Two-dimensional Metamaterials Research Articles

Hierarchical Fabrication of Plasmonic Superlattice Membrane by Aspect-Ratio Controllable Nanobricks for Label-Free Protein Detection.

Plasmonic superlattice membrane exhibits remarkable functional properties that are emerging from engineered assemblies of well-defined “meta-atoms,” which is featured as a conceptual new category of two-dimensional optical metamaterials. The ability to build plasmonic membranes over macroscopic surfaces but with nanoscale ordering is crucial for systematically controlling the light-matter interactions and represents considerable advances for the bottom-up fabrication of soft optoelectronic devices and circuits. Through rational design, novel nanocrystals, and by engineering the packing orders, the hybridized plasmon signature can be customized, promoting controllable near-field confinement for surface-enhanced Raman scattering (SERS) based detection. However, building such 2D architectures has proven to be remarkably challenging due to the complicated interparticle forces and multiscale interactions during self-assembly. Here, we report on the fabrication of ultralong-nanobrick-based giant plasmonic superlattice membranes as high-performance SERS substrates for ultrasensitive and label-free protein detection. Using aspect-ratio controllable short-to-ultralong nanobricks as building blocks, we construct three distinctive plasmonic membranes by polymer-ligand-based strategy in drying-mediated self-assembly at the air/water interfaces. The plasmonic membranes exhibit monolayered morphology with nanoscale assembled ordering but macroscopic lateral dimensions, inducing enhanced near-field confinement and uniform hot-spot distribution. By choosing 4-aminothiophenol and bovine serum albumin (BSA) as a model analyte, we establish an ultrasensitive assay for label-free SERS detection. The detection limit of BSA can reach 15 nM, and the enhancement factor reached 4.3 × 105, enabling a promising avenue for its clinical application in ultrasensitive biodiagnostics.

Dynamically tunable excellent absorber based on plasmon-induced absorption in black phosphorus nanoribbon

The realization of plasmon-induced absorption (PIA) via local plasmon resonance coupling on the surface of two-dimensional metamaterials based on nanostructures heavily depends on the well-designed patterned antenna. However, due to the limitation of nanostructures’ size and the difficulty of material formation, it is challenging to achieve the expected performance of such a device. We propose and numerically simulate PIA in response to mid-infrared using two black phosphorus (BP) layers that are composed of upper double BP ribbons and lower single BP ribbons to avoid BP chips patterning. The theoretical transmission spectrum of the structure calculated by the coupled mode theory is in good agreement with the simulated curve. The resonant intensity of the reflection window is affected by interlayer spacing, and the resonant wavelength of the reflection window can be realized by dynamically varying carrier density. The absorption performance of the system can be enhanced not only by the gold mirror that is totally reflected at the bottom of the structure but also by the polarization angle of the incident wave. The designed system could be expected on various optical devices, including plasmonic sensors, dual-frequency absorbers, and switch controllers.

Optical circular dichroism engineering in chiral metamaterials utilizing a deep learning network.

Here, a deep learning (DL) algorithm based on deep neural networks is proposed and employed to predict the chiroptical response of two-dimensional (2D) chiral metamaterials. Specifically, these 2D metamaterials contain nine types of left-handed nanostructure arrays, including U-like, T-like, and I-like shapes. Both the traditional rigorous coupled wave analysis (RCWA) method and DL approach are utilized to study the circular dichroism (CD) in higher-order diffraction beams. One common feature of these chiral metamaterials is that they all exhibit the weakest intensity but the strongest CD response in the third-order diffracted beams. Our work suggests that the DL model can predict CD performance of a 2D chiral nanostructure with a computational speed that is four orders of magnitude faster than RCWA but preserves high accuracy. The DL modelintroduced in this work shows great potentials in exploring various chiroptical interactions in metamaterials and accelerating the design of hypersensitive photonic devices.

Phase engineering with all-dielectric metasurfaces for focused-optical-vortex (FOV) beams with high cross-polarization efficiency

Metasurfaces, the two-dimensional (2D) metamaterials, facilitate the implementation of abrupt phase discontinuities using an array of ultrathin and subwavelength features. These metasurfaces are considered as one of the propitious candidates for realization and development of miniaturized, surface-confined, and flat optical devices. This is because of their unprecedented capabilities to engineer the wavefronts of electromagnetic waves in reflection or transmission mode. The transmission-type metasurfaces are indispensable as the majority of optical devices operate in transmission mode. Along with other innovative applications, previous research has shown that Optical-Vortex (OV) generators based on transmission-type plasmonic metasurfaces overcome the limitations imposed by conventional OV generators. However, significant ohmic losses and the strong dispersion hampered the performance and their integration with state-of-the-art technologies. Therefore, a high contrast all-dielectric metasurface provides a compact and versatile platform to realize the OV generation. The design of this type of metasurfaces relies on the concept of Pancharatnam-Berry (PB) phase aiming to achieve a complete 2π phase control of a spin-inverted transmitted wave. Here, in this paper, we present an ultrathin, highly efficient, all-dielectric metasurface comprising nano-structured silicon on a quartz substrate. With the help of a parameter-sweep optimization, a nanoscale spatial resolution is achieved with a cross-polarized transmission efficiency as high as 95.6% at an operational wavelength of 1.55 µm. Significantly high cross-polarized transmission efficiency has been achieved due to the excitation of electric quadrupole resonances with a very high magnitude. The highly efficient control over the phase has enabled a riveting optical phenomenon. Specifically, the phase profiles of two distinct optical devices, a lens and Spiral-Phase-Plate (SPP), can be merged together, thus producing a highly Focused-Optical-Vortex (FOV) with a maximum focusing efficiency of 75.3%.

Total phase shift of terahertz wave in a rectangular waveguide with zero-refractive index metamaterial

In many applications, appropriate spatial phase shifts in propagation of a THz wave are desired. Serving this purpose, a rectangular waveguide with two-dimensional photonic crystal zero-refractive index metamaterial is studied. In this structure, additional phase shift is computed in a numerical method in comparison with the same waveguide without zero-refractive index metamaterial. Modelling the characteristics of this waveguide, relations are presented which are shown to be compatible with numerical results. Then getting in inverse direction, a procedure is introduced in which, equivalent photonic crystals can be designed in terms of an arbitrary given phase shift with estimated errors of less than 1 degree. We also have calculated the sensitivity of additional phase difference with respect to the refractive index of rods, which showed relatively high dependence.

Cross-Entropy Method for Design and Optimization of Pixelated Metasurfaces

Electromagnetic metasurfaces are planar two-dimensional metamaterials, typically of subwavelength thickness. Unit cell elements of different shapes have been widely explored, including electric and magnetic dipoles, patches, arbitrary geometries and pixelated surfaces. Although pixelated metasurfaces have a great advantage of geometric versatility, their design and analysis requires algorithmic approach. One of the techniques for their design is via evolutionary simulation-driven optimization. Since full-wave electromagnetic simulations are time-consuming, optimization methods with fast convergence properties are preferable. In this article, we demonstrate the application of the cross-entropy optimization method to design of artificial magnetic conductors (AMCs) and thin printed phase shifters. Single-frequency AMCs at 10 GHz (X band) and dual-frequency AMCs at 8 and 12 GHz (X and Ku band) were produced that are more manufacturing-friendly, and thus cost effective, than previously reported AMCs. We also show that phase-shifting unit cells with transmission magnitudes over 0.9 (linear) can be designed using the proposed optimization technique. Other potential applications of these unit cells are in phase-correcting and beam-steering metasurfaces.

Tunable metasurfaces based on phase-change materials

Due to their superior ability to control light, metasurfaces, ultrathin two-dimensional metamaterials composed of subwavelength nanostructures, have attracted great attention in recent years. Exploring geometric and material freedom in designing elementary nanostructures and their ambient environment of metasurfaces enables versatile optical devices, such as planar metalenses, holographic imaging and thermal radiators. With phase-change materials (PCMs) such as GeSbTe and VO<sub>2</sub> integrated into metasurfaces, the optical functionalities of metasurfaces can be flexibly tuned by exploiting the phase transitions of PCMs induced by external stimuli, thereby opening up new directions and perspectives for dynamic tunable metamasurfaces. In this article, we review the recent progress of tunable metasurfaces based on PCMs, analyze their underlying working mechanisms and highlight their important applications. We conclude this review by bringing our perspectives on challenges and future directions in this field.

First-principles Modeling of Thermal Transport in Materials: Achievements, Opportunities, and Challenges

Thermal transport properties have attracted extensive research attentions over the past decades. First-principles-based approaches have proved to be very useful for predicting the thermal transport properties of materials and revealing the phonon and electron scattering or propagation mechanisms in materials and devices. In this review, we provide a concise but inclusive discussion on state-of-the-art first-principles thermal modeling methods and notable achievements by these methods over the last decade. A wide range of materials are covered in this review, including two-dimensional materials, superhard materials, metamaterials, and polymers. We also cover the very recent important findings on heat transfer mechanisms informed from first principles, including phonon–electron scattering, higher-order phonon–phonon scattering, and the effect of external electric field on thermal transport. Finally, we discuss the challenges and limitations of state-of-the-art approaches and provide an outlook toward future developments in this area.

Equilibrium of Two-Dimensional Cycloidal Pantographic Metamaterials in Three-Dimensional Deformations

A particular pantographic sheet, modeled as a two-dimensional elastic continuum consisting of an orthogonal lattice of continuously distributed fibers with a cycloidal texture, is introduced and investigated. These fibers conceived as embedded beams on the surface are allowed to be deformed in a three-dimensional space and are endowed with resistance to stretching, shearing, bending, and twisting. A finite element analysis directly derived from a variational formulation was performed for some explanatory tests to illustrate the behavior of the newly introduced material. Specifically, we considered tests on: (1) bias extension; (2) compressive; (3) shear; and (4) torsion. The numerical results are discussed to some extent. Finally, attention is drawn to a comparison with other kinds of orthogonal lattices, namely straight, parabolic, and oscillatory, to show the differences in the behavior of the samples due to the diverse arrangements of the fibers.

Synthesizing and reconfiguring metastable modular metamaterials for adaptive wave propagation control

This research uncovers new insights and novel methodology to synthesize tunable wave propagation characteristics in a metastable modular metamaterial by reconfiguring the modules and system metastable states. The reconfigurable criteria of the one-dimensional (1D) metastable modular metamaterial are rigorously investigated to provide insights on the tunability of such metamaterials. A sufficient condition for reconfigurability is derived analytically, following the numerical solutions of the sufficient and necessary condition. An inverse problem is then formulated to achieve desirable band structures via switching the modular internal configurations and metastable states in one-dimensional and two-dimensional (2D) metamaterials. Exploiting the correlation between the unique on-off feature of the modules’ metastable states and the binary nature of the Genetic Algorithm (GA) approach, GA is utilized to decide the reconfiguring action of each module to achieve the desired band structure. With this method, we show that wave propagation in 1D and 2D metastable modular metamaterials can be controlled adaptively by on-demand reconfiguration of the modules.

Direct-tuning methods for semiconductor metamaterials

Among various tunable optical devices, tunable metamaterials have exhibited their excellent ability to dynamically manipulate lights in an efficient manner. However, for unchangeable optical properties of metals, electromagnetic resonances of popular metallic metamaterials are usually tuned indirectly by varying the properties or structures of substrates around the resonant unit cells, and the tuning of metallic metamaterials has significantly low efficiency. In this paper, a direct-tuning method for semiconductor metamaterials is proposed. The resonance strength and resonance frequencies of the metamaterials can be significantly tuned by controlling free carriers’ distributions in unit cells under an applied voltage. This direct-tuning method has been verified in both two-dimensional and three-dimensional semiconductor metamaterials. In principle, the method allows for simplifying the structure of tunable metamaterials and opens the path to applications in ultrathin, linearly-tunable, and on-chip integrated optical components (e.g., tunable ultrathin lenses, nanoscale spatial light modulators and optical cavities with resonance modes switchable).

X-shaped chiral plasmonic nanostructured metasurfaces: A numerical study

In this paper, the author reports a numerical investigation of spectroscopic circular dichroism (CD) properties, near-field enhancement, and optical chirality near a chiral plasmonic nanostructured metasurface. The individual constituents of the metasurface consist of periodic X-shaped Au nanostructures on a glass substrate. The nanostructure is made of two overlapping nanorods, including one vertical nanorod and one tilted nanorod. Strong CD of the metasurface was observed and tunable upon rotation of the individual nanorods due to geometrical symmetry breaking. Near-field enhancement of up to 5 times and a large local optical chirality were found at a plane 20 nm above the X-shaped nanostructure. Electromagnetic modeling analysis provides valuable guidelines for designing alternative two-dimensional chiral metamaterials that have potential applications for enhanced molecule and chiral plasmon interaction.

Topology optimization of 2-D mechanical metamaterials using a parametric level set method combined with a meshfree algorithm

Two-dimensional (2-D) micro-architectured mechanical metamaterials are designed using a topology optimization approach that integrates a parametric level set method (PLSM) with a meshfree method based on compactly supported radial basis functions (CS-RBF). The PLSM is employed as the optimization algorithm to achieve desired microstructures with targeted material properties. The effective elastic properties, including the bulk modulus, shear modulus and Poisson’s ratio, are predicted using a strain energy-based homogenization method and the CS-RBF meshfree algorithm. Two sets of optimizations are implemented: one is for the case of a single solid material, and the other is for the case of two solid materials, each involving an additional void phase. Three numerical examples are provided for each case with the same optimization objectives: maximizing the effective bulk modulus, maximizing the effective shear modulus, and minimizing the effective Poisson’s ratio under given volume fraction constraints. The numerical results reveal that the newly proposed approach can generate smooth topological boundaries and optimal microstructures. In particular, the current method can topologically optimize auxetic metamaterials with a negative Poisson’s ratio. It can also be extended to design other periodic metamaterials, including those with a negative coefficient of thermal expansion or frequency bandgaps.

When metasurface meets hologram: principle and advances

Holography has numerous applications because of its capability of arbitrary wavefront modulation. Computer-generated holograms (CGHs) take it a big step forward. Conventional holography engineers the wavefront via phase accumulation, suffering from large size, low resolution, and small viewing angle. Metasurfaces, ultrathin two-dimensional metamaterials with subwavelength features, can manipulate the amplitude, phase, and polarization of the light, solving the above issues. In this review, advances of holography, CGH algorithms, and the principles of various metasurfaces are presented. Metasurface holography, realized by encoding the hologram in the metasurface, is investigated. Information multiplexing methods of metasurface holograms, including wavelength-multiplexed, polarization-multiplexed, complex amplitude modulated, nonlinear, and dynamic metasurfaces, are presented. The challenges and outlook of metasurface holograms are discussed.

High-Transmission Ultrathin Huygens’ Metasurface with 360° Phase Control by Using Double-Layer Transmitarray Elements

Metasurfaces (two-dimensional metamaterials) have attracted much attention in recent years. However, due to the symmetric design of its cascaded elements, a traditional transmission-type metasurface must be at least three layers thick to achieve high transmission and 360\ifmmode^\circ\else\textdegree\fi{} phase control simultaneously. This study presents an ultrathin Huygens' metasurface, composed of double-layer antisymmetric transmitarray elements, that can realize high transmission and 360\ifmmode^\circ\else\textdegree\fi{} phase control at once. Based on this metasurface, a high-gain ultrathin (3.3% of the wavelength) transmitarray antenna is created, with an aperture efficiency of 61.04% at the working frequency.

Multi-displacement continuum modelling of the metamaterial plate with periodical arranged resonators

• The wave propagation in a metamaterial plate with periodically arranged resonators is studied. • The additional displacement fields are introduced to characterize the response of resonators. • The function variation principle is used to derive the governing equations of Bloch waves. • The propagation along symmetric direction and any oblique direction are both considered. • The influences of interface conditions on the dispersion feature under the oblique propagation are first discussed. Multi-displacement continuum modelling of a two-dimensional (2D) elastic metamaterials plate with periodically arranged local resonator over the surface of the plate is studied in this paper. The additional displacement fields are introduced to model the response of the local resonators. The continuous conditions between the adjacent unit-cells are used to reflect the periodicity of the microstructured continuum and resultantly turned into the constraint conditions between the additional displacement field and the other continuous field. The dispersion features of the multiple-displacement coupled wave propagating along the high symmetrical direction and any oblique direction are both studied numerically. It is found that the multi-displacement coupled waves can be divided into the coupled longitudinal wave and the coupled transversal wave when propagating along the highly symmetric direction but cannot be divided into the coupled longitudinal wave and the coupled transversal wave when propagating along any oblique direction. The effects of boundary conditions on the dispersion of acoustic and optical branches of coupled waves are discussed in detail. At last, the influences of the parameters of resonator on the dispersion feature of the multi-displacement coupled waves are investigated numerically.

Tunable Dirac cones in two-dimensional acoustic metamaterials with matryoshka structure.

Dirac cones of an acoustic system are the foundation of most topological phase transitions and topological states and have recently become a research hotspot. Although the Dirac cones, Dirac-like cones, double Dirac cones, and semi-Dirac points are all skillfully designed, it is still indispensable to realize a tunable Dirac cone in a novel acoustic structure. This paper proposes two-dimensional acoustic metamaterials with matryoshka structure to achieve tunable Dirac cones and topological spin states. Dirac points can be obtained on the dispersion curves owing to the high symmetry. The concentric circular scattering units of the matryoshka structure are arranged in honeycomb lattices. By a rotating-scatterer mechanism to break the symmetry, the Dirac cone at K (K') is split and the topological spin states appear at the band valley. The existence of a topological transition with opposite Chern numbers as the rotating angle varies is also verified, and helical edge states are obtained along the interfaces separating the topologically opposite spin states insulators. Moreover, the frequency of the Dirac cone is tuned by rotating the inner structure in a double-layer matryoshka structure.

Wave propagation control and switching for wireless power transfer using tunable 2-D magnetic metamaterials

Abstract Magnetic metamaterials operating at low megahertz frequencies provide various important commercial and research applications. In this work, we investigate the control of wave propagation in two-dimensional (2-D) tunable magnetic metamaterials for wireless power transfer (WPT). The propagation control is achieved by using reconfigurable defect cavities formed in the metamaterial, which allows for the dynamic creation of various waveguide configurations with switching control. The physical mechanism for creating the cavity is described using Fano interference, in which the resonant frequency of the cavity falls into the bandgap of the metasurface. And the routing and transmission control of the proposed waveguide is easily achieved by resonant switching. The proposed approach allows highly localized, strong field confinement in the deep subwavelength scale of 2.6λ × 10−3. The transmission losses and bandwidths of various dynamically tunable metamaterial waveguides are experimentally characterized. This result can find useful applications for integrated surface wave devices and planar WPT.

Elastic Wave Propagation of Two-Dimensional Metamaterials Composed of Auxetic Star-Shaped Honeycomb Structures

In this paper, the wave propagation in phononic crystal composed of auxetic star-shaped honeycomb matrix with negative Poisson’s ratio is presented. Two types of inclusions with circular and rectangular cross sections are considered and the band structures of the phononic crystals are also obtained by the finite element method. The band structure of the phononic crystal is affected significantly by the auxeticity of the star-shaped honeycomb. Some other interesting findings are also presented, such as the negative refraction and the self-collimation. The present study demonstrates the potential applications of the star-shaped honeycomb in phononic crystals, such as vibration isolation and the elastic waveguide.

Deformation and stress concentration behavior of two-dimensional mechanical metamaterials

Deformation and stress concentration behavior of two-dimensional mechanical metamaterials