Advances and Frontiers in Metamaterials

In optics, the direction of light propagation is manipulated by the shapes of objects and their refractive indexes, thus achieving optical devices such as convex and concave lenses. With increased understanding of materials, researchers are exploring deeper into the microscopic fields and have focused on microstructures of materials. In condensed matters, crystals are solid-state materials with constituents and atoms arranged periodically in space resulting in a variety of extraordinary properties. When it comes to the classical systems, structures of subwavelength scales also exhibit many novel phenomena, such as negative refraction, invisible cloaking and superresolution imaging, and they are usually analyzed in the fields of wave optics or acoustics. In 1987, Eli Yablonovitch (Yablonovitch, 1987) and Sajeev John (John, 1987) first proposed the concept of photonic crystals to describe the propagation of optical waves in the refraction indexmodulated periodic structures, as well as the theory of photonic band structures, which paves a new way to manipulate light using photonic crystals and explore wave effects therein and applications (Cregan, 1999; Knight, 2003). Subsequently, a similar concept in acoustic systems was also presented in 1993, which is known as sonic/phononic crystals (Kushwaha et al., 1993; Sigalas and Economou, 1993) and has also been extended to practical applications (Miniaci et al., 2017). To better manipulate the wave-propagating behaviors, functional microstructures were designed to realize various extraordinary properties. These microstructures are known as metamaterials. Sir John Pendry proposed the idea of wire mesh (or cut-wire) systems to achieve negative values of effective permittivities in microwaves (Pendry et al., 1996) in 1996, and other periodically arranged local resonant structures (such as split resonant rings) for negative values of effective permeabilities in microwaves (Pendry et al., 1999) in 1999. Soon afterwards, metamaterials with simultaneously negative permittivity and permeability were realized and verified inmicrowave experiments by Smith et al. (Smith et al., 2000), as well as other negative refractive index materials (Smith, 2004). Other important local resonant structures in microwaves were also proposed, such as H-fractal structures (Wen et al., 2002). In addition, for acoustic systems, metamaterials with subwavelength scales have developed rapidly using locally resonant sonic structures (Liu, 2000), which exhibits spectral phononic band gaps in the long wavelength range and could be regarded as effective densities and elastic moduli. These properties pave the way for various applications of metamaterials, including perfect lenses (Pendry, 2000). In 2006, Leonhardt and Sir John Pendry et al. initiated the field of transformation optics (Leonhardt, 2006; Pendry, 2006) based on the form invariance of Maxwell’s equations under coordinate transformations. With the development of the above metamaterials with customized material parameters, invisibility cloaks (Schurig et al., 2006; Chen et al., 2007; Liu et al., 2009) and other intriguing devices (Chen et al., 2010) were implemented. Such a concept was later on extended to acoustics (Chen and Chan, 2007; Cummer and Schurig, 2007), surface water waves (Farhat et al., 2008; Chen et al., 2009; Li et al., 2018), and thermal dynamics (Fan et al., 2008; Schittny et al., 2013). Since then, the associated topics from metamaterials have greatly attracted research interests and have been studied for decades. Edited and reviewed by: Nicola Maria Pugno, University of Trento, Italy