Transfer Matrix Approach Research Articles

Uncertainties in the attenuation performance of a multi-frequency metastructure from additive manufacturing

Additive manufacturing has been used to propose several designs of phononic crystals and metamaterials due to the low cost to produce complex geometrical features. However, like any other manufacturing process, it can introduce material and geometrical variability in the nominal design and therefore affect the structural dynamic performance. Locally resonant metamaterials are typically designed such that the distributed resonators have the same natural frequency or, in the case of rainbow metastructures, a well-defined spatial profile. In this work, the effects of the break of periodicity caused by additive manufacturing variability on the attenuation performance of a multi-frequency metastructure is investigated. First, an experimental investigation on the manufacturing tolerances of test samples produced from a Selective Laser Sintering process are assessed and variability levels are used to propose a random field model for the metastructure. Subsequently, the stochastic model is used to investigate the vibration suppression performance of broadband multi-frequency metastructures. An analytical model based on a transfer matrix approach is used to calculate transfer receptance due to a point time harmonic force in a finite length metastructure, which is composed of evenly spaced non-symmetric resonators attached to a beam with Π-shaped cross-section. This design creates a multi-frequency metastructure, i.e. band gaps in more than one frequency band. Individual samples of the random fields are used to show that the mistuned resonators can change the vibration attenuation performance of the metastructure and that even small levels of variability, given by less than 1% for the mass and less than 3% for the Young’s modulus can have a significant effect on the overall vibration attenuation performance of the metastructure when considered together. It is also shown that different spatial profiles can have a significant effect on the vibration attenuation performance in both band gaps. Therefore, the modelling of the uncertainty metastructures has to take into account the spatial correlation of the properties of the metastructure resonators. The obtained results are expected to be useful for further robust design in mass produced industrial applications.

Polarization conversion and phase modulation of terahertz electromagnetic waves via graphene-dielectric structure

In this paper, by using the 4 × 4 transfer matrix approach, the reflection and transmission of circularly polarized (CP) waves which are obliquely incident to the periodic structure comprising of graphene-dielectric layers are investigated. The results indicate that by applying a magnetic field in appropriate direction there exists an omni-directional band gap in the transmission spectrum either left or right CP wave. The given structure can convert the linearly polarized wave to CP wave in reflected and transmitted waves. Furthermore, the dependence of the ellipticity of the reflected and transmitted waves to the applied magnetic field and the chemical potential of the graphene is studied. Such structures can be used as a polarization converter and phase modulator in the terahertz frequency range.

A General Description of the Performance of Surface Plasmon Sensors Using a Transmission Line Resonant Circuit Model

We analyze the response of surface plasmon (SP) sensors using a transmission line model. We illustrate this analysis with particular reference to a layered structure in which plasmon hybridization occurs. By applying the appropriate resonant condition to the system, we derive a circuit model which predicts the responsivity of different modes. This gives new physical insight into the sensing process. We discuss how the change in the sample region may be modeled as a change in the reactance in the equivalent circuit and from this, it follows that a single parameter can determine the change in resonance position with reactance. This approach is used to predict the response of a generic sensor to binding of an analyte and the bulk change of refractive index. This parameter arises naturally from the circuit representation in a way not readily accessible with the transfer matrix approach. The parameters can be expressed in terms of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${Q}$ </tex-math></inline-formula> of a resonant circuit and confirms the intuition that a high <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${Q}$ </tex-math></inline-formula> is associated with poor responsivity, however, we demonstrate that there is another circuit parameter, the resistance at resonance, that can mitigate this effect, providing a route for optimization of the sensor properties.

A Sandwich Coating Containing Micro-perforated Panel for Underwater Sound Absorption

This paper focuses on the underwater application of Micro-perforated panel (MPP) for broadband sound absorption. In this paper, MPP-rubber coating (MPPRC), a novel sandwich anechoic coating embedded with MPP in high-viscosity condition, is proposed. The acoustic impedance for MPP is derived from Maa’s equation and vibration modal modification, while the acoustic propagation property of the viscoelastic rubber layer is obtained by the wave propagation equation. The theoretical calculation for the absorbency of the composite structure is conduced based on electro-acoustic analogy method and transfer matrix approach. The sound absorption validation is carried on in a hydroacoustic impedance tube filled with water, and the experimental results match with the theoretical model. Compared with the equal-thickness rubber, the MPPRC performances better at a lower frequency of 1.6 kHz ∼15 kHz due to MPP, which shows the potential to be utilized as an underwater anechoic coating.

Surface plasmon polariton waves propagation at the boundary of graphene based metamaterial and corrugated metal in THz range

Herein we study theoretically surface plasmon polariton (SPP) wave propagation along the nanostructured graphene-based metamaterial/corrugated metal interface. We apply the effective medium approximation formalism aiming to physically model nanostructured metamaterial. The transfer matrix approach is applied to compute the dispersion relationship for SPP waves. It has been concluded that the groove width (a) and the chemical potential (µ) parameters have a dramatical impact aiming to engineer resonance surface plasmon frequencies of the propagation modes. Moreover, one can tune the bandgap corresponding to non-propagation regime by modifying groove width parameter. The impact of the groove width (a) and the chemical potential (µ) on the propagation length was investigated. The present work may have potential applications in optical sensing in terahertz frequency range.

Entanglement teleportation via a couple of quantum channels in Ising–Heisenberg spin chain model of a heterotrimetallic Fe–Mn–Cu coordination polymer**Project supported by the National Natural Science Foundation of China (Grant No. 11274102), the New Century Excellent Talents in University of Ministry of Education of China (Grant No. NCET-11-0960), and the Specialized Research Fund for the Doctoral Program of Higher Education of

We investigate the teleportation of an entangled state via a couple of quantum channels, which are composed of a spin-1/2 Heisenberg dimer in two infinite Ising–Heisenberg chains. The heterotrimetallic coordination polymer CuIIMnII(L1)][FeIII(bpb)(CN)2]·ClO4 · H2O (abbreviated as Fe–Mn–Cu) can be regarded as an actual material for this chain. We apply the transfer-matrix approach to obtain the density operator for the Heisenberg dimer and use the standard teleportation protocol to derive the analytical expression of the density matrix of the output state and the average fidelity of the entanglement teleportation. We study the effects of the temperature T, anisotropy coupling parameter Δ, Heisenberg coupling parameter J2 and external magnetic field h on the quantum channels. The results show that anisotropy coupling Δ and Heisenberg coupling J2 can favor the generation of the output concurrence and expand the scope of the successful average fidelity.

Mach–Zehnder interferometer with quantum beamsplitters

A one-dimensional waveguide enables a single two-level emitter to route the propagation of a single photon, as to provide a quantum mirror or a quantum beamsplitter. Here we present a fully-quantum Mach-Zehnder interferometer (QMZ) for single-photon pulses comprised of two quantum beamsplitters. We theoretically show how nonlinearities of the QMZ due to photon-emitter detunings and to the spectral linewidth of the pulse contribute to the versatility of the device with respect to the classical-beamsplitters scenario. We employ a quantum dynamics framework to obtain analytical expressions for the photodetection probabilities and prove, in the monochromatic regime, the equivalence with a transfer-matrix approach.

Breakdown of intermediate one-half magnetization plateau of spin-1/2 Ising-Heisenberg and Heisenberg branched chains at triple and Kosterlitz-Thouless critical points.

The spin-1/2 Ising-Heisenberg branched chain composed of regularly alternating Ising spins and Heisenberg dimers involving an additional side branching is rigorously solved in a magnetic field by the transfer-matrix approach. The ground-state phase diagram, the magnetization process and the concurrence measuring a degree of bipartite entanglement within the Heisenberg dimers are examined in detail. Three different ground states were found depending on a mutual interplay between the magnetic field and two different coupling constants: the modulated quantum antiferromagnetic phase, the quantum ferrimagnetic phase, and the classical ferromagnetic phase. Two former quantum ground states are manifested in zero-temperature magnetization curves as intermediate plateaus at zero and one-half of the saturation magnetization, whereas the one-half plateau disappears at a triple point induced by a strong-enough ferromagnetic Ising coupling. The ground-state phase diagram and zero-temperature magnetization curves of the analogous spin-1/2 Heisenberg branched chain were investigated using density-matrix renormalization group calculations. The latter fully quantum Heisenberg model involves, besides two gapful phases manifested as zero and one-half magnetization plateaus, gapless quantum spin-liquid phase. The intermediate one-half plateau of the spin-1/2 Heisenberg branched chain vanishes at Kosterlitz-Thouless quantum critical point between gapful and gapless quantum ground states unlike the triple point of the spin-1/2 Ising-Heisenberg branched chain.

Plasmon-polariton fractal spectra in quasiperiodic photonic crystals with graphene

In this work we study the plasmon-polariton spectra in one-dimensional photonic crystals based on the Fibonacci, Thue-Morse and double-period sequences, where we have graphene at the interface of one of the constituent building blocks (A = SiO2/graphene, B = SiO2). The dispersion relations for each quasicrystal are numerically calculated by using a transfer-matrix approach. The spectra of these structures are shown to be fractals (for the bulk bands distribution), obeying a power law in a particular frequency region and these are induced specifically by the quasiperiodic ordering in the unit cells of each system studied. We also report a strong dependence of the width of the bulk bands on the wave vector for this particular frequency region, whereas for large wave vectors the fractal properties in these spectra are absent.

The equilibrium landscape of the Heisenberg spin chain

We characterise the equilibrium landscape, the entire manifold of local equilibrium states, of an interacting integrable quantum model. Focusing on the isotropic Heisenberg spin chain, we describe in full generality two complementary frameworks for addressing equilibrium ensembles: the functional integral Thermodynamic Bethe Ansatz approach, and the lattice regularisation transfer matrix approach. We demonstrate the equivalence between the two, and in doing so clarify several subtle features of generic equilibrium states. In particular we explain the breakdown of the canonical \mathcal{Y}𝒴-system, which reflects a hidden structure in the parametrisation of equilibrium ensembles.

Topology optimization of metasurfaces for anomalous reflection of longitudinal elastic waves

A numerical method based on topology optimization is developed for designing a metasurface that anomalously reflects longitudinal elastic waves. While the analysis and design of metasurfaces and metamaterials have received much attention recently, no numerical method to design elastic metasurfaces for anomalous reflection has been explored. Here, we formulate a density-based topology optimization suitable for finding a set of phase-delaying unit cells forming a metasurface that anomalously reflects longitudinal waves impinged upon it. Each unit cell is designed to yield the specific phase delay between the incident and reflected elastic waves. The transfer matrix approach using the averaged finite element results is employed to efficiently and accurately calculate the phase delay while the wave phenomena are analyzed by the finite element analysis. As case studies, metasurfaces converting normally incident longitudinal waves to anomalously reflected longitudinal waves were designed. Various target anomalous reflection angles were considered including the extreme reflection angle of 90°. To investigate the numerical aspect of the developed method, we investigated the effect of the sizes of the unit cells, both along the perpendicular and normal directions to the wave incidence. The mesh dependence issue was also investigated. Finally, we applied the developed topology optimization method to design metasurfaces for wave focusing and trapping in a waveguide.

Tunable Cloaking of Mexican-hat Confined States in Bilayer Silicene

We present the ballistic quantum transport of a p-n-p bilayer silicene junction in the presence of spin-orbit coupling and electric field using a four-band model in combination with the transfer-matrix approach. A Mexican-hat shape of low-energy spectrum is observed similarly to bilayer graphene under an interalayer bias. We show that while bilayer silicene shares some physics with bilayer graphene, it has many intriguing phenomena that have not been reported for the latter. First, the confined state producing a significantly non-zero transmission in Mexican hat. Second, the cloaking of the Mexican-hat confined state is found. Third, we observe that the Mexican-hat cloaking results in a strong oscillation of conductance when the incident energy is below the potential height. Finally, unlike monolayer silicene, the conductance at large interlayer distances increases with the rise of electric field when the incident energy is above the potential height.

The specific heat and magnetic properties of two species of spin-1/2 ladders with butterfly-shaped unit blocks

Studies of the structural effects on the thermodynamic properties of two types of Ising–Heisenberg ladders are comprehensively reported. Each structure comprises spin-1/2 particles partitioned into adjoined blocks or cages formed from butterfly-shaped plaquettes and interacting in an Ising manner. We use the transfer-matrix approach to determine the partition functions of these models and numerically investigate their magnetization and specific-heat properties. Both models illustrate all characteristic features of low-temperature magnetization processes and thermodynamics properties such as abrupt variations of the magnetization curves, Schottky-type peak and a double-peak structure of the specific heat. Comparisons between the two ladders reveal some differences in their magnetic and thermodynamic behaviors. For instance, difference in the number of intermediate magnetization plateaus, also difference in the height and temperature-position of the specific heat peaks. We also present that the fluctuations of the specific heat with respect to the magnetic field are in highly accordance with the magnetization plateaus and magnetization jumps. Moreover, we find quite interesting threshold reentrance points within the matrix-plot of the specific heat shown in the (T/J − B/J) plane, at which the temperature-position of the Schottky peak alternatively change. Finally, we prove that the reentrance points can be satisfactorily considered as magnetization plateau witnesses even in the high temperatures.

Transfer matrix method for simulation of the fiber Bragg grating in polarization maintaining fiber

In this study, a new simulation method is proposed and verified for fiber Bragg grating patterned on polarization maintaining fiber(PM-FBG) using the transfer matrix approach. The method is designed to solve the twisted PM-FBG simulation. The four mode matrix element of a period grating is derived from the S matrix element and the method only involves the torsion-induced shear strain entry exy which can be considered as the rotation of the principal axis of the polarization maintaining fiber and ignores the torsion-induced shear strain entries exz and eyz. The validity of the method is confirmed by numerical simulation of the twisted PM-FBG. The novel method provides the ability to analyze any type of PM-FBG.

A Hubbard model with integrable impurity

We construct an integrable Hubbard model with impurity site containing spin and charge degrees of freedom. The Bethe ansatz equations for the Hamiltonian are derived and two alternative sets of equations for the thermodynamical properties. For this study, the thermodynamical Bethe ansatz (TBA) and the quantum transfer matrix (QTM) approach are used. The latter approach allows for a consistent treatment by use of a finite set of non-linear integral equations. In both cases, TBA and QTM, the contribution of the impurity to the thermodynamical potential is given by integral expressions.

Exact solution of a percolation analog for the many-body localization transition

We construct and solve a classical percolation model with a phase transition that we argue acts as a proxy for the quantum many-body localisation transition. The classical model is defined on a graph in the Fock space of a disordered, interacting quantum spin chain, using a convenient choice of basis. Edges of the graph represent matrix elements of the spin Hamiltonian between pairs of basis states that are expected to hybridise strongly. At weak disorder, all nodes are connected, forming a single cluster. Many separate clusters appear above a critical disorder strength, each typically having a size that is exponentially large in the number of spins but a vanishing fraction of the Fock-space dimension. We formulate a transfer matrix approach that yields an exact value $\nu=2$ for the localisation length exponent, and also use complete enumeration of clusters to study the transition numerically in finite-sized systems.

Acoustical characteristics of ultralight polylactic acid foams fabricated via solution phase inversion

The acoustic properties of highly porous polylactic acid (PLA) foams with very low densities (as low as 0.12 g/cm3) are evaluated using an impedance tube. PLA foams with a mesoporous or a combined meso/macroporous morphology exhibiting different mechanical and physical properties, are produced via nonsolvent induced phase separation (NIPS). The resulting foams exhibit an interesting resonance-like acoustic absorption behavior providing the opportunity to design acoustic materials to target specific frequency bands by controlling their microstructure. Despite very low densities, plane wave tube measurements suggest that these PLA foams may have the potential for sound barrier applications. Using the transfer matrix approach on multilayer configurations, we showed that the combined meso/macroporous morphology has the most significant impact on the absorption and transmission capacity of the foams. The knowledge produced from this study helps to understand the correlation between the characteristics of highly porous NIPS-derived foams and their acoustic properties.

Integrable quenches in nested spin chains I: the exact steady states

We consider quantum quenches in the integrable -invariant spin chain (Lai–Sutherland model) which admits a Bethe ansatz description in terms of two different quasiparticle species, providing a prototypical example of a model solvable by nested Bethe ansatz. We identify infinite families of integrable initial states for which analytic results can be obtained. We show that they include special families of two-site product states which can be related to integrable ‘soliton non-preserving’ boundary conditions in an appropriate rotated channel. We present a complete analytical result for the quasiparticle rapidity distribution functions corresponding to the stationary state reached at large times after the quench from the integrable initial states. Our results are obtained within a quantum transfer matrix (QTM) approach, which does not rely on the knowledge of the quasilocal conservation laws or of the overlaps between the initial states and the eigenstates of the Hamiltonian. Furthermore, based on an analogy with previous works, we conjecture analytic expressions for such overlaps: this allows us to employ the quench action method to derive a set of integral equations characterizing the quasi-particle distribution functions of the post-quench steady state. We verify that the solution to the latter coincides with our analytic result found using the QTM approach. Finally, we present a direct physical application of our results by providing predictions for the propagation of entanglement after the quench from such integrable states.

Integrable quenches in nested spin chains II: fusion of boundary transfer matrices

We consider quantum quenches in the integrable -invariant spin chain (Lai–Sutherland model), and focus on the family of integrable initial states. By means of a quantum transfer matrix approach, these can be related to ‘soliton-non-preserving’ boundary transfer matrices in an appropriate transverse direction. In this work, we provide a technical analysis of such integrable transfer matrices. In particular, we address the computation of their spectrum: this is achieved by deriving a set of functional relations between the eigenvalues of certain ‘fused operators’ that are constructed starting from the soliton-non-preserving boundary transfer matrices (namely the T- and Y-systems). As a direct physical application of our analysis, we compute the Loschmidt echo for imaginary and real times after a quench from the integrable states. Our results are also relevant for the study of the spectrum of -invariant Hamiltonians with open boundary conditions.

An application of the transfer matrix approach for a dynamic analysis of complex spatial pipelines

An effective method for the calculations of stress and residual strength of complex spatial pipelines at static and dynamic loading with taking into account the vibration of internal liquid and Puasson coupling is presented. It based on the well-known transfer matrix approach. The method utilizes the exact mechanical equations for the stress-strained state of straight beam with distributed mass, which connect unknown parameters of forces and displacements at the end of beam calculation element with the parameters at the beginning of the element. At a general level, the solution scheme and calculation models are the same for static and dynamic calculations, the only difference – are the equations. Two different methods are used to find natural vibration frequencies of the distributed mass system: straightforward (“brute force”) and quick, based on Williams-Wittrick frequencies counter. Within such counter a special procedure is developed for taking into account fluid vibration with consideration of volumetric balance condition at T-nozzles. The excellent accuracy of the method is demonstrated by the modeling of thin-walled, water filled pipe behavior after the rod impact. Two seismic analysis procedures are implemented on the base of developed method: standard response spectrum procedure and normal-mode summation procedure (“exact” dynamical), which uses accelerograms. These methods and procedures have been already implemented in calculation software for pipeline strength assessment with the possibility of building of arbitrary complexity models by the user-friendly, visual way. Their effectiveness is demonstrated by the seismic calculation for primary circuit pipings of Zaporizhia NPP.