Keywords

3.1 Opening Remarks

The intersection of theoretical modeling and experimental techniques has been pivotal in the advancement of metamaterials, enabling the realization of artificial properties with remarkable precision and versatility. Rooted in a variety of theoretical frameworks [1,2,3,4,5,6], experimental techniques under the effective medium theory range from the utilization of composites for inhomogeneous properties [7], to the employment of layered structures for pronounced anisotropic properties [8], and the application of rotating structures for tunability [9]. Further extending into the realm of adaptive or active responses, metamaterials incorporate intricate control mechanisms such as motors [10] and convection processes [11], showcasing their potential for dynamic and responsive applications. This chapter aims to elucidate the experimental realizations of these theoretical concepts, emphasizing how their practical implementation aligns with and enriches the theoretical predictions, thereby laying the groundwork for innovative applications in various scientific domains (Table 3.1).

Table 3.1 Common experimental methods employed in metamaterials for passive, adaptive and active regulation and their corresponding applications. Some of applications may work well in heat transfer, electromagnetic, Darcy fluid, particle diffusion, etc
Full size table

3.2 Passive Artificial Metamaterials Like Composites and Layered Structures

Both the Maxwell-Garnett and Bruggeman theories serve as core components of the effective medium theory (EMT) when dealing with composites. Given that we can perforate a single structure with varying shapes of holes, densities, and distributions [7, 12, 13], these theories are frequently used to model artificial isotropic yet inhomogeneous parameters using only one material and a single fabrication step. The Maxwell-Garnett theory applies particularly in scenarios where unconnected particles are uniformly embedded in an isotropic matrix, in which the deviation become larger when particle fraction is higher. In contrast, the Bruggeman theory is pertinent in systems where it’s impossible to distinguish between the overlapping particles and the matrix, allowing for a varied particle fraction ranging from 0 to 1. At some cases the embedded particle can be elliptical and ordered-oriented to achieve anisotropy, as confirmed by a thermal conduction experiment [14]. These models facilitate the design of materials with specific electromagnetic, thermal or diffusion parameters [15], essential for various practical applications.

Layered structures represent another critical aspect of effective medium theory. The first experimental demonstration of thermal metamaterials used layered structures to realize anisotropic material parameters [8]. The layered structures are later extended to diverse functions [12, 16, 17]. As an example, we use the isotropic materials B and C to construct an alternate layered structure A. The effective parameters in the perpendicular, \(A_\perp \), and parallel direction, \(A_\parallel \), are different, i.e., \(A_\perp =1/ (f_B / A_B+f_C / A_C )\) and \(A_\parallel =f_B A_B+f_C A_C\). \(f_B\) and \(f_C=1-f_B\) are their area/volume fractions. Here, interfacial resistance may slightly affect these parameters and reduce the effective anisotropy [18, 19], but this effect can be easily compensated by fine-tuning the fractions \(f_B\) and \(f_C\). Later the extremely anisotropic metamaterials is developed [20], with almost infinite thermal conductivity in one direction and zero in perpendicular directions. One can choose air as material C in layered structures to achieve such extreme anisotropy with only one natural material. And the designed metamaterials adaptively respond to environment change because of the transformation-invariance [21].

3.3 Adaptive Metamaterials with External Field-Dependent Response

Different with extremely anisotropic metamaterials, materials boasting adaptive capabilities are crucial for real-time responsiveness to environment changes in the domain of dynamic thermal or diffusion management. These include materials sensitive to external fields, such as shape-memory alloys [22] and certain ferroelectric substances [23], together with substances with nonlinear thermal radiation characteristics [2], which are the cornerstones of the engineering of adaptive thermal metamaterials.

Shape-memory alloy serves a prime example in temperature-dependent materials. This alloy undergoes a reversible phase transformation in response to changes in ambient temperature, which allows it to ’remember’ and revert to touched or untouched state upon heating cycle. Autonomous huge adjust of thermal conductivity can perform different functions in different backgrounds, such as temperature-dependent thermal diodes [22] or structures that maintain temperature without energy input [24]. This is of particular value in precision instruments where equilibrium must be maintained despite fluctuations, and in passive thermal management systems where active control is not feasible. On the other hand, ferroelectric materials such as Strontium Titanate (SrTiO3) cuboids illustrate the capacity of temperature-dependent materials to adaptively modify frequency bands [23], thereby enabling frequency-agile invisibility according to transformation optics. This adaptability eliminates the necessity for complex redesigns across varying frequency regions.

As for nonlinear thermal radiation, the \(\varepsilon \sigma T^4\) nature leads to nonlinear temperature-related emissivity \(\varepsilon \) [23] or combines radiative \(T^4\) with conductive \((\nabla T)^1\) for adaptive tuning [2]. Nanoscale Pt and Ag electrodeposition can exhibit a sharp emissivity transition at a specific temperature [25], enhancing infrared imaging around particular temperatures and increasing the sensitivity. Such materials adjust their radiation profiles, allowing for modulation that aligns with the surrounding thermal environment. Another kind of material, taking cues from omnithermal metamaterials [3], leverages the interplay of conduction, convection, and radiation to adaptively switch its thermal properties. With precise engineering, these materials demonstrate a dual behavior that they exhibit thermal transparency at normal temperatures through conduction, and switch to thermal cloaking at higher temperatures by prioritizing radiation.

In summary, the development of external field-dependent diffusion metamaterials signals a transformative leap in adaptive control strategies, offering a major advancement over traditional systems and heralding a new era of intelligent management systems.

3.4 Active Controllable Metamaterials

Active materials usually undergo real-time changes in their properties or behavior under artificial control, enabling a single structure to actively adapt to multiple application scenarios beyond fixed adaptive parameters. The adaptive materials typically respond passively to environmental changes. While the active materials not only adjust to suit various functional requirements but also possess additional capabilities, such as hall-like thermal chirality, spatiotemporal encircle, self-repair or environmental responsiveness and dynamical EP encircling with geometric phase.

The introduction of rotating structures [9, 26, 27] facilitates room-temperature, Hall-like heat transfer without magnetic influence [10]. This structure composed of a stationary solid framework interspersed with rotating particles, breaks the conventional Onsager reciprocal relations, resulting in a marked increase in thermal chirality, and pushing the boundaries of effective thermal conductivity to levels unachievable through the thermal Hall effect alone. When the rotating structure equipped with intelligent environment sensing, the thermal transport will react automatically with deep learning [28]. These breakthroughs light the way for novel explorations in topological and non-Hermitian thermal transport and propose innovative pathways for efficient heat utilization that deviate from phonon-dominated models.

Drawing upon temporal mechanical deformation cycles, active materials informed by spatiotemporal theory have been developed [29,30,31]. Structures can be engineered as composite systems [32,33,34], featuring concentric rings differentiated by their thermal conductivities. Designed for periodic structural modulation over time, they manipulate heat flow in a controlled manner. The metamaterials employ an advanced actuation mechanism that rotates the ring layers, creating an effectively time-variant structure. This adaptability allows the materials to oscillate between thermal states, ranging from insulating to conducting [34], echoing the dynamic control seen in electromagnetic metamaterials over wave propagation. The precision of these rotations facilitates the replication of sophisticated thermal phenomena such as thermal cloaking and concentration, granting the power to dictate thermal visibility. In addition to modulating thermal pathways, these materials can apply to thermoelectric encoding sequences [32], marking an evolution in adaptive material systems that are not only responsive to environmental changes but also exhibit intelligent, autonomous behavior.

The integration of rotation structures and mechanical cycles necessitates precise design parameters for both the structure and its background. To bolster robustness, advanced designs of active materials now incorporate mechanisms for energy gain and loss. For example, the integration of thermoelectric generators into active materials considerably broadens their applicability [35]. This union of materials with programmed control systems gives rise to real-time, self-adaptive metasurfaces capable of active temperature regulation. Such platforms function through the autonomous evaluation of thermoelectric heat sources and the real-time modulation of driven voltage, and maintain predefined thermal patterns irrespective of external environmental influences. Another strategic innovation within external gain and loss is the implementation of copper cylinders to delineate isothermal boundaries [36]. These cylinders serve as thermal dipoles, a concept extendable to quadrupoles and higher-order moments. By employing a core-shell structure with these dipoles, one can achieve simultaneous invisibility in thermal and electrical domains using commonplace materials and straightforward architectures. The exploration of dipole effects and the derivation of requirements for the shell and dipole, even in anisotropic materials, align with finite-element simulations. Such theoretical and practical alignments not only streamline thermal and electrical management but may also extend benefits to other physical domains, like electrostatics and magnetostatics. This multifaceted approach to material design underscores a trend towards integration and intellectualization in metamaterials, aiming to elevate the efficiency of physical field manipulation.

To obtain a topological Hamiltonian in thermal system, the convection pairs are considered to obtain relevant gain and loss [37], and \(\rho c\) in thermal system can mimic diffusive nonreciprocal SSH model [38]. The thermal dynamics thus reveal a previously underemphasized topological propagation with channel pairs with opposite convection velocity. Varying advective configurations lead to moving around the parameter space, creating the dynamic encircling of EP and realizing the geometric phase. The exponential gradient of \(\rho c\) corresponds to the nonreciprocal coupling coefficient between the nearest units, indicating the bulk and edge states in a thermal system. These approaches illuminates distinct phase transitions, offering pathways for robust thermal processes and nonchiral thermal diffusion, previously uncharted territories in conventional thermal materials. These advancements herald fresh prospects for topological thermal sciences.

3.5 Conclusions and Outlook

This chapter traces the evolution of metamaterials, with a particular focus on how experimental methods have enabled the progression from passive to adaptive, and ultimately to active metamaterials. Passive metamaterials, foundational to this field, mostly utilize effective medium theory with composites and layered structures, achieving control over properties like inhomogeneity and anisotropy. Despite their foundational role, the static nature of these materials lead to the exploration of more dynamic systems. Adaptive metamaterials emerge next, featuring materials with external field-dependent functions, showcasing adaptability to environmental changes through intricate experimental methods. However, their dependence on external stimuli for adaptation underscore the necessity for more autonomous systems. Addressing this, active metamaterials represent the current pinnacle of this evolution. Incorporating advanced experimental techniques such as motor-controlled units and thermoelectric elements, and applying principles like topological Hamiltonian in convection, these materials demonstrate a high degree of control and functionality, capable of dynamically responding to changes and user inputs. This chapter highlights the critical role of experimental methodologies in transforming the theoretical potential of metamaterials into reality, especially in the development of active systems that autonomously respond to environmental and operational conditions. The future of metamaterials points towards integrating sophisticated technologies such as artificial intelligence and machine learning, pushing the experimental capabilities to new frontiers.