Two-dimensional Periodic Structures Research Articles

Periodical plasma structures controlled by external magnetic field

The characteristics of two-dimensional periodical structures in a magnetized plasma are studied using kinetic simulations. Ridges (i.e. spikes in electron and ion density) are formed and became more pronounced with an increase of magnetic field incidence angle in the plasma volume in the cylindrical chamber. These ridges are shifted relative to each other, which results in the formation of a two-dimensional double-layer structure. Depending on Larmor radius and Debye length up to 19 potential steps appear across the oblique magnetic field. The electrical current gathered into the channels is associated with the electron and ion density ridges.

A novel method for identifying surface waves in periodic structures

In this study, the propagation of surface waves in both one- and two-dimensional periodic structures is investigated. By combining finite element method, an energy distribution parameter is defined and a new method for identifying surface wave modes is suggested. The effectiveness of this new method is validated by comparing with some related studies. Furthermore, this method is used to study a two-dimensional periodic pile-soil system based on a three-dimensional numerical model and the dispersion curves of surface waves are easily obtained. To show the efficiency of attenuation zone, the responses of a finite periodic pile-soil system to a surface wave input are simulated. Results demonstrate that the region of excitation frequency in which vibration reduction occurs is fully consistent with the theoretical attenuation zone for surface waves. The advantage of this method is that it makes the study of surface waves more convenient and accurate.

A matrix-exponential decomposition based time-domain method for calculating the defect states of scalar waves in two-dimensional periodic structures

A time-domain method for calculating the defect states of scalar waves in two-dimensional (2D) periodic structures is proposed. In the time-stepping process of the proposed method, the column vector containing the spatially sampled field values is updated by multiplying it with an iteration matrix, which is written in a matrix-exponential form. The matrix-exponential is first computed by using the Suzuki's decomposition based technique of the fourth order, in which the Floquet–Bloch boundary conditions are incorporated. The obtained iteration matrix is then squared to enlarge the time-step that can be used in the time-stepping process (namely, the squaring technique), and the small nonzero elements in the iteration matrix is finally pruned to improve the sparse structure of the matrix (namely, the pruning technique). The numerical examples of the super-cell calculations for 2D defect-containing phononic crystal structures show that, the fourth order decomposition based technique for the matrix-exponential computation is much more efficient than the frequently used precise integration technique (PIT) if the PIT is of an order greater than 2. Although it is not unconditionally stable, the proposed time-domain method is particularly efficient for the super-cell calculations of the defect states in a 2D periodic structure containing a defect with a wave speed much higher than those of the background materials. For this kind of defect-containing structures, the time-stepping process can run stably for a sufficiently large number of the time-steps with a time-step much larger than the Courant–Friedrichs–Lewy (CFL) upper limit, and consequently the overall efficiency of the proposed time-domain method can be significantly higher than that of the conventional finite-difference time-domain (FDTD) method. Some physical interpretations on the properties of the band structures and the defect states of the calculated periodic structures are also presented.

Synthesis and photoluminescence property of hexangular star MoSe2 bilayer

Transition metal dichalcogenides (TMDs) have received widespread attention because of their excellent performances in the field of optoelectronic, nanoelectronic device and photocatalytic exploration. The structures of TMDs can be expressed by the MX2, M=Mo, W; X=S, Se, Te, etc. As a typical TMD, MoSe2 has a graphene-like two-dimensional periodic structure with perfect physical, photoelcrtonic and catalytic properties. Currently, there are various methods to prepare the nanolevel MoSe2, such as the mechanical exfoliation, physical vapor deposition (PVD), hydrothermal method, chemical vapor deposition (CVD), etc, and most studies focused on regular triangular morphologies of the surfaces of different substrates. The new morphology, such as the hexangular star bilayer, has not been systematically investigated. In this study, the hexangular star MoSe2 nanosheets are successfully synthesized by using a simple CVD method in an atmosphere of mixed H2/Ar with a flow rate ratio of 1:4. Molybdenum trioxide(MoO3) and selenium (Se) powders are chosen to be the Mo and Se source, respectively. Moreover, the structure of the obtained MoSe2 nanosheet is characterized by Raman, SEM, EDS, XRD and TEM. The results of Raman spectrum and SEM indicate that the hexangular star MoSe2 possesses a bilayer structure. The TEM characterization reveals that the MoSe2 is a single crystal with a hexagonal lattice structure and good quality. The heating time at high temperature has a remarkable influence on the MoSe2 bilayer growth process. The growth process of the hexangular star MoSe2 bilayer is inferred to experience a three-step process. First, Mo and Se sources are gasified into gaseous molecules and then the Mo molecules are selenized into the MoSe2 crystal nucleus under high temperature. Next, these crystal nucleus are in a triangular epitaxial growth under the action of carrier gas. As heating time increases, the space steric effect leads to different interlayer separations between the two MoSe2 layers in various stacking configurations, eventually forming a hexangular star bilayer. The PL result shows that the spectra split into two main emission peaks, i.e., the direct and indirect bandgaps of the hexangular star structure appearing at 1.53 eV (810.2 nm) and 1.78 eV (696.9 nm), respectively. It might be due to the spin-orbit coupling interaction between the double MoSe2 molecules. The wide spectral range of the MoSe2 bilayer indicates that it has a potencial application in the photoelectric detectors.

Size effects in bending deformation of a two-dimensional periodic structure

Size effects in bending deformation of a two-dimensional periodic structure

Tunable optical bound states in the continuum beyond in-plane symmetry protection

The formation of tunable bound states in the continuum (BICs) within photonic crystal (PC) slabs has been investigated by using a semianalytical coupled-wave theory framework. An analytic expression of the radiative wave has been derived in order to depict the condition of BICs. As a result, in addition to well-known symmetry-protected BICs, a novel type of vertical-cancellation BIC can be realized through continuously varying a given parameter to eliminate radiative waves at the boundaries. We investigated one-dimensional and two-dimensional (2D) periodic structures, and found that such tunable BICs can occur for a wide range of wave vectors by the selection of appropriate slab thicknesses. For a 2D PC slab, a ring of high-$Q$ modes is predicted and confirmed by numerical simulation.

Development and analysis of electro-optical microresonator with low range natural frequency

Microresonators are fundamental components integrated in a hosts of MEMS applications: safety and stability systems, biometric sensors, switches, mechanical filters, micromirror devices, material characterization, gyroscopes, etc. A constituent part of the microresonator is a diffractive optical element (DOE). Different methods and materials are used to produce diffraction gratings for DOEs. Two-dimensional or three-dimensional periodic structures of micrometer-scale period are widely used in microsystems or their components. They can be used as elements for microscale synthesis, processing, and analysis of chemical and biological samples. On the other hand microresonator was designed using composite piezoelectric material. In case when microscopes, vibrometers or other direct measurement methods are destructive and hardly can be employed for in situ analysis, indirect measurement of electrical signal generated by composite piezoelectric layer allows to measure natural frequency changes. Also piezoelectric layer allows to create a novel microresonator with controllable parameters, which could assure much higher functionality of microelectromechanical systems. The novel microresonator for pollution detection is proposed. Mathematical model of the microresonator and its dynamical, electrical and optical characteristics are presented.

Size effect and dynamic properties of 2D lattice materials

Abstract The dynamic analysis of two-dimensional (2D) periodic material structures is proposed via a novel mechanical approach. General assumptions include: i) the representative unit cell of the square lattice can be modeled by means of a defined number of straight micro-beams; ii) both shear/flexural and axial strains are locally accounted for; iii) a microstructure-dependent scale length is introduced as an intrinsic parameter of the micro-beams, with possible different scale lengths for different considered beams. All these features allow to detect the influence of the characteristics of the lattice at the local scale on the global dynamic behavior. Moreover, the existence of frequency band gaps is also predicted.

Resonantly induced transparency for metals with low angular dependence

Thin (sub skin-depth) metal layers are known to almost completely reflect radiation at microwave frequencies. It has previously been shown that this can be overcome at resonance via the addition of closely spaced periodic structures on either side of the film. In this work, we have extended the original one-dimensional impedance mechanism to the use of two-dimensional periodic structures both experimentally and analytically using an equivalent circuit approach. The resulting device shows experimentally a low (<5% relative frequency shift) dependence in both angle of incidence and polarisation. We also show that the same principle can be used to transmit through a thicker (∼μm) perfectly conducting film perforated with a non-diffracting (short pitch) array of subwavelength holes with the cut-off frequency above 900 GHz showing resonant transmissivities in the 20–30 GHz range above 40%.

Enhanced acoustic insulation properties of composite metamaterials having embedded negative stiffness inclusions

Despite the fact that the concept of incorporating Negative Stiffness (NS) elements within mechanical systems was formulated and validated more than 40 years ago, it has only recently received consistent attention. In this work, the design of a layered mechanical metamaterial having implemented NS inclusions is presented and its acoustic wave propagation properties are modelled. A dedicated two-dimensional periodic structure theory scheme is developed in order to compute the frequency dependent damping loss factor of the metamaterial structure. The acoustic transmission properties through the modelled panel are computed within a Statistical Energy Analysis (SEA) scheme. It is demonstrated that the suggested layered metamaterial exhibits highly superior acoustic insulation performance close and above the acoustic coincidence range, thanks to the drastic increase of its structural damping properties implied by the NS elements. Additionally, the proposed configuration presents superior performance in a broadband frequency range when compared to a viscoelastic damping constraint layer of equivalent mass.

Tunable elastodynamic band gaps

The effect of nonlinear elastic pre-stress on coupled compressional and vertically polarised shear elastic wave propagation in a two-dimensional periodic structure is investigated. The medium consists of cylindrical annuli embedded on a periodic lattice in a uniform host material. An identical inhomogeneous deformation is imposed in each annulus and the theory of small-on-large is used to find the incremental wave equations governing subsequent small-amplitude elastic waves. The plane-wave-expansion method is employed in order to determine the permissable eigenfrequencies. It is found that the application of pre-stress has a significant effect on the band structure, allowing stop bands to be controlled. The sensitivity of the choice of constitutive behaviour is studied and it is shown that the fundamental shear wave mode is largely unchanged for the class of strain energy functions considered here, whereas the compressional mode is considerably more sensitive to this choice.

Solution methods for two key problems in multiscale asymptotic expansion method

The accuracy of decoupled multiscale asymptotic expansion method (MsAEM) depends completely on the accuracy of influence functions and the accuracy of homogenized displacement derivatives. Unit cell problem must be solved first for obtaining influence functions whose calculational accuracy depends largely on the boundary conditions of the unit cell problem; and homogenized problem must be solved for obtaining homogenized displacement derivatives whose accuracy depends largely on the order of used finite elements and meshes. In this work, as for two-dimensional (2D) periodical composite structures, super unit cell approach is proposed to solve for accurate influence functions, and quasi potential energy functional corresponding to influence functions (called quasi displacements in this paper), is constructed to evaluate the accuracy of influence functions or boundary conditions of unit cell problem, and it follows that clamp boundary condition is not always suitable for solving influence functions of different orders although it is exact for unit cell problem of one-dimensional (1D) rod. Finally, the differential quadrature finite element method is employed to improve the computational accuracy of homogenized displacement derivatives.

ЛОКАЛЬНО-НЕРАВНОВЕСНОЕ ВОЗДЕЙСТВИЕ СТОЯЧЕЙ ВОЛНЫ НА ДВ УХМЕРНЫЕ ПЕРИОДИЧЕСКИЕ ТЕПЛОВЫЕ СТРУКТУРЫ

ЛОКАЛЬНО-НЕРАВНОВЕСНОЕ ВОЗДЕЙСТВИЕ СТОЯЧЕЙ ВОЛНЫ НА ДВ УХМЕРНЫЕ ПЕРИОДИЧЕСКИЕ ТЕПЛОВЫЕ СТРУКТУРЫ

Optimization of two-dimensional periodic structures with cross-shaped aperture elements

The objective function for the optimization of frequency-selective structures with cross-shaped aperture elements is formulated. The electrodynamic characteristics of such systems are determined using a numerical model of a local section of a metasurface with periodic Floquet conditions, which demonstrates a good agreement with the experiments. The sizes of the aperture elements and the electrophysical properties of materials providing narrow-band filtering of electromagnetic signals in a given frequency range are found.

From Dark to Bright: First-Order Perturbation Theory with Analytical Mode Normalization for Plasmonic Nanoantenna Arrays Applied to Refractive Index Sensing.

We present a first-order perturbation theory to calculate the frequency shift and linewidth change of photonic resonances in one- and two-dimensional periodic structures under modifications of the surrounding refractive index. Our method is based on the resonant state expansion, for which we extend the analytical mode normalization to periodic structures. We apply this theory to calculate the sensitivity of bright dipolar and much darker quadrupolar plasmonic modes by determining the maximum shift and optimal sensing volume.

Element decoupling of 7 T dipole body arrays by EBG metasurface structures: Experimental verification

Metasurfaces are artificial electromagnetic boundaries or interfaces usually implemented as two-dimensional periodic structures with subwavelength periodicity and engineered properties of constituent unit cells. The electromagnetic bandgap (EBG) effect in metasurfaces prevents all surface modes from propagating in a certain frequency band. While metasurfaces provide a number of important applications in microwave antennas and antenna arrays, their features are also highly suitable for MRI applications. In this work we perform a proof-of-principle experiment to study finite structures based on mushroom-type EBG metasurfaces and employ them for suppression of inter-element coupling in dipole transceive array coils for body imaging at 7T. We firstly show experimentally that employment of mushroom structures leads to reduction of coupling between adjacent closely-spaced dipole antenna elements of a 7T transceive body array, which reduces scattering losses in neighboring channels. The studied setup consists of two active fractionated dipole antennas previously designed by the authors for body imaging at 7T. These are placed on top of a body-mimicking phantom and equipped with the manufactured finite-size periodic structure tuned to have EBG properties at the Larmor frequency of 298MHz. To improve the detection range of the B1+ field distribution of the top elements, four additional elements were positioned along the bottom side of the phantom. Bench measurements of a scattering matrix showed that coupling between the two top elements can be considerably reduced depending on the distance to the EBG structure. On the other hand, the measurements performed on a 7T MRI machine indicated redistribution of the B1+ field due to interaction between the dipoles with the structure. When the structure is located just over two closely spaced dipoles, one can reach a very high isolation improvement of −14dB accompanied by a strong field redistribution. In contrast, when put at a certain height over the antennas the structure provides a moderate isolation improvement together with a slight increase of B1+ level. This study provides a tool for the decoupling of dipole antennas in ultrahigh field transceive arrays, possibly resulting in denser element placement and/or larger subject-element spacing.

Topology optimization of photonic structures for all-angle negative refraction

This paper proposes a new topology optimization algorithm based on the bi-directional evolutionary structural optimization (BESO) method to design photonic crystals with broad all-angle negative refraction (AANR) frequency range. The photonic crystals are assumed to be two-dimensional periodical structures, which consist of dielectric materials and air. The conditions for the occurrence of AANR are identified and the design objective is to enlarge the AANR frequency range. The BESO algorithm is proposed based on finite element analysis for band diagrams of photonic crystals and the derived sensitivity numbers. Starting from a simple initial design without any AANR, BESO gradually re-distributes the dielectric materials within the periodical unit cell so that the AANR property emerges and its frequency range is enlarged accordingly. The numerical results show that the proposed BESO algorithm can effectively obtain AANR photonic crystals with novel patterns. The effects of dielectric permittivity contrast of two constituent materials, mesh-refinement and filter are discussed.

An Accurate and Efficient Method for Dynamic Analysis of Two-Dimensional Periodic Structures

In this paper, an accurate and efficient method is presented for analyzing the dynamic response of two-dimensional (2D) periodic structures. The algebraic structure of the corresponding matrix exponential is analyzed and, based on its special structure, an accurate and efficient method for its computation is proposed. Accuracy is maintained using the precise integration method (PIM), and great efficiency is achieved in the computational effort using the periodic properties of the structure and the energy propagation features of the dynamic system. The proposed method is compared with the conventional Newmark and Runge–Kutta (R–K) methods, and it is shown to be accurate, efficient and extremely frugal in its memory requirements.

Statistical analysis of digital images of periodic fibrous structures using generalized Hurst exponent distributions

Distinction of diverse two-dimensional periodic structures can be based on a large number of methods and parameters, while the quantitative description of differences between similar samples is usually difficult. This article aims, by the use of statistical random walk in a generalized q-order dimensional space, at introducing a methodology to qualify the networked structures on the basis of exemplary textile samples. The presented results were obtained at 1-bit monochromatic maps obtained from optical microscopic pictures. Significant features of samples were represented by the obtained distributions of Hurst exponents and Shannon entropy calculations.

Antiplane elastic wave propagation in pre-stressed periodic structures; tuning, band gap switching and invariance

The effect of nonlinear elastic pre-stress on antiplane elastic wave propagation in a two-dimensional periodic structure is investigated. The medium consists of cylindrical annuli embedded on a periodic square lattice in a uniform host material. An identical inhomogeneous deformation is imposed in each annulus and the theory of small-on-large is used to find the incremental wave equation governing subsequent small-amplitude antiplane waves. The plane-wave-expansion method is employed in order to determine the permissable eigenfrequencies. It is found that pre-stress significantly affects the band gap structure for Mooney–Rivlin and Fung type materials, allowing stop bands to be switched on and off. However, it is also shown that for a specific class of materials, their phononic properties remain invariant under nonlinear deformation, permitting some rather interesting behaviour and leading to the possibility of phononic cloaks.