Full-Parameter Omnidirectional Thermal Metadevices of Anisotropic Geometry

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.

Free-form and multi-physical metamaterials with forward conformality-assisted tracing

Transformation theory, active control and inverse design have been mainstream in creating free-form metamaterials. However, existing frameworks cannot simultaneously satisfy the requirements of isotropic, passive and forward design. Here we propose a forward conformality-assisted tracing method to address the geometric and single-physical-field constraints of conformal transformation. Using a conformal mesh composed of orthogonal streamlines and isotherms (or isothermal surfaces), this method quasi-analytically produces free-form metamaterials using only isotropic media. The geometric nature of this approach allows for universal regulation of both dissipative thermal fields and non-dissipative electromagnetic fields. We experimentally demonstrate free-form thermal cloaking in both two and three dimensions. Additionally, the multi-physical functionalities of our method, including optical cloaking, bending and thermo-electric transparency, confirm its broad applicability. Our method features improvements in efficiency, accuracy and adaptability over previous approaches. This study provides an effective method for designing complex metamaterials with arbitrary shapes across various physical domains.

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.

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.

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.

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.

Nonlinear thermal responses in geometrically anisotropic metamaterials

Nonlinear metamaterials have great potential in heat management, which has aroused intensive research interest in both theory and application, especially for their response to surroundings. However, most existing works focus on geometrically isotropic (circular) structures, limiting the potential versatile functionalities. On the other hand, anisotropy in architecture promisingly offers an additional degree of freedom in modulating directional heat transfer. Here, we investigate nonlinear composition effects in geometrically anisotropic (confocal elliptical) thermal medium under the framework of effective medium approximation, and deduce a series of general formulas for quantitatively predicting nonlinearity enhancement. Enhancement coefficients are analytically derived by the Taylor expansion method in different nonlinearity cases. In particular, we find that some coupling conditions can greatly promote the nonlinear modulation coefficients, introducing stronger enhancement beyond isotropic construction. Our theoretical predictions are verified by finite-element simulation, and feasible experimental suggestions are also given. For extending these results to practical scenes, two intelligent thermal metadevices are designed in proof of concept and demonstrated by numerical simulation. Our works provide a unified theory for anisotropic nonlinear thermal metamaterial design and may benefit flexible applications in self-adaptive thermal management, such as switchable cloaks, concentrators, or macroscopic thermal diodes.

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.

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

Novel connections and physical implications of thermal metamaterials with imperfect interfaces

Thermal metamaterials are of great importance in advanced energy control and management. Previous studies mainly focused on interfaces with perfect bonding conditions. In principle, imperfectness always exists across interface and the effect is intriguingly important with small-length scales. This work reports the imperfect interface effect in thermal metamaterials thoroughly. Low conductivity- and high conductivity-type interfaces are considered. We show that an object can always be made thermally invisible, with the effect of imperfect interface, as that of a homogeneous background material. This unprecedented condition is derived in an exact and analytic form, systematically structured, with much versatile and physical implications. Conditions for thermal shielding and enhancements are analytically found and numerically exemplified, highlighting the specific role of material and geometric parameters. We find that both types of interfaces are complementing with each other which, all together, will constitute a full spectrum to achieve the thermal invisibility. The analytic finding offers a general perception that adds to the understanding of heat transport mechanism across interfaces in thermal metamaterials, in ways that drastically distinct from that of ideal interfaces. This finding opens up new possibilities for the control and management of thermal metamaterials with imperfect bonding interfaces.

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.

Tunable thermal wave nonreciprocity by spatiotemporal modulation

Nonreciprocity is of particular importance to realize one-way propagation, thus attracting intensive research interest in various fields. Thermal waves, essentially originating from periodic temperature fluctuations, are also expected to achieve one-way propagation, but the related mechanism is still lacking. To solve the problem, we introduce spatiotemporal modulation to realize thermal wave nonreciprocity. Since thermal waves are completely transient, both the convective term and the Willis term induced by spatiotemporal modulation should be considered. We also analytically study the phase difference between two spatiotemporally modulated parameters, which offers a tunable parameter to control nonreciprocity. We further define a rectification ratio based on the reciprocal of spatial decay rate and discuss nonreciprocity conditions accordingly. Finite-element simulations are performed to confirm theoretical predictions, and experimental suggestions are provided to ensure the feasibility of spatiotemporal modulation. These results have potential applications in realizing thermal detection and thermal stabilization simultaneously.

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.

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.

Design of a reconfigurable broadband greyscale multiplexed metasurface hologram

Holograms are a promising state-of-the-art technique that are able to reproduce fully three-dimensional images. However, most elementary holograms only recover a nonadjustable image restricted by a certain amplitude and phase. Recently, the concept of the reconfigurable metasurface has come into sight. The reconfigurable metasurfaces can be tuned dynamically through a physics control signal from outside. Here we design and realize a series of novel, to the best of our knowledge, reconfigurable metasurfaces. Using these devices, an advanced metasurface hologram effect could be easier to achieve. Moreover, the reconfigurable property of such tunable metasurface enables independent control of advanced multiplexed channel functionalities to exist in comparison with the conventional static metasurface holograms. Our method creates unprecedented display and virtual effects, and it opens a novel way to a more flexible methodology of dynamic control of electromagnetic waves.

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.