Semi-infinite Structure Research Articles

Information preservation of two qubits in a structured environment

The environment-induced decoherence of a quantum open system makes it fundamentally import to preserve the initial quantum information of the system in its steady state. Here we study information preservation of two maximally entangled qubits lying inside a photonic-crystal waveguide with semi-infinite cavity-array structure. We generalize our study to arbitrary position and arbitrary frequency detuning of the qubits. We find that for weak qubits-waveguide couplings, the information preservation greatly depends on the position and the frequency detuning of the qubits, while for strong couplings, both of these dependence is significantly weakened. Interestingly, by suitably choosing the position and the frequency of the qubits, high information preservation could be achieved for both weak and strong couplings, irrespective to Markovian or non-Markovian dynamics. Physically, we analytically verify that the ability of information preservation is indeed determined by the existence of the bound states of the entire system, but the probability of information preservation is closely related to the probability of the initial state of the qubits in the bound states. Our results provide an alternative route getting high information preservation without any external controls of the system.

Influence of Circular through Hole in Pt-Rh Bushing on Temperature Propagation at High Temperature.

In the fiberglass industry, Pt-Rh bushings made of platinum and rhodium have very good characteristics, such as high temperature resistance, corrosion resistance, oxidation resistance, and creep resistance. In this paper, a semi-infinite lath structure model is constructed, and the expression of the surface temperature distribution of a Pt-Rh alloy plate with a circular through hole is obtained based on the non-Fourier heat conduction equation, complex function method and conformal mapping method. At the same time, the influence of the position of the circular through hole in the Pt-Rh bushing and the parameters of the incident light source (Non-diffusion incident wave number and relative thermal diffusion length) on the surface temperature distribution of the Pt-Rh bushing is studied by using this formula. It is found that: 1. heat concentration and fracture are occur easily at the through hole; 2. when the through hole is in the asymmetric center, the greater the asymmetry, the smaller the maximum temperature amplitude; 3. when the buried depth of the through hole increases, the maximum temperature amplitude decreases; 4. when the incident wave number and the relative thermal diffusion length of the incident light source are larger, the maximum temperature amplitude is smaller. The numerical results are almost consistent with those of ANSYS thermal simulation. The expression of the surface temperature distribution of the semi-infinite lath structure proposed in this paper can effectively reduce the loss of precious metal materials and the time of thermal simulation in the experimental process, as well as provide important significance for structural design, quality inspection, process optimization, and service life improvement of Pt-Rh bushings.

Spontaneous emission modulation in biaxial hyperbolic van der Waals material

As a natural van der Waals crystal, α-MoO3 has excellent in-plane hyperbolic properties and essential nanophotonics applications. However, its tunable properties are generally neglected. Here, we achieve effective modulation of spontaneous emission (SE) from a single-layer flat plate by changing the crystal directions. Numerical results and theoretical analysis show that α-MoO3 exhibits good tunability when the crystal directions of α-MoO3 are different in y–z or x–y planes. A modulation factor of more than three orders of magnitude is obtained at 634 cm−1. This phenomenon is caused by the excitation of hyperbolic phonon polaritons in α-MoO3 at specific bands. However, when the crystal directions of α-MoO3 are different in the x–z plane, the SE of the material exhibits strong angle independence. Additionally, for the semi-infinite α-MoO3 flat structure, we determine the distribution of the modulation factor of SE using the wavenumber and rotation angle. Finally, we extend the calculation results from semi-infinite media to finite thickness films. We obtain the general evolution law of the peak angle of the modulation factor with thickness, increasing the modulation factor to approximately 2000, which exceeds the maximum modulation factor observed in previous works by 48 times. We believe this work could guide the SE modulation of anisotropic materials and benefit the field of micro-/nano-lasers and quantum computing.

Plasmonic Tamm states in periodic stubbed MIM waveguides: analytical and numerical study

We investigate both analytically and numerically the existence of localized surface modes, the so-called plasmonic Tamm states (PTSs), in a new and versatile platform based on a periodic array of metal-insulator-metal (MIM) stubs grafted along a MIM waveguide. By considering a semi-infinite structure in which we modify the length of the segment at the surface, we show the existence of surface states inside the bandgaps of the periodic structure and investigate the dependence of the localized modes as a function of the geometrical parameters and the boundary conditions applied at the surface. Three types of surface boundary conditions are considered, namely, two limiting cases of zero surface impedance (or perfect electric conductor), infinite surface impedance (or perfect magnetic conductor), and a third case where the structure is in contact with a real metal. In the latter case, we show that the existence of the interface state can be demonstrated based on topological arguments using the Zak phase. We also demonstrate that if a finite size comb-crystal is vertically grafted along a horizontal waveguide, the PTSs can be detected from the dips in the amplitudes of transmission and reflection coefficients as well as from the peaks in their delay times and the local density of states (LDOS). Our theoretical study is first performed analytically with the help of a Green’s function method, which allows the calculation of the dispersion relations of the bulk and surface modes and the LDOS, as well as the transmission and reflection coefficients of the plasmonic comb-like structure. Then, these results are confirmed by a numerical simulation utilizing a 2D finite element method. Besides providing a deep physical analysis of the PTSs, our work demonstrates the capability of the analytical method as a predictive approach in more complex structures. The proposed designs in this paper can be useful to realize highly sensitive plasmonic nanosensors.

Semi-Infinite Structure Analysis with Bimodular Materials with Infinite Element.

The modulus of elasticity of some materials changes under tensile and compressive states is simulated by constructing a typical material nonlinearity in a numerical analysis in this paper. The meshless Finite Block Method (FBM) has been developed to deal with 3D semi-infinite structures in the bimodular materials in this paper. The Lagrange polynomial interpolation is utilized to construct the meshless shape function with the mapping technique to transform the irregular finite domain or semi-infinite physical solids into a normalized domain. A shear modulus strategy is developed to present the nonlinear characteristics of bimodular material. In order to verify the efficiency and accuracy of FBM, the numerical results are compared with both analytical and numerical solutions provided by Finite Element Method (FEM) in four examples.

Acoustic Tamm states in slender tubes

We present an analytical and numerical study of the possibility of existence of surface localized modes, the so-called Tamm states, in a one-dimensional (1D) comb-like phononic crystal (PnC). The structure is made out of periodic array of stubs of lengths d2 grafted along a waveguide and separated from each other by a tube of length d1. We show the existence of surface modes for the semi-infinite structure. In particular, when one considers two complementary semi-infinite systems obtained by cutting the infinite one into two parts, we obtain one surface mode per gap induced by the surface of the two complementary systems. Furthermore, we demonstrate that these surface modes can be detected from the maxima and minima of the transmission spectrum, when the finite structure is grafted vertically along a homogeneous acoustic waveguide. That means that one can observe experimentally this type of modes for acoustic waves in slender tubes. These results may find many practical applications in noise control and highly sensitive PnC sensors.

Surface modes in plasmonic stubbed structures

We present an analytical and numerical study about the existence of surface localized modes, known as Tamm states, in a one-dimensional (1D) comb-like plasmonic band gap structure. Surface plasmon polaritons (SPPs) waveguides with coupled resonators have been widely studied in recent years, because of their potential applications in highly integrated optical circuits. The system studied here is composed of an infinite 1D waveguide, along which stubs of length d1 are grafted periodically with spacing period d2. The analytical study has been performed by means of the Green’s function method which allows the calculation of the dispersion relations of the bulk, surface states of the plasmonic structure and the transmission coefficient. The band structure, as well as the transmission spectrum exhibit passbands separated by stopbands. The surface modes inside the gaps of the semi-infinite structure can be introduced by a defect at its surface. The analytical results are confirmed by numerical simulation using finite element method via Comsol Multiphysics software. These structures can be used to realize highly sensitive plasmonic sensors.

Reflection of plane waves on the stress-free and rigid boundary surfaces of pre-stressed piezoelectric-orthotropic substrate: A comparative approach

This study delves with the reflection phenomenon of plane-waves due to incidence of quasi-longitudinal (QL) wave at a semi-infinite structure comprising of pre-stressed piezoelectric-orthotropic substrate (POS) with stress-free (Case I) and rigid (Case II) bounding surfaces. The compact-form expressions of reflection-coefficients (RCs) of reflected QL wave, quasi-transverse (QT) wave and evanescent-electroacoustic (EA) wave for different cases of pre-stressed POS are deduced. To unravel effects of higher anisotropy in substrate, comparative analysis in pre-stressed transversely isotopic piezoelectric substrate (TIPS) medium with stress-free (Case III) and rigid (Case IV) boundaries is carried out. PVDF and ALN materials are considered for numerical computations. For validation, energy-partition and conditions of grazing incidence for all the undertaken cases are analyzed.

Finite element method and boundary element method iterative coupling algorithm for 2-D elastodynamic analysis

The coupling algorithm of the finite element method (FEM) and boundary element method (BEM) can make maximal use of both methods’ advantages. However, such coupling will reduce the computational efficiency because the systems’ degrees of freedom will increase sharply. Thus, a new coupling algorithm that achieves accuracy and computational efficiency is necessary. This study proposes the Newmark-based precise integration FEM (NBPI-FEM) and analytical-based time domain BEM (ABTD-BEM) coupling algorithm. In this coupling algorithm, the governing equation of the FEM is solved by Newmark-based precise integration, and the governing equation of the BEM is solved by the analytical method. First, the procedures of NBPI-FEM and ABTD-BEM are given. The coupling strategy is then provided, and the relationship between the iteration numbers and the relaxation parameter is investigated. Finally, two illustrative examples—i.e., 1-D rod and a semi-infinite structure—are selected to verify the coupling algorithm proposed in the study. The results show that the numerical solutions agree well with the analytical solutions for the 1-D rod example and coincide with the numerical solutions calculated by FEM. Thus, NBPI-FEM and ABTD-BEM can be applied for solving elastodynamic problems with high accuracy and efficiency.

Numerical Approach to a Nonlocal Advection-Reaction-Diffusion Model of Cartilage Pattern Formation

We propose a numerical approach that combines a radial basis function (RBF) meshless approximation with a finite difference discretization to solve a nonlinear system of integro-differential equations. The equations are of advection-reaction-diffusion type modeling the formation of pre-cartilage condensations in embryonic chicken limbs. The computational domain is four dimensional in the sense that the cell density depends continuously on two spatial variables as well as two structure variables, namely membrane-bound counterreceptor densities. The biologically proper Dirichlet boundary conditions imposed in the semi-infinite structure variable region is in favor of a meshless method with Gaussian basis functions. Coupled with WENO5 finite difference spatial discretization and the method of integrating factors, the time integration via method of lines achieves optimal complexity. In addition, the proposed scheme can be extended to similar models with more general boundary conditions. Numerical results are provided to showcase the validity of the scheme.

Quantum anomalous Hall effect in two-dimensional Cu-dicyanobenzene coloring-triangle lattice

Magnetic two-dimensional (2D) topological insulators with spontaneous magnetization have been predicted to host quantum anomalous Hall effects (QAHEs). For organic topological insulators, the QAHE only exists in honeycomb or Kagome organometallic lattices based on theoretical calculations. Recently, coloring-triangle (CT) lattice has been found to be mathematically equivalent to a Kagome lattice, suggesting a potential 2D lattice to realize QAHE. Here, based on first-principles calculations, we predict an organometallic CT lattice, Cu-dicyanobenzene (DCB), to be a stable QAH insulator. It exhibits ferromagnetic (FM) properties as a result of the charge transfer from metal atoms to DCB molecules. Moreover, based on the Ising model, the Curie temperature of the FM ordering is calculated to be around 100 K. Both the Chern numbers and the chiral edge states of the semi-infinite Cu-DCB edge structure, which occur inside the spin-orbit coupling band gap, confirm its nontrivial topological properties. These make the Cu-DCB CT lattice an ideal candidate to enrich the family of QAH insulators.

Computational of localized spinwaves at a stepped surface of an antiferromagnetic metallic monoxide

We investigate the spin excitations at the (001) stepped surface in semi-infinite antiferromagnetic monoxide cubic rocksalt structure of the type MO, made up from compounds of metal cations M[Formula: see text] and oxygen anions O[Formula: see text]. At the surface, of semi-infinite monoxide lattices, the translation symmetry along the direction normal to surface zone is broken. Therefore, significant changes of spin dynamics and magnetic properties are expected at the surface in question. The dependence on properties comes from the geometrical arrangement of the chemical species present at the surface, leading to appearing localized antiferromagnetic spin modes. The spin excitations and the amplitudes of precession due to variations in exchange and superexchange parameters generated by the stepped surface zone are simulated and analyzed, for different cases that can be considered, from softening to hardening effects. The technical formalism of matching method, associated to Green functions, is employed to determine the magnonic densities of states, for the spin components of the individual sites that constitute a complete representation of the stepped surface domain boundaries. Our results shown that the calculated localized spin modes are sensitive to the magnetic coupling between different spin sites at the surface. The simulated cases yield criteria under certain experimental conditions, as regards the interpretation of the measurements of the magnetic interactions in the surface zone and its boundaries. However, for a given material, the spin surfaces corresponding to different orientations are not equivalents and, in particular, they do not have the same stability.

Generalization of the mode-matching technique to the problems of scattering by semi-infinite slow-wave structures

Subject and purpose. The scattering matrix of a semi-infinite slow-wave structure formed by grooves in a rectangular waveguide is investigated. The purpose was to develop a method for calculating a semi-infinite periodic structure. Methods and methodology. A generalization of the mode-matching technique to semi-infinite periodic structures is built. The fields of the periodic part of the structure are expanded in series of the eigenmodes of the periodic structure, taking into account the condition at infinity, which makes it possible to obtain a linear matrix equation for finding the scattering matrix. Only the propagating modes of the periodic structure were considered. To make these expansions reliable the fields were matched at a period somewhat distant from the junction of the regular waveguide with the periodic one. Results. Matrix equations for determining the blocks of the scattering matrix of a semi-infinite structure are obtained. A number of investigations are carried out to check the reliability of the equations obtained. These include test of convergence, reciprocity, energy balance, and conservation of the scattering matrix while adding one period to a semi-infinite structure. The main confirmation was obtained by comparing the scattering matrix of a finite fragment of the slow-wave structure, obtained in two ways: through the scattering matrices of semi-infinite slow-wave structure and through a cascade assembly of the scattering matrices of the waveguide elements that make up the structure. Conclusions. An algorithm for calculating the scattering matrix of a semi-infinite structure is obtained. It can be used to build a rigorous hot model of vacuum electronics devices using slow-wave structures.

Effective mass dependence of the gyrotropic nihility in a BaM/6H-SiC multilayer structure

We investigated the magnetic polaritons in a semi-infinite ferrite-semiconductor binary structure at the microwave region of the spectrum. The permittivity and permeability tensors of the structure depend on the various factors including the characteristic frequencies of the semiconductor and ferrite material, the thickness ratio of two layers, the external magnetic flux density and its frequency. By changing these factors, we can control the optical properties to achieve some extraordinary behaviors. By controlling and adjusting some accessible factors, the longitudinal components of both permittivity and permeability tensors simultaneously acquire zero. This region is identified as the gyrotropic nihility region. At this region, the waves can easily pass through this structure as its resistance to the passage of the electromagnetic waves is negligible. In this paper, we have studied the circumstances under which this extraordinary phenomenon may occur.

Wave scattering by vertical porous block placed over flat and elevated seabed

The present study addresses the hydrodynamic characteristics of the incident wave through porous structure for both finite and shallow water depth. The oblique wave transformation due to the porous block over flat and elevated seabed and the submerged rigid block is presented. Analytical direct formulae are proposed to determine the wave reflection and transmission coefficient for the porous structure considering different configurations like porous block, porous block backed by wall, vertical wall away from the porous block and semi-infinite porous block at flat and elevated seabed. The analytical results for wave interaction with porous structure are presented considering the mode-coupling relation and eigenfunction expansion technique. Further, the significance of the semi-infinite porous block placed on the flat and elevated seabed is studied in detail. The analytical results obtained in the present study are validated with the numerical results available in the literature for specific cases. The significance of the critical angle and skin depth for the semi-infinite structure is explored in the wave structure interaction problems. The comparative study between various structural configurations suggests that, if the ratio of wavelength and width of the structure is greater or equal to unity $$\left( {d/\lambda \, \ge \, 1} \right),$$ then the structure can be regarded as semi-infinite porous block for flat and elevated seabed. The derived analytical formulae will be helpful in the preliminary design and analysis of the porous blocks.

Edge modes of chiral Berry plasmons in graphene nanoribbons

This study examines the edge modes of chiral Berry plasmons propagating along zigzag or armchair edges of a graphene nanoribbon under a finite Berry flux and Fermi pressure. A two-dimensional quantum hydrodynamic model is used to derive analytical expressions of the dispersion relation and transverse confinement length. Direction-dependent edge modes exist in armchair nanoribbons under antisymmetric or symmetric boundary conditions. A confined mode appears in the zigzag nanoribbon under hard-wall boundary conditions. The transverse confinement length of edge plasmons in the nanoribbon can be an order of magnitude shorter than that in the semi-infinite structure.

Surface and bulk plasmon-polaritons in semiconductor photonic crystals with embedded graphene sheets

A theoretical study is made for the bulk and surface plasmon-polaritons in one-dimensional semi-infinite layered semiconductor photonic crystals with graphene interlayers. The retarded dispersion relations are calculated in a general way and applied to two cases, depending on whether a graphene sheet is present or absent at the first interface of the semi-infinite structure. We apply the result to doped GaAs as the constituent material, considering the layers to be arranged in a periodic fashion with alternating layer thicknesses. Both s- and p-polarized modes are evaluated with the effects of retardation on the polaritons being included in the general expressions. Simplifications, particularly for the surface modes, are studied for the case when retardation effects are small. Through numerical examples, we illustrate the important role of the graphene sheets in modifying the plasmon-polariton properties (focusing on the region near the bulk plasma frequency). A strong dependence on the mode polarization is found.

Calculations of surface spin dynamics associated with biquadratic exchange and uniaxial anisotropy field in (S > 1) heisenberg ferromagnet by means of matching procedure.

Calculations within framework of both non-interacting spin-wave theory and random phase approximation have been carried out to investigate elementary magnetic excitations by scanning the occurrence of localized modes associated with surface spin dynamics. Mean field approximation and single spin-wave function theory in the context of semi-infinite Heisenberg ferromagnet are exploited. We exploit the mathematical formalism of matching method which starting from secular equation of spin motion established for the bulk of semi-infinite structure will make it possible to describe the symmetry properties of propagating (evanescent) precessional fields in parallel (perpendicular) direction to surface terrace. The localized states associated with surface are obtained by matching the properties of quantized propagating modes with evanescent modes occurring in vicinity of surface region. This mathematical procedure allows treating the continuity equations for spin precessional field amplitude operating in the border bulk media-surface region from their special suitable symmetry properties related to those induced by the broken translational symmetry arising from the existence of surface. The solutions are described considering the presence of uniaxial anisotropy field and biquadratic exchange as well as magnetic anisotropy field. The focus is on the existence, the nature as well as on the form and stability of localized surface modes. Also, obtained solutions are discussed qualitatively by observing the response of energy branches to the variation of strength of biquadratic exchange term and surface anisotropy field as well as magnetic exchange parameters occurring on the surface domain. Numerical examples of the localized modes energies associated with the surface are shown and they are found to exhibit various effects due to the strength of biquadratic exchange and magnetic anisotropy field under certain circumstances. The analytical formulation exposed in this work and its methodology based solely on the symmetry properties as well as the qualitative agreement describing our results with those obtained in the literature provide a considerable contribution to the surface spin dynamics calculations under the influence of biquadratic coupling and uniaxial anisotropy term. Moreover, the results obtained through matching procedure make it possible to remove an ambiguity concerning the existing disparities in analysis and interpretation of the main results already reported in literature.

Leaky property of the Dyakonov-like wave at the surface of a semi-infinite metal-dielectric multilayered structure.

We investigate the Dyakonov-like surface wave (DLSW) at the interface of a dielectric and a metal-dielectric multilayered (MDM) structure when this MDM structure serves as an elliptic medium according to the effective medium approximation (EMA). Different from the conventional Dyakonov surface waves, we find that this kind of DLSW possesses an unexpected leaky property due to an additional hyperbolic-like wave in the MDM structure, resulting in a significant increase of propagation loss compared to the results estimated by a simple effective model based on the EMA. Moreover, such leaky property is found to be sensitive to the period of the MDM structure. Thus, to diminish this non-negligible leaky loss, one can suppress the amplitude of the leaky component by designing the MDM structure with a smaller period. On the other hand, as the MDM structure sometimes can also support an additional elliptic-like dispersion when it is regarded as a hyperbolic medium, we discuss this condition for completeness. Based on this elliptic-like dispersion, an apparent leaky property is observed in the resultant DLSW. This DLSW propagates with a wider range of propagation direction but suffers from a poor field confinement to the interface it is propagating along.

A BEM for band structure and elastic wave transmission analysis of 2D phononic crystals with different interface conditions

In this paper, a boundary element method (BEM) is developed and applied to compute the band structures and the elastic wave transmission of 2D phononic crystals which have different interface conditions between the scatterers and the matrix. The 2D phononic crystals consist of circular or square solid cylinders periodically embedded in a solid matrix forming a square lattice. For a periodic unit-cell, the boundary integral equations for both the scatterer and the matrix are formulated. After discretizing the boundary integral equations and for an infinite periodic structure, a linear eigenvalue equation related to the Bloch wave vector is obtained by substituting the periodic boundary conditions and the interface conditions. While for the corresponding semi-infinite periodic structure, a linear equation set is obtained from which the elastic wave transmission can be obtained. To verify the present BEM, some representative numerical examples are presented for the phononic crystals with different acoustic impedance ratios. The numerical results indicate that the present BEM can efficiently provide accurate results for phononic crystals with arbitrary shapes and different interface conditions, and the interface conditions have important effects on the band structures and the elastic wave transmission.