One-dimensional Periodic Structure Research Articles

Quantization of topological edge mode in a one-dimensional photonic crystal heterostructure

The study of topological phases of matter has seen significant advancements in recent years, largely driven by the discovery and exploration of their distinctive topological edge states. Here, we delve into the edge properties of a one-dimensional periodic multilayer structure. The analysis reveals that this system exhibits characteristics akin to the Su–Schrieffer–Heeger model in optics. The theoretical analysis explores the impact of multiple interfaces on the emergence of a topological edge mode (TEM) within the structure. The proposed heterostructure functions as a general beam splitter. Moreover, when the interface is doubled, the heterostructure exhibits two TEM states, resulting from the quantization of an incoming beam into its two equally orthogonal constituents. As the number of interfaces increases, more quantized TEM states occur within the photonic bandgap. Also, it identifies that the quality factor of the original TEM mode at 382.08 THz frequency linearly increases with respect to the number of interfaces. The outcome suggests potential applications in photonic sensors, optoelectronics, and photonic devices, indicating the heterostructure’s pivotal role in advancing these fields.

Nanosecond laser annealing processed surface-structured hyperdoped silicon for efficient near-infrared detection

Surface-structured engineering of hyperdoped silicon can effectively facilitate the absorption of sub-bandgap photons in pristine single-crystal silicon (sc-Si). Here, we conducted different annealing approaches of ordinary thermal annealing (OTA) and nanosecond laser annealing (NLA) on modification of titanium-hyperdoped silicon (Si:Ti) surface structure, to achieve efficient near-infrared detection. It is presented that both OTA and NLA processes can improve the crystallinity of Si:Ti samples. In detail, atomic-resolved STEM characterization illustrates that NLA treatment will further eliminate the amorphous phase on Si:Ti surface to varying degrees. While one-dimensional periodic stacking fault structure of 9R-Si phase is formed at the surface of sc-Si and embedded in the Si matrix during the OTA process, which reveals the seamless interface of 9R-Si/sc-Si along with [11¯0] direction. Due to the high sub-bandgap light absorption and good crystal structure, the Si:Ti photodetector after NLA treatment with an energy density of 2.6 J cm-2exhibited the highest responsivity, reaching 151 mA W-1at 1550 nm even at a low operating voltage of 1 V. We assume the performance enhancement of NLA processed Si:Ti photodetectors can be attributed to two aspects, the one is NLA can reduce the recombination of photo-generated charge carriers in amorphous surface layer by improving crystallization, and the other is that NLA process can weaken the diffusion of titanium impurities due to the extremely rapid heating and cooling rates. This study presents prospects towards surface-structured silicon in infrared light detection.

Decomposition-assisted analysis of transmission in periodic resonator arrays using mode-matching method.

This paper focuses on analysing acoustic structures containing locally reacting resonators, aiming to establish a framework for discussing sound properties related to scattering and transmission in a periodic resonator array. The paper introduces an analytical model for the input surface impedance of non-uniform resonator arrays, which is a challenging task when addressing sound propagation to the opposite side of the array. To address this challenge, a mode-matching method is employed within a one-dimensional periodic structure combined with the decomposition of the initial mirror-symmetric system into symmetric and antisymmetric sub-systems. This procedure leads to simplified analytical solutions of transmission problems about non-uniform resonator arrays, and its accuracy is verified through numerical simulations. The proposed method provides insights into mode shapes and amplitudes, thereby complementing numerical simulations and enabling a comprehensive understanding of sound fields beyond conventional results such as pressure fields and sound absorption coefficients alone. The model of a periodic varying-height resonator array presented herein involves developing mathematical equations or simulations to capture the physical characteristics and interactions of the resonators. This approach empowers researchers to predict and comprehend the non-uniform array's transmission behaviour and performance characteristics, with diverse applications spanning various systems, including electromagnetic devices.

Quantum scattering in one-dimensional periodic structures: A Green's function approach solved through continued fractions

Quantum scattering in one-dimensional periodic structures: A Green's function approach solved through continued fractions

Non-reciprocal wave propagations in a one-dimensional periodic structure modified with a linkage mechanism

Non-reciprocal wave propagations in a one-dimensional periodic structure modified with a linkage mechanism

An accurate and efficient method for calculating surface waves in one-dimensional ideal and defective semi-infinite periodic structures

An accurate and efficient method for calculating surface waves in one-dimensional ideal and defective semi-infinite periodic structures

Photonic Bandgap Properties of One-Dimensional Bilayer Periodic Structure Composed of Silicon Dioxide and Gallium Phosphide Material Layers

Photonic Bandgap Properties of One-Dimensional Bilayer Periodic Structure Composed of Silicon Dioxide and Gallium Phosphide Material Layers

Non-reciprocity and selective wave amplification in nonlinear inertia-induced autoparametric periodic structures

Inspired by the spatiotemporally modulated metamaterials, we propose a one-dimensional autoparametric periodic structure induced by nonlinear inertia that is realized simply by constructing an array of pendula coupled to local oscillators. The mechanism of autoparametric modulation is revealed using a unit cell. The evolution equations for a superlattice describing the global dynamics of the wave-vibration coupling are obtained analytically by combining the Floquet-Bloch theorem and the multiple-time scales perturbation technique. The band structure exists corresponding to the fixed point in the phase space, wherein large amplitude local vibrations with distributed traveling phases modulate the inertial properties of the host pendula propagating with a small amplitude signal wave by playing the role of a pump wave. Non-reciprocal dispersion relations are demonstrated both by numerical results and perturbation results with two-order accuracy. Selective wave amplification with two-mode directional emission is observed in a two-port system which is composed of a sandwich composite medium. The present research based on the proposed autoparametric structure paves a way towards building tunable wave manipulators, vibration energy migrators and mechanical amplifiers.

Computation of the dynamic scalar response of large two-dimensional periodic and symmetric structures by the wave finite element method

In the past, the study of periodic media mainly focused on one-dimensional periodic structures (meaning periodic along one direction), on the one hand to determine the dispersion curves linking the frequencies to the wavenumbers and on the other hand to obtain the response of a structure to an external excitation, both for bounded or unbounded structures. In the latter case, effective approaches have been obtained, based on methods such as the Wave Finite Element (WFE). Two-dimensional periodic media are more complex to analyse but dispersion curves can be obtained rather easily as in the one-dimensional case. Obtaining the steady state response of two-dimensional periodic structures to time-harmonic excitations is much more difficult than for one-dimensional media and the results mainly concern infinite media. This work is about this last case of the steady state response of finite two-dimensional periodic structures to time-harmonic excitations by limiting oneself to structures described by a scalar variable (acoustic, thermal, membrane behaviour) and having symmetries compared to two orthogonal planes parallel to the edges of a substructure. Using the WFE for a rectangular substructure and imposing the wavenumber in one direction, we can numerically calculate the wavenumbers and mode shapes associated with propagation in the perpendicular direction. By building solutions with null forces on parallel boundaries, we can decouple the waves in the two directions parallel to the sides of the rectangle. The solution of each of these two problems is obtained by a fast Fourier transformation giving the amplitudes associated with the waves. By summing the contributions of all these waves we obtain the global solution for a two-dimensional periodic medium with a large number of substructures and a low computing time. Examples are given for the case of a two-dimensional membrane with many substructures and different types of heterogeneities.

An array of QDs on a one-dimensional periodic structure of graphene nanoribbons as a nanoscale plasmonic grating

An array of QDs on a one-dimensional periodic structure of graphene nanoribbons as a nanoscale plasmonic grating

A novel efficient method for transient heat analysis of cylindrical periodic structure based on the physical features and group theory

In this paper, a novel efficient and accurate numerical method is developed for analyzing the transient temperature responses of cylindrical periodic structures. By exploiting the structure’s circumferential cyclic periodic property and leveraging group theory, a circumferential decomposition strategy is presented to transform the temperature response analysis of the cylindrical periodic structure into the analyses of a series of one-dimensional periodic structures. Then, based on the physical nature of the transient heat conduction, an axial decomposition strategy is developed to convert the computations of the temperatures of these one-dimensional periodic structures into the calculations of the temperatures of a series of small-scale structures. The computational cost of these small-scale structures is further reduced by using the group theory. Several numerical examples demonstrate that the proposed method has higher accuracy and computational efficiency in comparison with the Crank-Nicolson method. When the Crank-Nicolson method attains the acceptable results, the proposed method is about 10 and 20 times faster than the Crank-Nicolson method with direct and preconditioning conjugate gradient solvers, respectively.

Metamaterials of Auxetic Geometry for Seismic Energy Absorption.

The propagation of earthquake energy occurs primarily through elastic waves. If the seismic force input to a structure can be directly reduced from the source, then the structure can be protected from seismic wave energy. Seismic metamaterials, regarded as periodic structures with properties different from conventional materials, use wave propagation characteristics and bandgaps to dissipate seismic wave energy. When the seismic wave is located in the bandgap, the transmission of seismic wave energy is effectively reduced, which protects the structure from the damage caused by seismic disturbance. In practical application, locating seismic frequencies below ten Hz is a challenge for seismic metamaterials. In the commonly used method, high-mass materials are employed to induce the effect of local resonance, which is not economically feasible. In this study, a lightweight design using auxetic geometry is proposed to facilitate the practical feasibility of seismic metamaterials. The benefits of this design are proven by comparing conventional seismic metamaterials with metamaterials of auxetic geometry. Different geometric parameters are defined using auxetic geometry to determine the structure with the best bandgap performance. Finite element simulations are conducted to evaluate the vibration reduction benefits of auxetic seismic metamaterials in time and frequency domains. Additionally, the relationship between the mass and stiffness of the unit structure is derived from the analytical solution of one-dimensional periodic structures, and modal analysis results of auxetic metamaterials are verified. This study provides seismic metamaterials that are lightweight, small in volume, and possess low-frequency bandgaps for practical applications.

Peculiarities of the Resonant Response of a Subwavelength Double Grating with Optical PT-Symmetry

In this paper, we study the features of the resonant response of a system consisting of two subwavelength one-dimensional periodic structures, considering the dispersion of the refractive index in the presence of optical PT-symmetry for TM polarization. For the considered structure in the green wavelength range, two possible resonance lines were identified at 514.86 nm and 518.5 nm. Ultra-narrow resonances (FWHM of 0.00015 nm) have been obtained for transmitted and reflected waves, and a significant enhancement of the resonant response has been achieved (up to 105 times). The dependence of the system’s optical response on the relative position of its two sub-wavelength gratings and the magnitude of the amplification coefficient of the active part was investigated. This can be used to tune the spectral characteristics of filters, modulate the optical radiation, and create optomechanical sensors such as strain gauges.

Bandgaps of microwave photonic crystals: Study of quasi-periodic metamaterial multilayers

A lossy double-negative index and air are used to investigate one-dimensional periodic and quasi-periodic multilayered structure using the transfer-matrix method. The transmittance of the lossy double-negative index and air quasi-system has been shown using the Fibonacci, Thue–Morse, double-period, Octonacci and Dedocanacci quasi-sequence. For the periodic structure, which is used here as the refereed structure for the comparison, a bandgaps called zero-n¯ appears near the frequency at which the permittivity and permeability of double-negative material are negative. Apart from this, zero-ϵ and zero-μ bandgaps have been found except for normal incidence along with the Bragg bandgaps.

Morphology dependent excitation of hybrid Tamm-bandedge state in metal coated opal three-dimensional photonic crystal

The optical Tamm state is a type of electromagnetic mode that exists at the interface between a periodic dielectric structure and a metal layer. While optical Tamm states have recently gained attention as a potential replacement for surface plasmon polaritons in various applications, most of these demonstrations have been limited to one-dimensional periodic dielectric structures, such as Bragg mirrors. In this article, we present a detailed study on the existence of optical Tamm states at the interface between a metal layer and opal-like three-dimensional photonic crystal (3D-PhC) structures, with a focus on two types of devices with different cross-sectional morphologies. One device consisted of a corrugated silver layer on self-assembled PS opals, while the second one was realized by self-assembling PS opals on a thin flat gold film. Our experimental and numerical observations revealed a dip in the reflection spectra for both configurations, but a hybrid Tamm-PhC bandedge state was found to exist only between the corrugated metal layer and 3D-PhC. Importantly, the nature of the hybrid Tamm-PhC bandedge states was found to strongly depend on the thickness of the metal layer. In contrast, no mode hybridization was observed at the interface between the flat metal and 3D-PhC, and the reflection dip in this case corresponded to a PhC edge mode. Our demonstration highlights the potential for realizing cost-effective and integrated hybrid plasmonic-photonic crystal structures for sensitive nanophotonic sensors.

Wave propagation analysis in laminated composite periodic frame structures using spectral finite element method

In this article, wave propagation in a one-dimensional (1-D) composite periodic frame structure is analyzed using spectral finite elements (SFE) method together with Bloch’s theorem. Each element in the periodic frame structure is modeled as a first-order shear deformation theory (FSDT) beam element and wave equations for the beam elements are derived using FSDT considering axial, flexural, and shear deformations. Next, these equations are solved using the frequency domain SFE method to obtain an elemental dynamic stiffness matrix which on assembly gives the dynamic stiffness matrix for the unit cell of the periodic structure. A polynomial eigenvalue problem is formulated thereafter using Bloch’s theorem to evaluate the dispersion coefficients and wave amplitude ratios. Finally, the entire periodic frame is modeled as homogenized two-noded elements capturing the wave response of the PS with a drastic reduction in computational cost. The results obtained using the present method are validated with finite element simulation using ANSYS mechanical Ansys Parametric Design Language (APDL). The frequency band gaps observed in the frequency domain responses are investigated and corroborated with those predicted by the dispersion relations. This is followed by a detailed parametric study on the influence of different parameters on the band gap characteristics. The present method provides a scheme of wave propagation analysis of composite periodic frames with substantial computational efficiency.

Numerical and experimental analysis of the stiffness and band-gap properties of shell structures with periodically variable cross sections

This paper describes one-dimensional periodic shell structures that have variable cross sections, a new type of periodic shell structures made from photopolymer. This paper will discuss the stiffness of periodic sub-cells that have variable cross sections and the band gaps of Bragg scattering shell structures based on numerical analysis and a series of experiments. This paper uses the Bloch theorem and lumped-mass method to create a band gap model for periodic shell structures. In this paper, an equivalent stiffness model for sub-cells is also created based on the principle of superposition and validated by experiments. Numerical studies and experiments are conducted to examine the effects of geometrical parameters, number of sub-cells, and stiffness of sub-cells on band gaps of one-dimensional periodic shell structures and to test the effectiveness of the models. The findings in this paper prove that by varying the stiffness of sub-cells under a fixed lattice constant, band gaps of one-dimensional periodic shell structures can be decreased. The findings also confirmed that the initial band gap of one-dimensional periodic shell structures can be lowered by increasing the number of sub-cells in a period. Unlike other types of Bragg scattering periodic structures, one-dimensional periodic shell structures allow their longitudinal band gaps to be adjusted under a fixed lattice constant. Those findings serve as a theoretical foundation for the application of Bragg scattering periodic shell structures in low-frequency vibration.

Free Vibration Characteristics of CFRP Laminate with One-Dimensional Periodic Structures.

This paper proposes an approach of stacking prepreg periodically for carbon fiber-reinforced polymer composites (CFRP) laminate. This paper will discuss the natural frequency, modal damping, and vibration characteristics of CFRP laminate with one-dimensional periodic structures. The damping ratio of CFRP laminate is calculated using the semi-analytical method which combines modal strain energy with the finite element method. The finite element method is used to calculate the natural frequency and bending stiffness which are verified with experiments. The numerical results of the damping ratio, natural frequency, and bending stiffness are in good agreement with the experiment results. Finally, the bending vibration characteristics of CFRP laminate with one-dimensional periodic structures and traditional CFRP laminate are investigated with experiments. The finding confirmed that the CFRP laminate with one-dimensional periodic structures exists band gaps. This study provides theoretical support for the promotion and application of CFRP laminate in the field of vibration and noise.

Exact solutions of nonlinear dynamical equations for large-amplitude atomic vibrations in arbitrary monoatomic chains with fixed ends

Intermode interactions in one-dimensional nonlinear periodic structures have been studied by many authors, starting with the classical work by Fermi, Pasta, Ulam, and Tsingou (FPUT) in the middle of the last century. However, symmetry selection rules for the energy transfer between nonlinear vibrational modes of different symmetry, which lead to the possibility of excitation of some bushes of such modes, were not revealed. Each bush determines an exact solution of nonlinear dynamical equations of the considered system. The collection of modes of a given bush does not change in time, while there is a continuous energy exchange between these modes. Bushes of nonlinear normal modes (NNMs) are constructed with the aid of group-theoretical methods and therefore they can exist for the case of large amplitude atomic vibrations and for any type of interatomic interactions. In most publications, bushes of NNMs or similar dynamical objects in one-dimensional systems are investigated under periodic boundary conditions. In this paper, we present a detailed study of the bushes of NNMs in monoatomic chains for the case of fixed boundary conditions, which sheds light on a series of new properties of the intermode interactions in such systems. We prove some theorems that justify a method for constructing bushes of NNMs by continuation of conventional normal modes to the case of large atomic oscillations. Our study was carried out for FPUT chains, for the chains with the Lennard-Jones interatomic potential, as well as for the carbon chains (carbynes) in the framework of the density functional theory. For one-dimensional bushes (Rosenberg nonlinear normal modes), the amplitude–frequency diagrams are presented and the possibility of their modulational instability is briefly discussed. We also argue in favor of the fact that our methods and main results are valid for any monoatomic chain.

A diffraction problem for the biharmonic wave equation in one-dimensional periodic structures

This work concerns the propagation of flexural waves through one-dimensional periodic structures embedded in thin elastic plates. We show that the out-of-plane displacement of the plate only contains the Helmholtz wave component and the modified Helmholtz wave component is not supported when the Navier boundary condition is imposed. An adaptive finite element method with transparent boundary condition is developed for solving the associated boundary value problem. Numerical results show that the method is effective to solve the diffraction grating problem of the biharmonic wave equation.