Effective Properties Of Metamaterials Research Articles

Graph-based metamaterials: Deep learning of structure-property relations

The effective properties of metamaterials are tailored through the design of their internal structures. According to their main building block, the family of porous three-dimensional metamaterials is divided into truss-, plate- and shell-lattices. The exploration of their full design-space is hampered in practice by a lack of a systematic method to represent their topologies. Here, we demonstrate for the first time that graph models provide an effective representation of shell-lattices. This new graph representation is then leveraged to obtain deep learning-based structure–property models. Using finite element simulations, the stiffness and heat conductivity tensors are established for more than 40,000 microstructural configurations. We find that a modified crystal graph convolutional neural network model provides an accurate description of the structure–property relations. We anticipate the proposed graph-based modeling framework to be applicable to any man-made periodic microstructure, thereby enabling the design and discovery of new materials exhibiting exceptional mechanical, thermal, electrical or magnetic properties.

Beyond local effective material properties for metamaterials

To discuss the properties of metamaterials on physical grounds and to consider them in applications, effective material parameters are usually introduced and assigned to a given metamaterial. In most cases, only weak spatial dispersion is considered. It allows to assign local material properties, i.e. a permittivity and a permeability. However, this turned out to be insufficient. To solve this problem, we study here the effective properties of metamaterials with constitutive relations beyond a local response and take strong spatial dispersion into account. The isofrequency surfaces of the dispersion relation are investigated and compared to those of an actual metamaterial. The significant improvement provides evidence for the necessity to use nonlocal material laws in the effective description of metamaterials. The general formulation we choose here renders our approach applicable to a wide class of metamaterials.

Hybridization effect in coupled metamaterials

Although the invention of the metamaterials has stimulated the interest of many researchers and possesses many important applications, the basic design idea is very simple: composing effective media from many small structured elements and controlling its artificial EM properties. According to the effective-media model, the coupling interactions between the elements in metamaterials are somewhat ignored; therefore, the effective properties of metamaterials can be viewed as the "averaged effect" of the resonance property of the individual elements. However, the coupling interaction between elements should always exist when they are arranged into metamaterials. Sometimes, especially when the elements are very close, this coupling effect is not negligible and will have a substantial effect on the metamaterials' properties. In recent years, it has been shown that the interaction between resonance elements in metamaterials could lead to some novel phenomena and interesting applications that do not exist in conventional uncoupled metamaterials. In this paper, we will give a review of these recent developments in coupled metamaterials. For the "meta-molecule" composed of several identical resonators, the coupling between these units produces multiple discrete resonance modes due to hybridization. In the case of a "meta-crystal" comprising an infinite number of resonators, these multiple discrete resonances can be extended to form a continuous frequency band by strong coupling. This kind of broadband and tunable coupled metamaterial may have interesting applications. Many novel metamaterials and nanophotonic devices could be developed from coupled resonator systems in the future.

A method to determine effective metamaterial properties based on stratified metafilms

Metamaterials’ properties may be quantified through the assignment of bulk material parameters such as magnetic permeability and electric permittivity. These assignments rely on the assumption that metamaterials are effective media, in this context meaning that their electromagnetic properties are independent of the sample size. This assumption is not always valid, particularly for metafilms, the surface equivalents of metamaterials. However, metamaterials comprised of numerous metafilm and dielectric layers can be uniquely characterized in the effective medium approximation when all aspects of the metamaterial are properly integrated. We present a simple model based on stratified systems to illustrate this fact. The model further assists in the interpretation of novel metamaterial behaviors and offers a rapid and accurate method to determine the functionality of bulk metamaterial-based devices.

Effective properties of amorphous metamaterials

We experimentally and numerically study the propagation of light through amorphous metamaterials. For this purpose we introduce a precisely controllable degree of positional disorder into a perfectly periodic system, transforming it to a partially disordered and ultimately an amorphous metamaterial. The observable spectral features occurring upon this transition and the impact of coherent interactions among neighboring unit cells are revealed. Backed by numerical simulations, the effective properties of the metamaterials are retrieved, most notably for the amorphous one. The most important finding with respect to negative index materials is that their magnetic properties are not affected by an arbitrarily high degree of disorder. This work enables the quantitative evaluation of effective properties of amorphous metamaterials fabricated by bottom-up approaches.