Metamaterials and Their Devices

Over the past two decades, metamaterials (MMs) have led to major advancements in new material science through the artificial arrangement of electric and magnetic resonance structures (meta-atoms) at the subwavelength scale. In particular, they have enriched the fundamental rules behind matter–light interactions, encompassing phenomena such as slow light, super-resolution, super-lensing, and electromagnetic (EM) cloaking. MMs have received considerable attention as they have a very similar appearance to real-world devices, such as perfect absorbers. EM MMs have demonstrated remarkable responses to incident EM waves, such as a negative refraction index, extraordinary optical transmission, electromagnetically induced transparency-like effects, and the potential for use as ultra-thin and broadband absorbers. The optimal structures, structural parameters, and material properties used to yield the effective electric permittivity [εeff(ω)] and effective magnetic permeability [μeff(ω)] of MMs have been formulated based on the effective medium theory. Research on controlling EM responses and their spatial distribution and dispersion has undergone considerable advancement and led to the development of devices with a range of potential real-world applications. In MM research, emerging areas of interest include nonlinear, switchable, gain-assisted sensor quantum, and coding MMs. This Special Issue on “Metamaterials and their devices” aims to cover a broad range of MMs, lattice MMs, crystal materials and structures, plasmonic and dielectric MMs, photonic crystals, phononic crystals, and metasurfaces, along with relevant fundamental issues and emerging research fields for MMs. In addition, an exploration of the electromagnetic response, magnetic resonance, and electric resonance of MMs is carried out, along with a discussion of relevant numerical methods and applications. This Special Issue contains a mixture of review articles and original contributions.

A tellurium photonic crystal-based terahertz polarization splitter using a diamond-shaped ferrite pillar array was investigated by Zhang et al. [1]. A T-shaped photonic crystal waveguide was designed with square lattice tellurium photonic crystals. A diamond-shaped ferrite pillar array was inserted into the junction of the waveguide to create a novel terahertz polarization splitter. Both the electric and magnetic transverse modes were numerically investigated using the plane wave expansion method, which covered all photonic band gaps ranging from 0.138 to 0.144 THz. For fully polarized band gaps in this frequency domain, the transmission efficiency of the photonic crystal waveguide reached values of up to −0.21 dB and −1.67 dB for the electric and magnetic transverse modes, respectively. Under the action of a DC magnetic field, the THz waves were rotated 90 degrees by the diamond-shaped ferrite pillar array. Transverse electric waves or transverse magnetic waves can be separated (using six smaller tellurium rods) from the fixed waves with a polarization isolator. The characteristics of the polarization splitter were analyzed using the finite element method, and its transmission efficiency was optimized to 95 percent by fine-tuning the radii of the thirteen ferrite pillars. The future development of an integrated sky–earth–space communication network would require fully polarized devices in the millimeter and terahertz wavebands. The polarization splitter designed in this study has a unique function and provides a promising method for the realization of fully polarized 6G devices.

Analyses of the low-frequency sound absorption performance and optimization of structural parameters for acoustic metamaterials were studied by Luo et al. for their use in spatial double-helix resonators [2]. Low-frequency noise absorbers often require large structural dimensions, constraining their development for practical applications. In order to improve space utilization, an acoustic metamaterial with a spatial double helix, called a spatial double-helix resonator, was proposed. An analytical model of the spatial double-helix resonator was established and verified by numerical simulations and impedance tube experiments. When comparing the acoustic absorption coefficients of the spatial double-helix resonator, the results of the analytical model, the numerical model, and the experiments were found to be in good agreement, demonstrating the accuracy of the theoretical model. The effects of different structural parameters on the peak sound absorption coefficient and resonance frequency were shown quantitatively. The impedance variation law of the model was obtained, and the resistance and reactance distributions at the resonance frequency were analyzed. In the optimization model, a Back Propagation (BP) network was used to construct a mapping between the structural parameters and the resonance frequency and sound absorption coefficient, and this was used as a constraint in the equation. This formulation was then combined with Wild Horse Optimization (WHO) to establish the BP-WHO model, which was used to minimize the volume of the spatial double-helix resonator. The results show that, for a given noise frequency, the optimized structural parameters enhanced space utilization without affecting the performance of the space double-helix resonator.

Directional acoustic bulk waves in a two-dimensional (2D) phononic crystal were examined by Deymier et al. [3]. They used the transfer matrix method to investigate conditions conducive to the existence of directional bulk waves in a 2D phononic crystal. The 2D crystal was a square lattice of unit cells composed of rectangular subunits, comprising two different isotropic continuous media. They established the geometry of the phononic crystal and its constitutive media for the emergence of waves, which, for the same handedness, exhibited a non-zero amplitude in one direction within the crystal’s 2D Brillouin zone and zero amplitude in the opposite direction. Due to time-reversal symmetry, the crystal supported wave propagation in the reverse direction for the opposite handedness. These features may enable the robust directional propagation of bulk acoustic waves, and topological acoustic technology.

Duong et al. [4] enhanced the electromagnetic wave absorption properties of an FeCo-C alloy by using a metamaterial structure. This study presents a tri-layer broadband metamaterial absorber that operates in the GHz range. The absorber was composed of a polyhedral iron–cobalt alloy/graphite nanosheet material arranged in a flat sheet configuration, with two punched-in rings for the top layer, a continuous FR-4 layer in the middle, and a continuous copper layer at the bottom. For an electromagnetic wave with normal incidence, the proposed absorber demonstrated exceptional broadband absorption in a frequency range of 7.9–14.6 GHz, exceeding 90%. The absorption magnitude remained above 90% in a frequency range of 8–11.1 GHz for transverse electrically polarized waves at incident angles of up to 55°. For both transversely-polarized magnetic and electric waves, the absorption exceeded 90% in a frequency range of 9.5–14.6 GHz. The physical mechanism behind these absorption properties was analyzed thoroughly by examining the electric and magnetic field distributions. The obtained results could contribute to the development of microwave applications based on metamaterial absorbers, such as radar stealth technology, electromagnetic shielding for health and safety, and reduced electromagnetic interference for high-performance communications and electronic devices.

Sun et al. [5] proposed a locally disordered metamaterial for directing and trapping water waves. Manipulating the flow of water wave energy is crucial for ocean wave energy extraction or coastal protection, and the emergence of metamaterials could lead to a new method for controlling water waves. In this work, by introducing local disorder into a cavity-type metamaterial constructed with split-tube resonators, they showed that water waves could be guided in an open channel, with multiple energy flow paths formed by disconnected concurrent resonators surrounding the metamaterial. These resonators serve as invisible walls without the need for a whole array system, such as general periodic structures or waveguides. Specifically, they numerically and experimentally validated that a T-shaped metamaterial can be used to freely guide water waves in a narrow band and a band-edge state along a distinct path. This open-space water waveguide process was found to be dominated by Fano-type interference and Fabry–Pérot resonance. Two distinct propagating modes, a low-frequency “trapping mode” and a high-frequency “following mode”, were identified. By simply rotating two configuration-dependent unit cells at the intersection of the metamaterial, they produced a variety of water-waveguiding paths tuned along the rectilinear or bending (splitting or turning) directions, which rely on the two different propagating modes.

Qian et al. [6] theoretically investigated optical bistability in superconductor–semiconductor photonic crystals composed of graphene to ascertain the temperature dependence. The photonic crystals were symmetric about their center and arranged with alternating superconductor (HgBa₂Ca₂Cu₃O₈+δ) and semiconductor (GaAs) layers. This system supports a defect mode, and graphene is located at the layer interface where the local electric field is the strongest. Consequently, the optical nonlinearity of graphene was greatly enhanced, and low-threshold optical bistability can be achieved with an incident wavelength that is red-detuned to the defect mode. The upper and lower thresholds of bistability increase with increasing environmental temperature, while the interval between the upper and lower thresholds decreases. This research has the potential to facilitate further research into temperature-controlled optical switches and temperature-controlled optical memory.

This Special Issue on “Metamaterials and Their Devices” can be considered a status report reviewing the progress that has been achieved over the past two decades in the field of metamaterials and devices.