Plane-wave Set Research Articles

Light switching between localized and delocalized states in chiral moiré-like photonic lattice

Abstract We constructed a chiral moiré-like lattice pattern by the interference between two sets of plane waves and two circular polarized beams. The study shows that the intensity distributions of the lattice pattern are a moiré-like structure in the transverse direction and a spiral structure in the longitudinal direction. By tuning the relative rotation angle between two sets of beams, moiré-like lattice pattern can be switched between periodic to aperiodic systems. Further, we numerically study the impacts of relative rotation angle, the screw pitch of the lattice waveguide, the width and incident direction of the probe beam on the light behavior in chiral moiré-like photonic lattice fabricated with photon-induction method. It turns out that light propagation can be switched between localization and delocalization. Our study enriches the physical content of moiré-like lattice patterns and paves a novel way to the light modulation in photonic lattices.

Three-dimensional transfer function of optical microscopes in reflection mode.

Three-dimensional (3D) transfer functions build the basis for a comprehensive characterization of optical imaging systems in the spatial frequency domain. Utilizing the projection-slice theorem, the 2D modulation transfer function of an incoherent imaging system can be derived from a 3D transfer function by integration with respect to the axial spatial frequency. For a diffraction limited microscope with homogeneous incoherent pupil illumination, the modulation transfer function equals the 2D autocorrelation function of a circular disc. However, until now to the best of our knowledge no 3D transfer function has been published, which exactly leads to the 2D modulation transfer function of a diffraction limited microscope in reflection mode. In this article, we derive a formula, which after integration with respect to the axial spatial frequency coordinate perfectly fits to the diffraction limited 2D modulation transfer function. The inverse three-dimensional Fourier transform of the 3D transfer function results in a complex-valued 3D point spread function, from which the depth of field, the lateral resolution and, in addition, the corresponding 3D point spread function of both, a conventional and an interference microscope, can beobtained.

Shape optimization by conventional and extended isogeometric boundary element method with PSO for two-dimensional Helmholtz acoustic problems

In this paper, a new approach is developed for applications of shape optimization on the two-dimensional time harmonic wave propagation (Helmholtz equation) in acoustic problems. The particle swarm optimization (PSO) algorithm - a gradient-free optimization method avoiding the sensitivity analysis - is coupled with two boundary element methods (BEM) and isogeometric analysis (IGA). The first method is the conventional isogeometric boundary element method (IGABEM). The second method is the eXtended IGABEM (XIBEM) enriched with the partition-of-unity expansion using a set of plane waves. In both methods, the computational domain is parameterized and the unknown solution is approximated using non-uniform rational B-splines basis functions (NURBS).In the optimization models, the advantage of IGA is the feature of representing the three models; i.e. shape design/analysis/optimization, using a set of control points, which also represent control variables and optimization parameters, making communication between the three models easy and straightforward.A numerical example is considered for the duct problem to validate the presented techniques against the analytical solution. Furthermore, two different applications for various frequencies are studied; the vertical noise barrier and the horn problems, and the obtained results are compared against previously published numerical methods using sensitivity analysis and genetic algorithms to verify the efficiency of the proposed approaches.

A Flexible SIE-DDM for EM Scattering by Large and Multiscale Problems

A flexible surface integral equation domain decomposition method (SIE-DDM) with reverse operation self-consistent evaluation (ROSE) is proposed to analyze the electromagnetic (EM) scattering by electrically large, multiscale, perfect electrically conducting objects. ROSE is developed for the robust implementation of the Robin transmission condition between adjacent subdomains in SIE-DDM. By interpolating a set of plane waves on the touching faces, small linear systems are constructed, and the entries of the transmission matrix can be solved algebraically. In doing this, direct numerical integration involving complicated geometrical operations over a nonconformal mesh can be avoided. Several numerical results will be presented to validate the effectiveness of the proposed method.

Rapid simulation of borehole electromagnetic response in axially symmetric and transversely isotropic formations

Downhole well-logging data acquired by modern electromagnetic (EM) tools enables determining not only conductivity but also conductivity anisotropy of reservoirs. The most popular anisotropic model for EM data interpretation is a horizontally layered model with transverse isotropic conductivity in each layer. Such a model ignores the conductivity change caused by the mud-filtrate invasion that often occurs in a permeable layer. The invasion effect can be so strong that the conductivity derived using the 1D model can be substantially affected. We have developed an efficient forward-modeling approach that includes the invasion in the formation model so that the invasion effect can be properly accounted for in data interpretation and inversion. The approach uses a Fourier series expansion for the electric field in the azimuthal direction to take advantage of the invariance of conductivity in this direction. Each harmonic in the expansion is expressed in terms of numerical eigenmodes in the radial direction and exponential functions in the vertical direction. Physically, the latter describes a set of plane waves propagating upward or downward in the vertical direction. This property allows us to use reflection and transmission matrices to couple EM fields from layer to layer, making it highly efficient to simulate EM logging response because the two matrices are computed only once for all logging points. The approach is best suited for a multilayer and transversely isotropic formation in which each layer can have an arbitrary number of radial discontinuities. Numerical experiments demonstrate that the new approach can accurately model the response of induction and propagation tools in various formations. A speedup of two orders of magnitude is obtained in a multilayer case compared with a previous 2D method using a different hybridization strategy.

A Reverse Operation Self-Consistent Evaluation Approach for Singular Integrals in the SIE Analysis of PEC Targets

Discussed herein is a novel approach entitled reverse operation self-consistent evaluation (ROSE). Specifically, we applied ROSE for the treatment of weak-singular and hypersingular kernels in surface integral equations (SIEs) for the computation of electromagnetic (EM) scattering from perfect electrical conductors (PECs). Different from the existing forward methods, ROSE is based on reverse operations. The singular entries are not evaluated directly by analytical or numerical evaluation; instead, they are introduced as unknowns and are solved algebraically. For EM scattering from PEC, SIEs can be set up by using the Stratton–Chu representation formula. An auxiliary problem with the same meshed boundary is then formulated, of which any plane waves are the self-consistent solutions. It is shown that by applying a consistent discretization, the matrix of the auxiliary problem can be made identical with the original one. As a consequence, these self-consistent solutions can be utilized to solve the singular entries of the original system. Explicitly, a set of plane waves are interpolated using the appropriate basis functions. Subsequently, the corresponding coefficient vectors are utilized to construct small linear systems to solve the troublesome singular entries in the underlying matrix. The proposed ROSE approach is applicable to different singular kernels as well as different discretization schemes. In this paper, we restrict our discussion to the weak-singular and hypersingular kernels using, respectively, div-conformal Rao–Wilton–Glisson basis functions and nonconformal piecewise constant vector basis functions. Accelerated by the multilevel fast multipole algorithm, the proposed method is applicable for real-life applications.

On the Alternative Approach to Active Control

Paper is devoted to problem of acoustical visibility reduction and gives brief description of alternative approach to active control. This approach allows satisfy jointly the four conditions: a) effective suppression of acoustical radiation and scattering caused by elastic body immersed in compressible medium (water); b) cloacking at any important temporal frequencies of ob-servant sound waves; c) cloacking at any important spatial frequencies or at any observation directions; (d) thickness of the masking shell is much smaller than the length of suppressed waves. Technological development gives more and more fast and miniature control elements and fast, accurate calculations. On the other hand, the lengths of waves to be damped are con-stant due to the constant conditions of their far propagation. The approach suggested uses operations of high space-time resolution for long waves controlling. Because the joint fulfillment of the conditions of acoustic support absence and the thinness of the shell and also the causality of control lead to the need to operate at frequencies of much higher than frequencies of waves to be damped. It is assumed that the incident waves are represented by a discrete set of plane waves of finite duration. Also it is assumed only that the characteristic spatial scale of the distribution of normal velocities on the surface of the protected body is limited from below. The boundary value problem with initial conditions is considered.

Dispersion and density of states of phonons and electrons in an α-B12 crystal determined from first principles

Using the DFT method, we study the phonon properties of an α-B12 rhombohedral crystal in the basis set of plane waves and its electronic structure in the localized basis set of Gaussians. It follows from the phonon dispersion that the crystal possesses a dynamical stability. The effective Born charges, the oscillator strengths, the transverse–longitudinal splitting, and the dielectric functions of dipole modes are calculated. We show that charge transfer from polar to equatorial atoms takes place in a В12 icosahedron, while В–В bonds have predominantly a covalent character. In the density of states of acoustic modes, we reveal a structure that can manifest itself in the spectra of disordered boron compounds. From the dispersion of electronic bands, the occurrence of an indirect energy gap follows. The overlap of partial densities implies the hybridization of s and p electronic states in boron atoms.

Effect of oxidation state and coordination with Hg(II) on the electronic spectra of an anthraquinone–rhodamine sensor

ABSTRACTIn this study, a computational examination of the electronic transitions and through-space energy transfer processes lends insight into the experimental electronic spectra of a redox-sensitive rhodamine–anthraquinone dyad. Electronic transitions were calculated using density functional theory (DFT) and time-dependent DFT (TDDFT) based on models optimised from single-crystal X-ray diffraction (XRD) ion positions. DFT calculations were performed on gas-phase models using the Vienna Ab Initio Software Package (VASP) with the functional developed by Perdew, Burke, and Ernzerhof (PBE) on a basis set of plane waves. Using the DFT results, select transitions were evaluated based on a dipole–dipole coupling mechanism to find the Förster resonance energy transfer coupling, the square of which is approximately proportional to the rate of energy transfer between the donor and the acceptor. Electronic transitions during the relaxation of charge carriers are also investigated using nonadiabatic molecular dynamics. In order to investigate the transitions contributing to key peaks in the experimental absorbance spectra, TDDFT calculations were performed in Gaussian 09 with the B3LYP functional on the sensor in solution phase, which is simulated using a polarisable continuum model (PCM). The computed electron transfer process from the excited rhodamine to the quinone correlates better with the experimental data than does the computed Förster resonance energy transfer (FRET) process. This computed electron transfer process is faster than the radiative lifetime of the fluorescent state, which collectively suggests that the charge transfer process quenches fluorescence. These results support the observation that fluorescence is more prominent in the oxidised sensor than in the reduced sensor.

Orbital angular momentum in electron diffraction and its use to determine chiral crystal symmetries

In this work we present an alternative way to look at electron diffraction in a transmission electron microscope. In stead of writing the scattering amplitude in Fourier space as a set of plane waves, we use the cylindrical Fourier transform to describe the scattering amplitude in a basis of orbital angular momentum (OAM) eigenstates. We show how working in this framework can be very convenient when investigating e.g. rotation and screw axis symmetries. For the latter we find selection rules on the OAM-coefficients that unambiguously reveal the handedness of the screw axis. Detecting the OAM-coefficients of the scattering amplitude thus offers the possibility to detect the handedness of crystals without the need for dynamical simulations, the thickness of the sample nor the exact crystal structure. We propose an experimental setup to measure the OAM-components where an image of the crystal is taken after inserting a spiral phase plate in the diffraction plane and perform mulsti-slice simulations on $\alpha$-quartz to demonstrate how the method indeed reveals the chirality. Experimental feasibility of the technique is discussed together with its main advantages with respect to chirality determination of screw axes. The method shows how the use of a spiral phase plate can be extended from a simple phase imaging technique to a tool to measure the local OAM-decomposition of an electron wave, widening the field of interest well beyond chiral space group determination.

The Partition of Unity Finite Element Method for the simulation of waves in air and poroelastic media.

Recently Chazot et al. [J. Sound Vib. 332, 1918-1929 (2013)] applied the Partition of Unity Finite Element Method for the analysis of interior sound fields with absorbing materials. The method was shown to allow a substantial reduction of the number of degrees of freedom compared to the standard Finite Element Method. The work is however restricted to a certain class of absorbing materials that react like an equivalent fluid. This paper presents an extension of the method to the numerical simulation of Biot's waves in poroelastic materials. The technique relies mainly on expanding the elastic displacement as well as the fluid phase pressure using sets of plane waves which are solutions to the governing partial differential equations. To show the interest of the method for tackling problems of practical interests, poroelastic-acoustic coupling conditions as well as fixed or sliding edge conditions are presented and numerically tested. It is shown that the technique is a good candidate for solving noise control problems at medium and high frequency.

On Scattering From an Array of Absorptive Material Coated Cones by the PWS Approach

The electromagnetic scattering from periodical coated pyramids/cones array is important information in design and evaluation of a calibration source for the microwave radiometer system. In this paper, we implemented the plane-wave spectrum (PWS) composition method in finding the scattering of arbitrary concentrated beam from a finite-sized absorptive material coated array. In this method, the incident beam is decomposed into a set of plane-waves, then the total scattering from the periodical structure is constructed by re-composing the array scattering to each plane-wave, which can be obtained efficiently by general periodic modeling. Therefore a large-scale problem is turned into a set of small-scale ones. Further more, the results by periodic modeling are reusable in obtaining the total scattering of concentrated illuminating beams with various parameters. Meanwhile, we performed scattering modeling directly of the whole finite-sized calibration source structure to provide reference results. As demonstrated, the scattering results by the whole structure modeling and the PWS approach agree well with each other. The PWS composition method is proven to be simple in implementation and with good efficiency and accuracy, in finding the scattering of arbitrary concentrated beams from the finite-sized periodical microwave calibration source structure.

Application of quasi-forbidden multilayer Bragg reflection for monochromatization of hard X-ray FEL SASE pulses

Preserving and manipulating the complex time structure of the X-ray Free Electron Laser (XFEL) pulses on subfemtosecond scales presents a new challenge for X-ray optics. Promising candidates for ultra-short X-ray pulses optics are periodic multilayer (ML) structures. We present a theoretical investigation of the XFEL pulse propagation through ML structures by an approach based on decomposition of short pulses into a set of plane waves by Fourier transform and application of known methods of X-ray optics. An analysis of coherent properties of XFEL pulse propagated through the ML structures is also presented. It is shown that bandwidth of quasi-forbidden reflections from the small d-spacing Al 2O 3/B 4C structure can be less than pulse bandwidth with reflectivity up to 80%. Such structures can be used for hard X-ray FEL pulses monochromatization and diagnostics.

Plane wave basis in Galerkin BEM for bidimensional wave scattering

This paper considers the problem of scattering of a time-harmonic acoustic incident wave by a bidimensional hard obstacle. The numerical solution to this problem is found using a Galerkin wave boundary integral formulation whereby the functional space is built as the product of conventional low order piecewise polynomials with a set of plane waves propagating in various directions. In this work we improve the original method by presenting new strategies when dealing with irregular meshes and corners. Numerical results clearly demonstrate that these improvements allow the handling of scatterers with complicated geometries while maintaining a low discretization level of 2.5–3 degrees of freedom per full wavelength. This makes the method a reliable tool for tackling high-frequency scattering problems.

Shape Reconstruction of Perfectly Conducting Targets From Single-Frequency Multiview Data

In this letter, we address the problem of reconstructing the shape of a perfectly conducting object illuminated by a set of plane waves at a fixed frequency. The proposed method is made up of two parts. In the first one, for each incident wave, the field in the vicinity of a scatterer is reconstructed by means of a regularized single-layer potential approach. In the second part, the reconstructed fields are simultaneously exploited to build a system of polynomial equations whose solution yields to the unknown contour. As shown by numerical examples, the method is effective, robust against noise on data, and provides satisfactory reconstructions for star-shaped scatterers.

An integration scheme for electromagnetic scattering using plane wave edge elements

Finite element techniques for the simulation of electromagnetic wave propagation are, like all conventional element based approaches for wave problems, limited by the ability of the polynomial basis to capture the sinusoidal nature of the solution. The Partition of Unity Method (PUM) has recently been applied successfully, in finite and boundary element algorithms, to wave propagation. In this paper, we apply the PUM approach to the edge finite elements in the solution of Maxwell’s equations. The electric field is expanded in a set of plane waves, the amplitudes of which become the unknowns, allowing each element to span a region containing multiple wavelengths. However, it is well known that, with PUM enrichment, the burden of computation shifts from the solver to the evaluation of oscillatory integrals during matrix assembly. A full electromagnetic scattering problem is not simulated or solved in this paper. This paper is an addition to the work of Ledger and concentrates on efficient methods of evaluating the oscillatory integrals that arise. A semi-analytical scheme of the Filon character is presented.

Linearized augmented cylindrical wave method for chiral nanotubes

The linearized augmented cylindrical wave (LACW) method has been developed for calculation of the electronic structure of carbon nanotubes [1‐3]. The LACW method is an extension of the well-known linearized augmented plane wave method (LAPW), one of the most exact methods in the band theory of crystals [4‐6], to cylindrical molecules. The major argument for the use of cylindrical waves to describe nanotubes is that such a choice of a basis set allows explicit consideration of the cylindrical geometry of nanotubes, which, in particular, ensures fast convergence of a computational procedure. However, all previous calculations of single- and double-walled carbon and non-carbon nanotubes by the LACW method dealt only with achiral nanotubes, ( n , n ) armchair and ( n , 0 ) zigzag nanotubes with a small number of atoms per translational unit cell [1‐3, 7‐12]. For even small-diameter chiral nanotubes, the number of atoms in the translational unit cell can be very large. For example, the translational cell of the achiral (10,10) nanotube comprises 40 atoms, whereas the translational cell of the chiral (10,9) tube of somewhat smaller diameter comprises 1084 atoms. As is known, the basis set required for convergence rapidly increases with an increase in the number of atoms in the unit cell, which renders impracticable calculations of chiral tubes. It is worth noting that alternative ab initio quantum-chemical calculations of the electronic structure of nanotubes, such as the tight binding method with an atomic basis set and the pseudopotential method with a basis set of plane waves, face the same problem as the LACW method. Therefore, all ab initio band calculations of nanotubes have been restricted to armchair and zigzag tubes or, at best, have dealt with some of the simplest chiral tubes of the smallest diameter and, thus, with a minimal number of atoms in the translational cell. These facts indicate that all rather than only translational symmetry properties of nanotubes should be considered in development of the theory of their electronic structure.

Theoretical prediction of the nondiffractive propagation of sonic waves through periodic acoustic media

We predict theoretically the nondiffractive propagation of sonic waves in periodic acoustic media (sonic crystals) by expansion into a set of plane waves (Bloch mode expansion) and by finite-difference time-domain calculations of finite beams. We also give analytical evaluations of the parameters for nondiffractive propagation, as well as the minimum size of the nondiffractively propagating acoustic beams.

A planar active sound control system using two-dimensional spatial harmonics

An active sound control system based on the extraction of orthogonal spatial harmonics is considered. The system comprises two parallel planar rectangular receiving arrays consisting of small monopole receivers and two planar rectangular transmitting arrays (installed parallel to the receiving arrays) consisting of small monopole transmitters. The field received by the receiving arrays is approximated by a finite number of propagating plane waves with the help of the Fourier transform. The transmitting arrays excite the same set of plane waves outside the system, their amplitudes being chosen so as to cancel the incident external field in a certain region near the system behind the transmitting arrays. The performance of the system is considered for both continuous and discrete distributions of transmitters and receivers. Allowance is made for random errors in the transmitters and receivers, individual to each device.

A plane wave expansion of spherical wave functions for modal analysis of guided wave structures and scatterers

A new finite plane wave series expansion for spherical wave functions of the first kind is presented in this paper. The formulation converts the spherical wave function described in the spherical coordinate system into a series of plane wave functions represented in the Cartesian coordinate system. The series expansion will be very useful in modal analysis of three dimensional guided wave structures and scatterers containing planar boundary surfaces. For a given range of orders m and degree n and for a region with |r~|<R, the same set of plane waves can be used. The theory is numerically verified for a wide range of parameters, showing its fast convergence characteristics. The plane wave expansions of the vector multipole fields can also be obtained.