Semi-infinite Array Research Articles

Diffraction of acoustic waves by multiple semi-infinite arraysa).

Analytical methods are fundamental in studying acoustics problems. One of the important tools is the Wiener-Hopf method, which can be used to solve many canonical problems with sharp transitions in boundary conditions on a plane/plate. However, there are some strict limitations to its use, usually the boundary conditions need to be imposed on parallel lines (after a suitable mapping). Such mappings exist for wedges with continuous boundaries, but for discrete boundaries, they have not yet been constructed. In our previous article, we have overcome this limitation and studied the diffraction of acoustic waves by a wedge consisting of point scatterers. Here, the problem is generalised to an arbitrary number of periodic semi-infinite arrays with arbitrary orientations. This is done by constructing several coupled systems of equations (one for every semi-infinite array) which are treated independently. The derived systems of equations are solved using the discrete Wiener-Hopf technique and the resulting matrix equation is inverted using elementary matrix arithmetic. Of course, numerically this matrix needs to be truncated, but we are able to do so such that thousands of scatterers on every array are included in the numerical results. Comparisons with other numerical methods are considered, and their strengths/weaknesses are highlighted.

A mechanistic evaluation of the local Bloch wave approximation in graded arrays of vertical barriers

Wave interaction with graded metamaterials exhibits the phenomenon of rainbow reflection, in which broadband wave signals slow down and separate into their frequency components before being reflected. This phenomenon has been qualitatively understood by describing the wave field in the metamaterial using the local Bloch wave approximation (LBWA), which locally represents the wave field as a superposition of propagating wave solutions in the cognate infinite periodic media (so-called Bloch waves). We evaluate the performance of the LBWA quantitatively in the context of two-dimensional linear water-wave scattering by graded arrays of surface-piercing vertical barriers. To do this, we implement the LBWA numerically so that the Bloch waves in one region of the graded array are coupled to Bloch waves in adjacent regions. This coupling is computed by solving the scattering of Bloch waves across the interface between two semi-infinite arrays of vertical barriers, where the barriers in each semi-infinite array can have different submergence depths. Our results suggest that the LBWA accurately predicts the free surface amplitude across a wide range of frequencies, except those just above the cutoff frequencies associated with each of the vertical barriers in the array. This highlights the importance of decaying Bloch modes above the cutoff in rainbow reflection.

Array scattering resonance in the context of Foldy’s approximation

This article provides an overview of resonance phenomena in wave scattering by infinite and semi-infinite periodic arrays of small cylindrical scatterers, in the context of Foldy’s approximation. It briefly summarizes well-known results from the literature. Moreover, for infinite arrays, the asymptotics of the resonant wave amplitudes in the double resonance case is investigated. This leads to the rediscovery of non-uniqueness of the solution in this context, and to a discussion of the validity of Foldy’s approximation for double resonance. For semi-infinite arrays, a new and improved uniform far-field approximation is derived, uniqueness issues are considered and the validity of Foldy’s approximation is discussed.

Diffraction of Acoustic Waves by a Wedge of Point Scatterers

This article considers the problem of diffraction by a wedge consisting of two semi-infinite periodic arrays of point scatterers. The solution is obtained in terms of two coupled systems, each of which is solved using the discrete Wiener--Hopf technique. An effective and accurate iterative numerical procedure is developed to solve the diffraction problem, which allows us to compute the interaction of thousands of scatterers forming the wedge. A crucial aspect of this numerical procedure is the effective truncation of slowly convergent single and double infinite series, which requires careful asymptotic analysis. A convergence criterion is formulated and shown to be satisfied for a large class of physically interesting cases. A comparison to direct numerical simulations is made, highlighting the accuracy of the method.

Diffraction by a truncated planar array of dipoles:A Wiener–Hopf approach

We present a rigorous solution to the problem of scattering of a semi-infinite planar array of dipoles, i.e., infinite in one direction and semi-infinite in the other direction, thus presenting an edge truncation, when illuminated by a plane wave. Such an arrangement represents the canonical problem to investigate the diffraction occurring at the edge-truncation of a planar array. By applying the Wiener–Hopf technique to the Z-transformed system of equations derived from the electric field integral equation, we provide rigorous close form expressions for the dipoles’ currents. We find that such currents are represented as the superposition of the infinite array solution plus a perturbation, which comprises both edge diffraction and bound surface waves excited by the edge truncation. Furthermore, we provide an analytical approximation for the double-infinite sum involved in the calculation which drastically reduces the computational effort of this approach and also provides physically-meaningful asymptotics for the diffracted currents.

Simulation of nanoparticle penetration through mesh screens using a hybrid lattice-Boltzmann Lagrangian method and comparison with experiments

2-D hybrid lattice-Boltzmann Lagrangian simulations are conducted to predict the experimental results for nanoparticle filtrations in mesh screens. Comparisons between simulations and experimental data are made for pressure drops across the screens and screen-collection efficiencies. The penetration of 10–300 nm particles through a screen is evaluated for three screen opening sizes (60, 100 and 180 µm) at different flow rates (2.5, 4 and 6 LPM). The computational results are obtained in a 2-D cross-sectional domain that represents a semi-infinite array of clean fibers. In order to simplify the 3-D configuration where two fibers interweave, three 2-D models that take into account the physical parameters of mesh screens are investigated: opening-size-, open-area- and volume-fraction-based modeling. Regarding the prediction accuracy, the results identify the most suitable mesh parameters for being used in a 2-D model to predict particle filtration. In addition, the spatial distributions of particle deposition on a single fiber are in accordance with structural growth during fiber loading in the regimes of diffusion and interception.

Surface vector plasmonic lattice solitons in semi-infinite graphene-pair arrays.

We investigate the surface vector plasmonic lattice solitons (PLSs) in semi-infinite graphene-pair arrays (GPAs). The surface vector PLSs are composed of two components which are associated with different band gaps. Both components undergo mutual self-trapping at the boundary of the semi-infinite structure when the self-focusing nonlinearity of graphene and the light diffraction reach a balance. Thanks to the strong confinement of SPPs, the surface vector PLSs can be squeezed into a deep-subwavelength width of ~0.003λ. By comparing with bulk solitons, the surface PLSs are more readily to excite by external waves and more sensitive to the surrounding environment. The study may develop promising applications in all-optical switching devices and optical sensors on deep-subwavelength scale.

Filtration of aerosol particles by clean elliptical fibers with relevance to pore size: A lattice Boltzmann-cellular automaton model

Aerosol filtration is fundamental to environmental and industrial applications. Among several computational methods for the estimation of particle-laden flows, the lattice Boltzmann-cellular automata (LB-CA) has shown great promise. After validation, a 2-D LB-CA model is proposed to investigate the effect of pore size on particle-fiber collisions in a laminar free-stream flow over a semi-infinite array of clean elliptical fibers. The study contrasts the particle deposition characteristics of elliptical and cylindrical fibers, towards understanding the effect of ellipse eccentricity and orientation on the particle-fiber collision efficiency. Particle motion mechanisms considered comprise drag, lift, net gravitational and Brownian forces. The results show that the pore size needs to be small enough to show the significant correlation between the particle-fiber collision efficiency and elliptical fiber geometry. In the inertial impaction regime, enhancement of the particle-collision efficiency, reduction of the packing density and decreases of the pressure drop can be simultaneously achieved by employing a high-eccentricity elliptical fiber with an angle of 30° to 90° between the major axis and inflow direction. In the diffusion dominated regime, particle-collision efficiency is found to be influenced only by the fiber surface area.

Surface Plasmonic Lattice Solitons in Semi-Infinite Graphene Sheet Arrays

We investigate the surface plasmonic lattice solitons (PLSs) in semi-infinite graphene sheet arrays. The surface soliton is formed as the SPPs tunneling is inhibited by the graphene nonlinearity, and meanwhile the incident power should be above a threshold value. Thanks to the strong confinement of surface plasmon polaritons (SPPs) on graphene, the effective width of surface PLSs can be squeezed into deep-subwavelength scale of ~ 0.001{\lambda}. Based on the stable propagation of surface PLSs, we find that the light propagation can be switched from the array boundary to the inner graphene sheets by reducing the incident power or increasing the chemical potential of graphene. The study may find promising application in optical switches on deep-subwavelength scale.

Interaction-induced edge states in anisotropic non-Fermi liquids.

We devise an approach to calculation of scaling dimensions of generic operators describing scattering within multi-channel Luttinger liquid. The local impurity scattering in arbitrary configuration of conducting and insulating channels is investigated and the problem is reduced to a single algebraic matrix equation. The application to a semi-infinite array of chains described by Luttinger liquid models demonstrates that for a weak inter-chain hybridisation and intra-channel electron-electron attraction the edge wire is robust against disorder whereas bulk wires, on contrary, become insulating in some region of inter-chain interaction parameters. This result proves that the edge states may exist in disordered anisotropic strongly correlated systems without time-reversal symmetry breaking or spin-orbit interaction and provide quantized low-temperature transport.

Controlling Flexural Waves in Semi-Infinite Platonic Crystals with Resonator-Type Scatterers

We address the scattering and transmission of a plane flexural wave through a semi-infinite array of point scatterers/resonators, which take a variety of physically interesting forms. The mathematical model accounts for several classes of point defects, including mass-spring resonators attached to the top surface of the flexural plate and their limiting case of concentrated point masses. We also analyse the special case of resonators attached to opposite faces of the plate. The problem is reduced to a functional equation of the Wiener–Hopf type, whose kernel varies with the type of scatterer considered. A novel approach, which stems from the direct connection between the kernel function of the semi-infinite system and the quasi-periodic Green's functions for corresponding infinite systems, is used to identify special frequency regimes. We thereby demonstrate dynamically anisotropic wave effects in semi-infinite platonic crystals, with particular attention paid to designing systems that exhibit dynamic neutrality (perfect transmission) and localisation close to the structured interface.

Non-Markovian dynamics of a qubit coupled to a waveguide in photonic crystals with infinite cavity-array structure

We evaluate exactly the non-Markovian effect on the decoherence dynamics of a qubit coupling with a waveguide in photonic crystals. In our study, we extend the previous investigation that the waveguide is structured as a semi-infinite cavity array to the case that it is set as an infinite cavity array. For the infinite cavity array, we utilize the quantity of fidelity to characterize the ability of the system to preserve its initial quantum information. We make a discussion for different initial states of the qubit. Similar to the case of semi-infinite cavity array, we find that the quantum information of the qubit in the long-time scale could also be partially preserved when the qubit–waveguide coupling strength goes beyond a critical value. This is a strong non-Markovian memory effect induced by the strong qubit–waveguide coupling strength. Interestingly, the critical coupling strength for infinite cavity array happens to be zero, which means that in this real physical system, the quantum-to-classical transition behavior of the qubit never occurs. Therefore, by reasonably choosing the structure of the environment, the quantum information of the quantum systems could be more easily preserved. Moreover, we find that the higher probability of the qubit initially in its ground state, the more easily for it to preserve its initial information in the long-time scale, which proves that the quantum open system always tends to stay in its ground state.

ANALYTICAL DESCRIPTION OF PLASMON REFLECTION FROM THE FREE EDGES OF METAL SLIT STRUCTURES

n this paper we consider gap surface plasmon (GSP) propagation properties in slit milled in metal. Developed theoretical model allows to derive equations describing the reflection and transmission of the GSP from the free edge of semi-infinite slit or periodic array of semi-infinite slits in metallic host, analytically. Using these equations we calculate the transmitted power efficiency from the slit and from the array of slits. For the conditions when slit width (d) is very small compared to incident wavelength, the transmitted power efficiency is increased proportional with d3/2, otherwise the dependence is linear. The relation of transmitted power through periodic array of slits to the transmitted power from single slit depends on slit period for the fixed wavelength. The derived equations give mathematical mechanism to calculate theoretical resonant length, losses and Q-factor of plasmon gap microresonator structures and can be used as a preliminary guideline upon designing plasmon gap microresonator.

Theoretical formalism for collective spin-wave edge excitations in arrays of dipolarly interacting magnetic nanodots

A general theory of edge spin wave excitations in semi-infinite and finite periodic arrays of magnetic nanodots existing in a spatially uniform magnetization ground state is developed. The theory is formulated using a formalism of multi-vectors of magnetization dynamics, which allows one to study edge excitations in arrays having arbitrary complex primitive cells and lattice geometry. The developed formalism can describe edge excitations localized both at the physical edges of the array and at the internal "domain walls" separating array regions existing in different static magnetization states. Using a perturbation theory in the framework of the developed formalism it is possible to calculate damping of edge modes and their excitation by external variable magnetic fields. The theory is illustrated on the following practically important examples: (i) calculation of the FMR absorption in a finite nanodot array having the shape of a right triangle, (ii) calculation of nonreciprocal spin wave spectra of edge modes, including modes at the physical edges of an array and modes at the domain walls inside an array, (iii) study of the influence of the domain wall modes on the FMR spectrum of an array existing in a non-ideal chessboard antiferromagnetic ground state.

Dynamic localization of light in squeezed-like photonic lattices

We investigate the dynamic localization of light in the sinusoidal bent squeezed-like photonic lattices, a class of inhomogeneous semi-infinite waveguide arrays. Our findings show that, dynamic localization takes place for the normalized amplitude of sinusoidal profile (α) above a critical value αc. In this regime, for any normalized amplitude α>αc, there is a specific spatial period (ℓ) of waveguides, in which the dynamical oscillation, with the same spatial period occurs. Moreover, the specific spatial period is a decreasing function of the normalized amplitude α. Accordingly, the dynamical oscillation and self-imaging is realized, in spite of the existence of inhomogeneous coupling coefficients and semi-infinite nature of the squeezed-like photonic lattices. In addition, a comparison between the dynamic localization and Bloch oscillation in squeezed-like photonic lattices reveals that for the same values of α (>αc), the variation in the width and the mean center of the Bloch oscillation profile are less than the corresponding values of the dynamic localization. Also, we propose the experimental conditions to observation of dynamic localization in squeezed photonic lattices.

Dynamic interfacial trapping of flexural waves in structured plates

The paper presents new results on the localization and transmission of flexural waves in a structured plate containing a semi-infinite two-dimensional array of rigid pins. In particular, localized waves are identified and studied at the interface boundary between the homogeneous part of the flexural plate and the part occupied by rigid pins. A formal connection has been made with the dispersion properties of flexural Bloch waves in an infinite doubly periodic array of rigid pins. Special attention is given to regimes corresponding to standing waves of different types as well as Dirac-like points that may occur on the dispersion surfaces. A single half-grating problem, hitherto unreported in the literature, is also shown to bring interesting solutions.

Floquet modes-based asymptotic analysis of scattering from FSS-type reflectarray/transmitarray for near-zone-focused radiations

This paper presents the asymptotic formulation of ray fields in the decomposition of electromagnetic (EM) scattering mechanisms from a one-dimensional, semi-infinite and periodic array when it is illuminated by a line source. This technique can be applied to analyze the passive FSS (frequency selective surface) type periodic structures with identical elements, or the reflectarray and transmitarray type antennas that are phased to radiate EM fields focused in the near zone of the array aperture. The solutions are built up based on the Floquet mode expansion of the scattering fields, and are obtained by asymptotically evaluating the resulted integrals to express the fields in terms of reflected/transmitted and edge diffracted fields as previously addressed in the framework of uniform geometrical theory of diffraction (UTD). The theoretical investigations over the scattering mechanisms and propagation phenomena are performed. Numerical examinations are presented to demonstrate the utilization of these solutions.

One-dimensional reflection by a semi-infinite periodic row of scatterers

Three methods are described in order to solve the canonical problem of the one-dimensional reflection by a semi-infinite periodic row of identical scatterers. The exact reflection coefficient R is determined. The first method is associated with shifting the domain by a single period and subsequently considering two scatterers, one being a single scatterer and the second being the entire semi-infinite array. The second method determines the reflection coefficient RN associated with a finite array of N scatterers. The limit as N→∞ is then taken. In general RN does not converge to R in this limit, although we summarize various arguments that can be made to ensure the correct limit is achieved. The third method considers direct approaches. In particular, for point masses, the governing inhomogeneous ordinary differential equation is solved using the discrete Wiener–Hopf technique.

An Early Stage of Aerosol Particle Transport in Flows Past Periodic Arrays of Clear Staggered Obstructions: A Computational Study

Transport of aerosol particles is a fundamental phenomenon in many environmental and industrial applications. Among the several computational fluid dynamical schemes used to study this problem, the lattice Boltzmann methods (LBMs) have shown great promise. Using a 2-D LBM model coupled with a Lagrangian formalism, this study investigates an early stage of particle–surface collisions in a free-stream flow over a semi-infinite array of staggered obstructions at operating conditions of woven-wire screens. After an initial validation of the model, the particle–surface collision efficiency with different diameters is then examined as functions of the number of staggered obstructions, obstruction morphology, and separation distance between two center points of obstructions. Particle motion mechanisms include drag, lift, and Brownian forces. Enhanced collision efficiency of particles to obstructions due to the presence of multiple staggered cylindrical obstructions is identified and highlighted. Based on these i...

Truncation Diffraction Phenomena of Floquet Waves Radiated From Semi-Infinite Phased Array Antenna in a General Focus Problem

This paper presents uniform formulations of radiation mechanisms, analogous to the ray decompositions of diffraction theory, from a semi-infinite and periodic array of antennas. The antenna array is excited to radiate the electromagnetic (EM) fields focused at a relatively arbitrarily selected location. The ray decomposition results from a closed-form formulation by asymptotically evaluating the radiation integral of Floquet modes that are obtained by applying the Poisson sum formula to the summation of elemental radiations. The analysis is relatively general and will reduce to the case of a conventional phased array antenna that is excited to radiate directive beams focused in the far zone, and exhibits consistent phenomena. Theoretical investigations as well as numerical examinations are presented to demonstrate the radiation mechanisms.