage device are presented numerically. In addition, we further transform the monolayered structure of the camouflage device into an alternating multilayered one to enrich the omnidirectional illusion effects. The results show that the functional illusion device with monolayered structure could realize omnidirectional thermal-electric illusion effects perfectly. When the monolayered structure is replaced by the alternating multilayered one, the functional illusion device with alternating multilayered structure could achieve different illusion effects with different scattering signatures under different directional heat flux and electric current launching. This article may open a new avenue to realize omnidirectional illusion effects of functional device in multiphysical fields.

Deep-Learning-Enabled Intelligent Design of Thermal Metamaterials

Thermal metamaterials are mixture-based materials that are engineered to manipulate, control, and process the flow of heat, enabling numerous advanced thermal metadevices. Conventional thermal metamaterials are predominantly designed with tractable regular geometries owing to the delicate analytical solution and easy-to-implement effective structures. Nevertheless, it is challenging to achieve the design of thermal metamaterials with arbitrary geometry, letting alone intelligent (automatic, real-time, and customizable) design of thermal metamaterials. Here, an intelligent design framework of thermal metamaterials is presented via a pre-trained deep learning model, which gracefully achieves the desired functional structures of thermal metamaterials with exceptional speed and efficiency, regardless of arbitrary geometry. It possesses incomparable versatility and is of great flexibility to achieve the corresponding design of thermal metamaterials with different background materials, anisotropic geometries, and thermal functionalities. The transformation thermotics-induced, freeform, background-independent, and omnidirectional thermal cloaks, whose structural configurations are automatically designed in real-time according to shape and background, are numerically and experimentally demonstrated. This study sets up a novel paradigm for an automatic and real-time design of thermal metamaterials in a new design scenario. More generally, it may open a door to the realization of an intelligent design of metamaterials in also other physical domains.

Non-Equilibrium Thermodynamics of Heat Transport in Superlattices, Graded Systems, and Thermal Metamaterials with Defects

In this review, we discuss a nonequilibrium thermodynamic theory for heat transport in superlattices, graded systems, and thermal metamaterials with defects. The aim is to provide researchers in nonequilibrium thermodynamics as well as material scientists with a framework to consider in a systematic way several nonequilibrium questions about current developments, which are fostering new aims in heat transport, and the techniques for achieving them, for instance, defect engineering, dislocation engineering, stress engineering, phonon engineering, and nanoengineering. We also suggest some new applications in the particular case of mobile defects.

Non-Hermitian Chiral Heat Transport

Exceptional point (EP) has been captivated as a concept of interpreting eigenvalue degeneracy and eigenstate exchange in non-Hermitian physics. The chirality in the vicinity of EP is intrinsically preserved and usually immune to external bias or perturbation, resulting in the robustness of asymmetric backscattering and directional emission in classical wave fields. Despite recent progress in non-Hermitian thermal diffusion, all state-of-the-art approaches fail to exhibit chiral states or directional robustness in heat transport. Here we report the first discovery of chiral heat transport, which is manifested only in the vicinity of EP but suppressed at the EP of a thermal system. The chiral heat transport demonstrates significant robustness against drastically varying advections and thermal perturbations imposed. Our results reveal the chirality in heat transport process and provide a novel strategy for manipulating mass, charge, and diffusive light.

Homogeneous Zero-Index Thermal Metadevice for Thermal Camouflaging and Super-Expanding

The infinite effective thermal conductivity (IETC) can be considered to be an equivalence of the effective zero index in photonics. A recent highly rotating metadevice has been discovered to approach near IETC, subsequently demonstrating a cloaking effect. However, this near IETC, related to a rotating radius, is quite inhomogeneous, and the high-speed rotating motor also needs a high energy input, limiting its further applications. Herein, we propose and realize an evolution of this homogeneous zero-index thermal metadevice for robust camouflaging and super-expanding through out-of-plane modulations rather than high-speed rotation. Both the theoretical simulations and experiments verify a homogeneous IETC and the corresponding thermal functionalities beyond cloaking. The recipe for our homogeneous zero-index thermal metadevice involves an external thermostat, which can be easily adjusted for various thermal applications. Our study may provide meaningful insights into the design of powerful thermal metadevices with IETCs in a more flexible way.

Architected material with independently tunable mass, damping, and stiffness via multi-stability and kinematic amplification

We report on a class of architected material lattices that exploit multi-stability and kinematic amplification to independently adjust the local effective mass, damping, and stiffness properties, thereby realizing congruent alterations to the acoustic dispersion response post-fabrication. The fundamental structural tuning element permits a broad range in the effective property space; moreover, its particular design carries the benefit of tuning without altering the original size/shape of the emerging structure. The relation between the tuning element geometry and the achieved variability in effective properties is explored. Bloch's theorem facilitates the dynamic analysis of representative one- and two-dimensional (1D/2D) systems, revealing, e.g., bandgap formation, migration, and closure and positive/negative metadamping in accordance with the tuning element configuration. To demonstrate a utility, we improvise a waveguide by appropriately patterning the tuning element configuration within a 2D system. We believe that the proposed strategy offers a new way to expand the range of performance and functionality of architected materials for elastodynamics.

Biphysical undetectable concentrators manipulating both heat flux and direct current via topology optimization

Recent remarkable developments in metamaterials and metadevices manipulating diffusive processes, such as thermal and electrical conduction, have enabled the control of multiple phenomena and the development of multifunctional devices. However, only either multiphysics operations or multiple functionalities are usually implemented on single metadevices. In this paper, we describe a method for the optimal design of metadevices that achieves both cloaking and focusing in the control of both heat flux and direct current by a single device, i.e., biphysical-bifunctional metadevices having four capabilities. Our design scheme performs well in terms of providing cloaking and focusing bifunctionality. Additionally, it assumes bulk natural materials without the use of metamaterials, which improves the manufacturability of the designed metadevices. Moreover, multidirectional metad evices are optimally designed for thermal-electrical conductions transmitted from multiple directions or from heat and voltage sources at various locations.

Active exterior cloaking for the two-dimensional Helmholtz equation with complex wavenumbers and application to thermal cloaking

We design sources for the two-dimensional Helmholtz equation that can cloak an object by cancelling out the incident field in a region, without the sources completely surrounding the object to hide. As in previous work for real positive wavenumbers, the sources are also determined by the Green identities. The novelty is that we prove that the same approach works for complex wavenumbers which makes it applicable to a variety of media, including media with dispersion, loss and gain. Furthermore, by deriving bounds on Graf's addition formulas with complex arguments, we obtain new estimates that allow to quantify the quality of the cloaking effect. We illustrate our results by applying them to achieve active exterior cloaking for the heat equation. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 2)'.

Mass Diffusion Metamaterials with "Plug and Switch" Modules for Ion Cloaking, Concentrating, and Selection: Design and Experiments

The outstanding abilities of metamaterials to manipulate physical fields are extensively studied in both wave-based and diffusion-based fields. However, mass diffusion metamaterials, with the ability to manipulate diffusion with practical applications associated with chemical and biochemical engineering, have not yet been experimentally demonstrated. In this work, ion cloaking, concentrating, and selection in liquid solvents are verified by both simulations and experiments, and the concept of a "plug and switch" metamaterial is proposed based on scattering cancellation (SC) to achieve switchable functions by plugging modularized functional units into a functional motherboard. Plugging in any module barely affects the environmental diffusion field, but the module choice impacts different diffusion behaviors in the central region. Cloaking strictly hinds ion diffusion, and concentrating increase diffusion flux, while cytomembrane-like ion selection permits the entrance of some ions but blocks others. In addition, these functions are demonstrated in special applications like the catalytic enhancement by the concentrator and the protein protection by the ion selector. This work not only experimentally demonstrates the effective manipulation of mass diffusion by metamaterials, but also shows that the "plug and switch" design is extensible and reconfigurable. It facilitates novel applications including sustained drug release, catalytic enhancement, bioinspired cytomembranes, etc.

Geometric heat pump and no-go restrictions of nonreciprocity in modulated thermal diffusion

Thermodynamics strongly restricts the direction of heat flow in static macroscopic thermal diffusive systems. To overcome this constraint, spatiotemporal modulated systems are used instead. Here, we unveil the underlying geometric heat pump effect in macroscopic driven thermal diffusion, which is crucial for achieving thermal nonreciprocity. We obtain a geometric expression to formulate the nontrivial current in a driven system, manifesting as an extra pumped heat ably diffusing from cold to hot that has no analogy in static setups. Moreover, we analyze the underlying geometric curvature of driven diffusive systems and derive no-pumping restriction theorems that constrain the thermal action under modulations and guide the optimization of driving protocols. Following the restrictions from geometry, we finally implement a minimum experiment and observe the predicted pumped heat in the absence of thermal bias at every instant, which is independent of the driving speed in the adiabatic limit, clearly validating the geometric theory. An extension of the geometric pump effect and no-pumping restrictions to macroscopic mass diffusion governed by Fick's law is also discussed. These results pave the way for designing and implementing nonreciprocal and topological diffusive systems under spatiotemporal modulations.

Long-wavelength infrared selective emitter for thermal infrared camouflage under a hot environment

Thermal infrared camouflage as a kind of counter-surveillance technique has attracted much attention owing to the rapid development of infrared surveillance technology. Various artificial optical structures have been developed for infrared camouflage applications under cold ambient environment (low thermal radiation), but the realization of infrared camouflage under a hot environment (high thermal radiation) is also highly desirable and has been rarely reported. Here, a lithography-free, ultra-thin, high performance long-wavelength infrared (LWIR) selective emitter for thermal infrared camouflage in a high radiation environment is proposed and experimentally demonstrated. Experimental results show that our designed selective emitter exhibits average emissivity higher than 90% over the LWIR range from 8 to 14 µm and low emissivity less than 35% outside this window. Numerical simulations were performed to optimize the geometrical structures and reveal that such a selective emission effect is attributed to the combination of multiple hybrid plasmonic resonances. LWIR thermal images show that the selective emitter can perfectly blend into the high radiation backgrounds. Furthermore, it is found that the sample displays angle-independent emission properties, indicating that our emitter offers great potential for application in evading large-angle detection.

A Real-Time Self-Adaptive Thermal Metasurface

Emerging metamaterials have served as an efficient strategy for the realization of unconventional heat control and management using structural thermal properties, and many functional thermal metadevices have been investigated. However, thermal functions are usually fixed or limited in the switching range. Thus far, real-time thermal regulation is elusive for thermal metamaterials because of deterministic artificial metastructures and uncontrollable phase transitions, coupled with the absence of dynamic adaptability. Here, a self-adaptive metasurface platform to implement programmable thermal functions via the automatic evolution of thermoelectric heat sources and real-time control of the driven voltage is reported. The proof-of-concept smart platform experimentally demonstrates arbitrary switching between elaborate thermal patterns consolidated into an active thermoelectric element matrix. Further, thermal pixels and feedback control systems are integrated into printed circuit boards, resulting in self-adaptability to any thermal requirements. This study sets up a new paradigm for arbitrary transitions between exquisite thermal patterns and is expected to pave the way for real-time thermal management in a programming formation.

Heat transfer control using a thermal analogue of coherent perfect absorption

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.

A thermal analogue of coherent perfect absorption would allow to control heat transfer using heat, but the lack of momentum propagation in a thermal field seems to prevent any role for coherence. Here, the authors allow this by introducing an imitated momentum for steady-state heat diffusion.

Design of an omnidirectional camouflage device with anisotropic confocal elliptic geometry in thermal-electric field

The designed confocal elliptical core-shell structure can realize the omnidirectional camouflage effect without disturbing temperature and electric potential profiles as the directions of heat flux and electric current change. Based on the anisotropy of the confocal ellipse, the anisotropic effective parameters of the confocal elliptical core-shell structure are derived under different heat flux and electric current launching. Then, the matrix material should be anisotropic as the effective parameters to satisfy the omnidirectional camouflage effect, which is demonstrated numerically. In addition, we present a composite structure to realize the anisotropic matrix. The experimental results show that the camouflage device embedded in the composite structure can eliminate the scattering caused by the elliptical core under different directions of heat flux and electric current, thus achieving the omnidirectional thermal-electric camouflage effect experimentally. The omnidirectional camouflage effect in thermal and electric fields can greatly widen the application fields of this device with anisotropic geometry.

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Omnidirectional camouflage device with anisotropic geometry is constructed

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Anisotropic matrix dominates the thermal-electric camouflage effect omnidirectionally

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A multilayered composite structure contributes to the experimental implementation

Passive Ultra-Conductive Thermal Metamaterials

Ultra-conductive heat transport showcases significant potentials in popular thermal managements with convection, phase change, and heat source. However, it is captivated impossible for passive thermal manipulation, usually bounded by intrinsic thermal conductivities of natural materials, to outperform these active recipes in need of extra energy payload. Here, a robust recipe to create passive ultra-conductive thermal metamaterials consisting of nothing but bulk natural materials is reported. Thanks to the local thermal resistance regulation by vertical thermal transport channel, the proof-of-concept thermal metamaterials experimentally demonstrate extreme effective conductivity (1915 W m^-1  K^-1 ) solely with naturally occurring materials. The purely conductive modulation without any external energy is comparable to active counterparts, and further reveals its robustness and unexpected convenience. The findings construct a high-efficient paradigm of passive thermal management with ultra-conductive heat transport, and further hint potentials in other Laplace fields, e.g., DC and magnetostatics.

Study on Phonon Localization in Silicon Film by Molecular Dynamics

In recent years, nanoscale thermal cloaks have received extensive attention from researchers. Amorphization, perforation, and concave are commonly used methods for building nanoscale thermal cloaks. However, the comparison of the three methods and the effect of different structural proportions on phonon localization have not been found. Therefore, in this paper, an asymmetrical structure is constructed to study the influence of different structure proportions on phonon localization by amorphization, perforation, and concave silicon film. We first calculated the phonon density of states (PDOS) and the mode participation rate (MPR). To quantitatively explore its influence on phonon localization, we proposed the concept of the degree of phonon localization (DPL) and explored the influence of center and edge effects on phonon localization. We found that for different processing methods, the degree of phonon localization increased with the increase in the processing regions. Compared to the edge, the center had a stronger influence on phonon localization, and the higher the degree of disorder, the stronger the phonon localization. Our research can guide the construction of a nanoscale thermal cloak.

Thermal Cloaking in Nanoscale Porous Silicon Structure by Molecular Dynamics

Nanoscale thermal cloaks have great potential in the thermal protection of microelectronic devices, for example, thermal shielding of thermal components close to the heat source. Researchers have used graphene, crystalline silicon film, and silicon carbide to design a variety of thermal cloaks in different ways. In our previous research, we found that the porous structure has lower thermal conductivity compared to bulk silicon; thus, so we tried to use the porous structure to construct the functional region to control the heat flux. We first calculated the thermal conductivity of crystalline silicon and porous silicon films by means of nonequilibrium molecular dynamics, proving that the porous structure satisfied the conditions for building a thermal cloak. A rectangular cloak with a porous structure was constructed, and a crystalline silicon film was used as a reference to evaluate its performance by the index of the ratio of thermal cloaking. We found that the thermal cloak built with a porous structure could produce an excellent cloaking effect. Lastly, we explain the mechanism of the cloaking phenomenon produced by a porous structure with the help of phonon localization theory. Porous structures have increased porosity compared to bulk silicon and are not conducive to phonon transport, thus producing strong phonon localization and reducing thermal conductivity. Our research expands the construction methods of nanocloaks, expands the application of porous structure materials, and provides a reference for the design of other nanodevices.

Nanoscale Thermal Cloaking in Silicon Film: A Molecular Dynamic Study

Nanoscale thermal shielding is becoming increasingly important with the miniaturization of microelectronic devices. They have important uses in the field of thermal design to isolate electronic components. Several nanoscale thermal cloaks based on graphene and crystalline silicon films have been designed and experimentally verified. No study has been found that simultaneously treats the functional region of thermal cloak by amorphization and perforation methods. Therefore, in this paper, we construct a thermal cloak by the above methods, and the ratio of thermal cloaking and response temperature is used to explore its cloaking performance under constant and dynamic temperature boundary. We find that compared with the dynamic boundary, the cloaking effect produced under the constant boundary is more obvious. Under two temperature boundaries, the thermal cloak composed of amorphous and perforated has a better performance and has the least disturbance to the background temperature field. The phonon localization effect produced by the amorphous structure is more obvious than that of the perforated structure. The phonon localization of the functional region is the main reason for the cloaking phenomenon, and the stronger the phonon localization, the lower the thermal conductivity and the more obvious the cloaking effect. Our study extends the nanoscale thermal cloak construction method and facilitates the development of other nanoscale thermal functional devices.

Thermal Cloak: Theory, Experiment and Application

In the past two decades, owing to the development of metamaterials and the theoretical tools of transformation optics and the scattering cancellation method, a plethora of unprecedented functional devices, especially invisibility cloaks, have been experimentally demonstrated in various fields, e.g., electromagnetics, acoustics, and thermodynamics. Since the first thermal cloak was theoretically reported in 2008 and experimentally demonstrated in 2012, great progress has been made in both theory and experiment. In this review, we report the recent advances in thermal cloaks, including the theoretical designs, experimental realizations, and potential applications. The three areas are classified according to the different mechanisms of heat transfer, namely, thermal conduction, thermal convection, and thermal radiation. We also provide an outlook toward the challenges and future directions in this fascinating area.

Robustly printable freeform thermal metamaterials

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.

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.

Configurable Phase Transitions in a Topological Thermal Material

Diffusive nature of thermal transportation fundamentally restricts topological characteristics due to the absence of a sufficient parametric space with complex dimensionalities. Here, we create an orthogonal advection space with two advective pairs to reveal the unexplored topological transitions in thermal material. We demonstrate four types of configurable thermal phases, including the nontrivial dynamic-equilibrium distribution, nonchiral steplike π-phase transition, and another two trivial profiles related to the anti-parity-time symmetry nature. Our findings provide a recipe for realizing a topologically robust thermal system under arbitrary perturbations.

Evolution of the Electromagnetic Manipulation: From Tunable to Programmable and Intelligent Metasurfaces

Looking back on the development of metamaterials in the past 20 years, metamaterials have gradually developed from three-dimensional complex electromagnetic structures to a two-dimensional metasurface with a low profile, during which a series of subversive achievements have been produced. The form of electromagnetic manipulation of the metasurface has evolved from passive to active tunable, programmable, and other dynamic and real-time controllable forms. In particular, the proposal of coding and programmable metasurfaces endows metasurfaces with new vitality. By describing metamaterials through binary code, the digital world and the physical world are connected, and the research of metasurfaces also steps into a new era of digitalization. However, the function switch of traditional programmable metamaterials cannot be achieved without human instruction and control. In order to achieve richer and more flexible function regulation and even higher level metasurface design, the intelligence of metamaterials is an important direction in its future development. In this paper, we review the development of tunable, programmable, and intelligent metasurfaces over the past 5 years, focusing on basic concepts, working principles, design methods, manufacturing, and experimental validation. Firstly, several manipulation modes of tunable metasurfaces are discussed; in particular, the metasurfaces based on temperature control, mechanical control, and electrical control are described in detail. It is demonstrated that the amplitude and phase responses can be flexibly manipulated by the tunable metasurfaces. Then, the concept, working principle, and design method of digital coding metasurfaces are briefly introduced. At the same time, we introduce the active programmable metasurfaces from the following aspects, such as structure, coding method, and three-dimensional far-field results, to show the excellent electromagnetic manipulation ability of programmable metasurfaces. Finally, the basic concepts and research status of intelligent metasurfaces are discussed in detail. Different from the previous programmable metamaterials, which must be controlled by human intervention, the new intelligent metamaterials control system will realize autonomous perception, autonomous decision-making, and even adaptive functional manipulation to a certain extent.

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.

Path-Dependent Thermal Metadevice beyond Janus Functionalities

Janus metamaterials, metasurfaces, and monolayers have received intensive attention in nanophotonics and 2D materials. Their core concept is to introduce asymmetry along the wave propagation direction, by stacking different materials or layers of meta-atoms, or breaking out-of-plane mirror asymmetry with external biases. Nevertheless, it has been hitherto elusive to realize a diffusive Janus metadevice, since scalar diffusion systems such as heat conduction normally operate in the absence of polarization control, spin manipulation, or electric-field stimuli, which all are widely used in achieving optical Janus devices. It is even more challenging, if not impossible, for a single diffusive metadevice to exhibit more than two thermal functions. Here a path-dependent thermal metadevice beyond Janus characteristics is proposed, which can exhibit three distinct thermal behaviors (cloaking, concentrating, and transparency) under different directions of heat flow. The rotation transformation mechanism of thermal conductivity provides a robust platform to assign a specific thermal behavior in any direction. The proof-of-concept experiment of anisotropic in-plane conduction successfully validates such a path-dependent trifunction thermal metamaterial device. It is anticipated that this path-dependent strategy can provide a new dimension for multifunctional metamaterial devices in the thermal field, as well as for a more general diffusion process.

Tunable analog thermal material

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.

Thermal Metamaterial: Fundamental, Application, and Outlook

Thermal metamaterials have amazing properties in heat transfer beyond naturally occurring materials owing to their well-designed artificial structures. The idea of thermal metamaterial has completely subverted the design of thermal functional devices and makes it possible to manipulate heat flow at will. In this perspective, we review the up-to-date progress of thermal metamaterials starting from 2008. We focus on both the key theoretical fundamentals and techniques for applications and give a perspective of scale-based classification on thermal metamaterials' theories and applications. We also discuss the junction between macroscale and microscale design methods and propose some prospects for the future trend of this field.

Novel cloaking lamellar structures for a screw dislocation dipole, a circular Eshelby inclusion and a concentrated couple

Using conformal mapping techniques, we design novel lamellar structures which cloak the influence of any one of a screw dislocation dipole, a circular Eshelby inclusion or a concentrated couple. The lamellar structure is composed of two half-planes bonded through a middle coating with a variable thickness within which is located either the dislocation dipole, the circular Eshelby inclusion or the concentrated couple. The Eshelby inclusion undergoes either uniform anti-plane eigenstrains or uniform in-plane volumetric eigenstrains. As a result, the influence of any one of the dislocation dipole, the circular Eshelby inclusion or the concentrated couple is cloaked in that their presence will not disturb the prescribed uniform stress fields in both surrounding half-planes.

A Continuously Tunable Solid-Like Convective Thermal Metadevice on the Reciprocal Line

The emerging thermal metamaterials and metadevices demonstrate significant potential to transform thermal conduction. However, the thermal conductivities of existing devices are all restricted at fixed values if the configuration or constituent materials are static. Thermal convection provides an additional tool to boost and flexibly modify the heat transfer in moving matter, but it is essentially distinct from thermal conduction since the Onsager reciprocity is generally broken in the former but preserved in the latter. Therefore, it is difficult to use convective components for sophisticated control of conductive heat. Here, it is shown that a convective system can be made undistinguishable from a conductive one in principle, by discovering and operating on the reciprocal line of mechanically rotating systems. The realized thermal metadevice can thus mimic a solid-like material whose thermal conductivity dynamically covers a wide range. It offers great possibilities of real-time smooth control over heat transfer for broad applications.

Geometric phase and bilayer cloak in macroscopic particle-diffusion systems

Particle diffusion is a fundamental process in various systems, so its effective manipulation is crucially important. For this purpose, here we design a basic structure composed of two moving rings with equal-but-opposite velocities and a stationary intermediate layer, which can realize multiple functions to control particle diffusion. On the one hand, the intermediate layer allows particle exchange between the two moving rings, which gives birth to an exceptional point of velocity. As a result, a geometric phase appears for a loop evolution of velocity containing the exceptional point. On the other hand, the two moving rings also enhance the effective diffusivity of the intermediate layer, which helps design a bilayer particle-diffusion cloak. The present cloak only requires homogeneous parameters and simple structures, and meanwhile, its on and off can be flexibly controlled by velocity. These results broaden the scope of geometric phase and provide hints for designing particle-diffusion metamaterials.

Effective medium theory for thermal scattering off rotating structures

Controlling heat transfer with artificial functional materials has been a promising route towards the efficient and smart utilization of thermal energy in modern society. At the macroscopic scale, thermal metamaterials have demonstrated versatile functionalities in manipulating thermal conduction. One major method is the effective medium theory, which provides a reliable approximation for the material parameters of the composite. Although most of thermal metamaterials use static components, recent devices with integrated moving parts are attracting great interest thanks to their high efficiency and flexibility. However, the effective medium theory for thermal scattering off such devices has not been well established, due to the fundamental difference between thermal convection and conduction. Here, we provide a thorough study on heat transfer through mechanically rotating structures. It is shown that the effective thermal conductivity of a rotating structure can be rigorously described in a complex plane. The analytical expressions of the effective thermal conductivity for structures with rotating multiple layers are formulated, which explicitly capture their influences on the surrounding temperature field. We validate the theory and numerically demonstrate the rotated and unrotated temperature distributions generated around a single structure. Our theory is expected to become a design recipe for novel thermal metamaterials and meta-devices.

Nanostructured Color Filters: A Review of Recent Developments

Color plays an important role in human life: without it life would be dull and monochromatic. Printing color with distinct characteristics, like hue, brightness and saturation, and high resolution, are the main characteristic of image sensing devices. A flexible design of color filter is also desired for angle insensitivity and independence of direction of polarization of incident light. Furthermore, it is important that the designed filter be compatible with the image sensing devices in terms of technology and size. Therefore, color filter requires special care in its design, operation and integration. In this paper, we present a comprehensive review of nanostructured color filter designs described to date and evaluate them in terms of their performance.

Bio-inspired Photonic Masquerade with Perturbative Metasurfaces

Camouflage is critical for many living organisms to survive in the natural world and has stimulated applications, such as optical cloaking and military affairs. However, most applications adopt crypsis-type camouflage that prevents the organisms from being detected by matching the environment, which is challenging to realize the large angle-of-view and broadband operation at optical frequencies. Here, as inspired by nature's system of masquerade, we demonstrate an optical masquerade, being detected but not recognized, with perturbative metasurfaces that could camouflage an object into another unrelated one under the oblique (±69°) illumination of visible light with an ∼160 nm bandwidth. Predicted by the perturbation theory, the dielectric metastructures encircling a pistol-shaped object have a thin layer of nanodisk array, which can suppress the electromagnetic resonances of nanomodes for mimicking the transmitted intensity and phase of the camouflaged object. We also exhibit that optical masquerade is an invasive, environment-independent, object-unlimited, and material-extendable camouflage, which might benefit optical security, anticounterfeiting, and encoding.

Quantum simulation of particle pair creation near the event horizon

Though it is still a big challenge to unify general relativity and quantum mechanics in modern physics, the theory of quantum field related with the gravitational effect has been well developed and some striking phenomena are predicted, such as Hawking radiation. However, the direct measurement of these quantum effects under general relativity is far beyond present experiment techniques. Fortunately, the emulation of general relativity phenomena in the laboratory has become accessible in recent years. However, up to now, these simulations are limited either in classical regime or in flat space whereas quantum simulation related with general relativity is rarely involved. Here we propose and experimentally demonstrate a quantum evolution of fermions in close proximity to an artificial black hole on a photonic chip. We successfully observe the acceleration behavior, quantum creation, and evolution of a fermion pair near the event horizon: a single-photon wave packet with positive energy escapes from the black hole while negative energy is captured. Our extensible platform not only provides a route to access quantum effects related with general relativity, but also has the potentiality to investigate quantum gravity in future.

Environmental Response of 2D Thermal Cloak under Dynamic External Temperature Field

As a typical representative of transformation thermodynamics, which is the counterpart of transformation optics, the thermal cloak has been explored extensively while most current research focuses on the structural design instead of adaptability and practicability in a dynamic environment. The evaluation of energy processes involved in the thermal cloak under dynamic conditions are also lacking, which is essential to the engineering application of this functional structure. In this paper, based on the dynamic environment of a sinusoidal form with ambient amplitude, distribution density, phase, and temperature difference as variables, we evaluated the cloaking performance and environmental response of a 2D thermal cloak. Considering the heat dissipation and energy loss in the whole procedure, local entropy production rate and response entropy were introduced to analyze the different influences of each environmental parameter on the cloaking system. Moreover, we constructed a series of comprehensive schemes to obtain the fitting equation as well as an appropriate scope to apply the thermal cloak. The results are beneficial to the novel use of the concept of entropy and valuable for further improving the working efficiency and potential engineering applications of the thermal cloak.

Physical Realization of Elastic Cloaking with a Polar Material

An elastic cloak is a coating material that can be applied to an arbitrary inclusion to make it indistinguishable from the background medium. Cloaking against elastic disturbances, in particular, has been demonstrated using several designs and gauges. None, however, tolerate the coexistence of normal and shear stresses due to a shortage of physical realization of transformation-invariant elastic materials. Here, we overcome this limitation to design and fabricate a new class of polar materials with a distribution of body torque that exhibits asymmetric stresses. A static cloak for full two-dimensional elasticity is thus constructed based on the transformation method. The proposed cloak is made of a functionally graded multilayered lattice embedded in an isotropic continuum background. While one layer is tailored to produce a target elastic behavior, the other layers impose a set of kinematic constraints equivalent to a distribution of body torque that breaks the stress symmetry. Experimental testing under static compressive and shear loads demonstrates encouraging cloaking performance in good agreement with our theoretical prediction. The work sets a precedent in the field of transformation elasticity and should find applications in mechanical stress shielding and stealth technologies.

Designing bistability or multistability in macroscopic diffusive systems

We theoretically design a kind of diffusion bistability (and even multistability) in the macroscopic scale, which has a similar phenomenon but different underlying mechanism from its microscopic counterpart [Phys. Rev. Lett. 101, 267203 (2008)10.1103/PhysRevLett.101.267203]; the latter has been extensively investigated in literature, e.g., for building nanometer-scale memory components. By introducing second- and third-order nonlinear terms (that opposite in sign) into diffusion coefficient matrices, a bistable energy or mass diffusion occurs with two different steady states identified as "0" and "1." In particular, we study heat conduction in a two-terminal three-body system and show that this bistable system exhibits a macroscale thermal memory effect with tailored nonlinear thermal conductivities. The theoretical analysis is confirmed by finite-element simulations. Also, we suggest experiments with metamaterials based on shape memory alloys. This theoretical framework blazes a trail on constructing intrinsic bistability or multistability in diffusive systems for macroscopic energy or mass management.

Dipole-assisted thermotics: Experimental demonstration of dipole-driven thermal invisibility

Thermal management has made considerable progress in the past decade for the emerging field of thermal metamaterials. However, two severe problems still handicap the development of thermal metamaterials. That is, thermal conductivities should be singular and uncommon as required by corresponding theories. To solve these problems, here we establish the theory of dipole-assisted thermotics. By tailoring the thermal dipole moment, thermal invisibility can be achieved without the requirements of singular and uncommon thermal conductivities. Furthermore, finite-element simulations and laboratory experiments both validate the theoretical analyses. The performance of the dipole-driven scheme is excellent in both two and three dimensions, and in both steady and transient states. Dipole-assisted thermotics not only offers a distinct mechanism to achieve thermal invisibility, but also has potential applications in thermal management such as infrared signature reduction, thermal protection, and infrared camouflage.

Radiative metasurface for thermal camouflage, illusion and messaging

Thanks to the conductive thermal metamaterials, novel functionalities like thermal cloak, camouflage and illusion have been achieved, but conductive metamaterials can only control the in-plane heat conduction. The radiative thermal metamaterials can control the out-of-plane thermal emission, which are more promising and applicable but have not been studied as comprehensively as the conductive counterparts. In this paper, we theoretically investigate the surface emissivity of metal/insulator/metal (MIM, i.e., Au/Ge/Au here) microstructures, by the rigorous coupled-wave algorithm, and utilize the excitation of the magnetic polaritons to realize thermal camouflage through designing the grating width distribution by minimizing the temperature standard deviation of the overall plate. Through this strategy, the hot spot in the original temperature field is removed and a uniform temperature field is observed in the infrared camera instead, demonstrating the thermal camouflage functionality. Furthermore, thermal illusion and thermal messaging functionalities are also demonstrated by resorting to using such an emissivity-structured radiative metasurface. The present MIM-based radiative metasurface may open avenues for developing novel thermal functionalities via thermal metasurface and metamaterials.