Dipolar Arrays Research Articles

Seismoelectric wave conversions at an interface: a quantitative comparison between laboratory data and full-waveform modelling

SUMMARYSeismo-electromagnetic phenomena, electrokinetic in nature, take place whenever a seismic wave propagates in fluid-bearing media, its energy depending mainly on the electrical properties of the fluid and the hydraulic properties of the porous medium. They result from a conversion of mechanical into electromagnetic (EM) energy due to the transient ionic interactions occurring at the pore scale. Two of these phenomena are usually studied: the electric field accompanying seismic waves, and the EM field that travels independently, generated at discontinuities of physicochemical properties in the porous medium. Although the first event is sensitive to physical parameters of the surrounding medium, the second catches information about interfaces in the subsurface, with the resolution of seismic methods, making it very attractive to near surface exploration. In this context, we propose a new experimental setup where both phenomena can be simultaneously studied. At first, we use a porous medium composed of homogeneous water-saturated sand and study the characteristics of the coseismic electric field. Afterwards, a thin layer of Vosges sandstone is inserted into the sand, which allows the study of the EM waves generated at the two closely spaced sand-sandstone interfaces. We record the seismic displacement field at the upper surface of the sand volume using a laser vibrometer, and use stainless steel electrodes buried in the sand to acquire individual electric potentials rather than electric fields, seeking to favour the measurement of the EM interface-generated signals. With the help of direct numerical simulations, we compare experimental measurements and theoretical predictions, based on a well established set of seismoelectric governing equations. In both types of experiments, this comparison shows very good agreements between experimental and numerical waveforms, thus confirming the relevant theory. The electric potential data also show that the EM signals generated at interfaces are clearly recorded at distances of about 10 seismic P wavelengths away from the interface. By contrast, the same events are barely noticeable near the inserted layer when measured using classical electric dipolar arrays.

Topological robust corner states of a two-dimensional square lattice with C4 symmetry in fully coupled dipolar arrays

A profound insight into topological photonic systems will empower us to harness their maximum potential and discover uncharted topological phenomena. For the square quadripartite lattice with only nearest-neighbor reciprocal couplings, in the out-of-plane mode, sublattice symmetry makes the eigenvalues of the Hamiltonian symmetric around zero energy, while C 4 symmetry closes the gap between the central bands. Meanwhile, topological corner states (CSs) are fixed at zero energy due to chiral symmetry. Thereby, the CSs cannot appear in a gap, but are embedded in the bulk. In this paper, the full coupling between dipoles is considered in the Hamiltonian, i.e., not only the near-field of nearest-neighbor, but also the far-field dipole-dipole interactions are taken into account to investigate the new potential topological properties. The results show that the sublattice symmetry of the system will be broken, leading to the appearance of a zero-energy band gap. Nevertheless, the generalized chiral symmetry ensures that the CSs are still pinned to zero energy. That is, in-gap CSs are provided. Additionally, the silicon carbide materials used in this paper can confine light to the deep subwavelength scale, which has great potential in enhancing light-matter interactions in the terahertz range.

Classical-linear-chain behavior from dipolar droplets to supersolids

We investigate the classicality of linear dipolar droplet arrays through a normal mode analysis of the dynamical properties in comparison to the supersolid regime. The vibrational patterns of isolated-droplet crystals that time-evolve after a small initial kick closely follow the properties of a linear droplet chain. For larger kick velocities, however, droplets may coalesce and separate again, showing distinct deviations from classicality. In the supersolid regime the normal modes are eliminated by a counterflow of mass between the droplets, signaled by a reduction of the center-of-mass motion. Our study effectively captures the vibrational patterns of isolated droplets in the presence of three-body loss and can be generalized to systems with a larger number of droplet arrays.

Dispersion braiding and band knots in plasmonic arrays with broken symmetries

Abstract Periodic arrays can support highly nontrivial modal dispersion, stemming from the interplay between localized resonances of the array elements and distributed resonances supported by the lattice. Recently, intentional defects in the periodicity, i.e., broken in situ symmetries, have been attracting significant attention as a powerful degree of freedom for dispersion control. Here we explore highly nontrivial dispersion features in the resonant response of linear arrays of plasmonic particles, including the emergence of braiding and band knots caused by band folding. We show that these phenomena can be achieved within simple dipolar arrays for which we can derive closed-form expressions for the dispersion relation. These phenomena showcase powerful opportunities stemming from broken symmetries for extreme dispersion engineering, with a wide range of applications, from plasma physics to topological wave phenomena. Our theoretical model can also be generalized to higher dimensions to explore higher-order symmetries, e.g., glide symmetry and quasi-periodicity.

Anisotropy and domain formation in a dipolar magnetic metamaterial

Long-range magnetic ordering can be stabilized in arrays of single-domain nanomagnets through dipolar interactions. In these metamaterials, the magnetic properties are determined by geometric parameters such as the nanomagnet shape and lattice symmetry. Here, we demonstrate engineering of the anisotropy in a dipolar magnetic metamaterial by tuning of the lattice parameters. Furthermore, we show how a modified Kittel's law explains the resulting domain configurations of the dipolar ferromagnetic arrays.

Pinning of thermal excitations at defects in artificial dipolar arrays: A theoretical investigation

In this theoretical investigation we address the effect of defects on thermal excitations in square-lattice dipolar arrays. The samples consist of nanomagnets, whose geometry is adopted from recent experiments [A. Farhan et al., Nat. Phys. 9 (2013) 375] [13] and allows for thermal activation at room temperature. Various types of defects, all of which may be produced by microstructuring techniques, are introduced into the systems. It turns out that excitations can efficiently be pinned at defects. Furthermore, it is possible to produce ferromagnetic strings of nanomagnets that connect a pair of defects; their lengths are closely related to the distance of the defects and the topology of the magnetic ground-state configuration.

Real space electrostatics for multipoles. I. Development of methods.

We have extended the original damped-shifted force (DSF) electrostatic kernel and have been able to derive three new electrostatic potentials for higher-order multipoles that are based on truncated Taylor expansions around the cutoff radius. These include a shifted potential (SP) that generalizes the Wolf method for point multipoles, and Taylor-shifted force (TSF) and gradient-shifted force (GSF) potentials that are both generalizations of DSF electrostatics for multipoles. We find that each of the distinct orientational contributions requires a separate radial function to ensure that pairwise energies, forces, and torques all vanish at the cutoff radius. In this paper, we present energy, force, and torque expressions for the new models, and compare these real-space interaction models to exact results for ordered arrays of multipoles. We find that the GSF and SP methods converge rapidly to the correct lattice energies for ordered dipolar and quadrupolar arrays, while the TSF is too severe an approximation to provide accurate convergence to lattice energies. Because real-space methods can be made to scale linearly with system size, SP and GSF are attractive options for large Monte Carlo and molecular dynamics simulations, respectively.

Thermal string excitations in artificial spin-ice square dipolar arrays

We report on a theoretical investigation of artificial spin-ice dipolar arrays using a nanoisland shape adopted from recent experiments (Farhan et al 2013 Nature Phys. 9 375). The number of thermal magnetic string excitations in the square lattice is drastically increased by a vertical displacement of rows and columns. We find large increments especially for low temperatures and for string excitations with quasi-monopoles of charges ±4. By kinetic Monte Carlo simulations we address the thermal stability of such excitations, thereby providing time scales for their experimental observation.

Patterned time-orbiting potentials for the confinement and assembly of magnetic dipoles

We present an all-magnetic scheme for the assembly and study of magnetic dipoles within designed confinement profiles that are activated on micro-patterned permalloy films through a precessing magnetic field. Independent control over the confinement and dipolar interactions is achieved by tuning the strength and orientation of the revolving field. The technique is demonstrated with superparamagnetic microspheres field-driven to assemble into closely packed lattice sheets, quasi-1D and other planar structures expandable into dipolar arrays that mirror the patterned surface motifs.

Polarizability, Susceptibility, and Dielectric Constant of Nanometer‐Scale Molecular Films: A Microscopic View

AbstractThe size‐dependence of the polarizability, susceptibility, and dielectric constant of nanometer‐scale molecular layers is explored theoretically. First‐principles calculations based on density functional theory are compared to phenomenological modeling based on polarizable dipolar arrays for a model system of organized monolayers composed of oligophenyl chains. Size trends for all three quantities are primarily governed by a competition between out‐of‐plane polarization enhancement and in‐plane polarization suppression. Molecular packing density is the single most important factor controlling this competition and it strongly affects the bulk limit of the dielectric constant as well as the rate at which it is approached. Finally, the polarization does not reach its “bulk” limit, as determined from the Clausius–Mossotti model, but the susceptibility and dielectric constant do converge to the correct bulk limit. However, whereas the Clausius–Mossotti model describes the dielectric constant well at low lateral densities, finite size effects of the monomer units cause it to be increasingly inaccurate at high lateral densities.

Magnetic multipole analysis of kagome and artificial spin-ice dipolar arrays

We analyze an array of linearly extended monodomain dipoles forming square and kagome lattices. We find that its phase diagram contains two (distinct) finite-entropy kagome ice regimes---one disordered, one algebraic---as well as a low-temperature ordered phase. In the limit of the islands almost touching, we find a staircase of corresponding entropy plateaux, which is analytically captured by a theory based on magnetic charges. For the case of a modified square ice array, we show that the charges (``monopoles'') are excitations experiencing two distinct Coulomb interactions: a magnetic ``three-dimensional'' one as well as a logarithmic ``two-dimensional'' one of entropic origin.

Molecular Rotors and Motors: Recent Advances and Future Challenges

At the "Molecular Rotors and Motors" symposium of the Spring 2009 ACS National Meeting in Salt Lake City (March 22-26), a diverse mix of talks addressed many current issues in the field. Speakers described topics that varied from single-molecule rotors and nanomachines to exquisite synthetic approaches toward building functional materials and mathematical and computational methods aimed at uncovering design opportunities and highlighting the fundamental limitations of molecular motors. While the realization of building useful nanomachines remains far off, a general consensus abounded that investigating biological systems and understanding the implications of the laws of thermodynamics and quantum mechanics for the behavior of nanostructures will help drive important advances in the quest for molecular machinery. Molecular rotors were demonstrated to have practical applications as probes for microviscosity, and many speakers presented experimental studies that indicated that highly directed translation and rotation of individual molecules, as well as interacting dipolar arrays, are just around the corner. While this Nano Focus is not intended to be a comprehensive review of the subject, it will focus on several key advances that were presented at the ACS meeting and highlight future challenges for the field of molecular rotors and motors.

Depolarization field of spheroidal particles

A compact analytical formula up to the order of k3, where k is a wave vector, is derived for the depolarization field Ed of a spheroidal particle by performing explicitly the steps of the recipe outlined by Meier and Wokaun [Opt. Lett.8, 581 (1983)]. For the static component of Ed a general electrostatic formula valid for a particle of a general shape is rederived within the Meier and Wokaun framework. The dynamic k2-dependent depolarization component of Ed is shown to depend on dynamic geometrical factors, which can be expressed in terms of the standard geometrical factors of electrostatics. The Meier and Wokaun recipe itself is shown to be equivalent to a long-wavelength limit of the Green's function technique. The resulting Meier and Wokaun long-wavelength approximation is found to exhibit a redshift compared against exact T-matrix results. At least for a sphere, it is possible to get rid of the redshift by assuming a weak nonuniformity of the field Eint inside a particle, which can be fully accounted for by a renormalization of the dynamic geometrical factors. My results may be relevant for various plasmonic, or nanoantenna, applications of spheroidal particles with a dominant electric dipole scattering, whenever it is necessary to go beyond the Rayleigh approximation and to capture the essential size-dependent features of scattering, local fields, SERS, hyper-Raman and second-harmonic-generation enhancements, decay rates, and photophysics of dipolar arrays.

Understanding the structural properties of a homologous series of bis-diphenylphosphine oxides

A homologous series of bis-diphenylphosphine oxides (C6H5)2PO(CH2)(n)PO(C6H5)2 (with n = 2-8; denoted 2-8] have been investigated to explore the effects of a range of competing and cooperative intermolecular and intramolecular interactions on the structural properties in the solid state. The important factors influencing the structural properties include intramolecular aspects such as the conformation of the aliphatic chain and the intramolecular interaction between the two P=O dipoles in the molecule, and intermolecular aspects such as long-range electrostatic interactions (dominated by the arrangement of the P=O dipoles), C-H...O interactions, C-H...pi interactions and pi...pi interactions. Compounds 3 and 5 could be crystallized only as solvate co-crystals (3 water and 5 x (toluene)2], whereas the crystal structures of all the other compounds contain only the bis-diphenylphosphine oxide molecule. The crystal structures have been determined from single-crystal X-ray diffraction data, with the exception of 7 (which has been determined here from powder X-ray diffraction data) and 4 (which was known previously). The compounds with even n represent a systematic structural series, exhibiting characteristic, essentially linear P=O...P=O...P=O dipolar arrays, together with C-H...O and C-H...pi interactions. For the compounds with odd n, on the other hand, uniform structural behaviour is not observed across the series, although certain aspects of these crystal structures contribute in a general sense to our understanding of the structural properties of bis-diphenylphosphine oxides. Importantly, for the compounds with odd n, there is "frustration" with regard to the molecular conformation, as the preferred all-anti conformation of the aliphatic chain gives rise to an unfavourable parallel alignment of the two P=O dipoles within the molecule. Clearly the importance of avoiding a parallel alignment of the P=O dipoles becomes greater as n decreases. Local structural aspects (investigated by high-resolution solid-state 31P NMR spectroscopy) and thermal properties of the bis-diphenylphosphine oxide materials are also reported.

Effect of dipolar arrays on the localization of charge carriers in molecular materials

The paper presents results of calculations of the depth and distribution of local states for charge carriers created by polar impurities in a model molecular material. Equations resulting from the electrostatic model due to Lyons have been employed in the calculations. The presence of polar species in a non-polar molecular material locally modifies the polarization energy, thus creating local states (traps) on neighboring molecules. Calculations performed for an isolated dipolar defect show that traps as deep as /spl sim/0.4 eV to /spl sim/0.5 eV can result in such a way, their depths and cross-sections depending on the dipole moment of the guest molecule. Results of similar calculations carried out for arrays of spatially connected dipoles indicate that local states of a considerable density may be created, modifying the density-of-states function, and hence influencing the effective mobility of charge carriers.

Strain relaxation in buried strained layers by mixture of single and dipolar dislocation arrays

The strain relaxation in buried strained layers is investigated using an elastic continuum model. The mixture of single dislocations residing at the substrate/strained layer interface (lower interface) and dipolar dislocations in which one is at the lower interface and the other at the strained layer/capping layer interface (upper interface), is proposed. In the mixture, the dislocation distributions are denoted by a parameter which is the ratio of the density of misfit dislocations at the upper interface to that at the lower interface. In a buried strained layer, relaxation of mean strain occurs by introduction of two orthogonal arrays of mixture of single and dipolar dislocations. Considering both the free surface and interactions between dislocations, the total elastic energy per unit area of buried strained layer containing two orthogonal arrays of mixture of single and dipolar dislocations is calculated. The energy is dependent on the misfit dislocation distributions. On energy minimization considerations, the expression of the misfit dislocation distributions in a buried strained layer with arbitrary strain relaxation and capping layer thickness is derived. It is demonstrated that the strain is initially relaxed by the single misfit dislocations and relaxed by the mixture of single and dipolar misfit dislocations in the final stage of strain relaxation in many buried layers of practical interest.

A TEM study of dislocation structures in fatigued Cu-16 at.% A1 single crystals

Dislocation structures in fatigued Cu-16 at.% A1 single crystals were studied by TEM as a function of total strain amplitude and stress level. The results show that planar arrays of primary dislocations are preserved at all stages of cyclic deformation. With increasing stress level, the density of both primary and secondary dislocations increases and the spacing of the activated primary slip planes decreases. At all stages of deformation, primary edge dislocations dominate the structure, forming dipolar and multipolar arrays which sometimes show evidence of intersection along the traces of the cross slip planes. Primary screw dislocations are rarely observed to form multipoles. Numerous small prismatic loops are formed at the higher stress levels. Dislocation behavior during cyclic deformation, especially concerning strain localization, is discussed in comparison with that of copper.

The cyclic stress—Strain response and dislocation structures of Cu16 at.%Al alloy III: Single crystals fatigued at low strain amplitudes

Monocrystalline Cu16at.%Al alloy shows a conventional cyclic stress-strain curve containing a plateau associated with strain localization but the dislocation structures associated with this behavior have not yet been reported. To rectify this situation, we have cycled specimens to saturation at amplitudes below, within and above the plateau and sectioned them for transmission electron microscopy examination. Our observations show that, below the plateau, the saturation structures consist of dipolar arrays of primary dislocations. At higher amplitudes these structures coexist with more complex structures which have nucleated from the dipolar arrays, giving rise to persistent slip, which we call persistent Lüder's bands (PLBs) to distinguish them from regular persistent slip bands. PLBs contain a very high density of primary dislocations, much secondary activity and internal stress fields associated with the primary dislocation arrays. The relationship of these structures to those in wavy slip materials and the role of stacking fault energy and friction stress in determining their nature are discussed.

Order-Disorder Model of PO4 Dipoles for KDP and ADP

The order-disorder models of PO4 dipoles are examined for KDP type ferro- and antiferroelectrics. The Fourier transforms of dipole-dipole interactions between PO4 dipoles have been numerically computed. As far as this interaction is concerned, the dipolar arrays of the minimum energy are the KDP type ferroelectric array for the “upper” and “lower” dipoles, and the Nagamiya type antiferroelectric one for ”lateral” dipoles. The Slater type model and the Ising spin type model have been reexamined in the light of recent experimental results, and their validities are discussed with reference to the ice constraint.

Excited-State Dipole Moments, Polarizabilities, and Local Fields in Molecular Crystals; Polarizabilities of Benzophenone in its Lowest Singlet and Triplet nπ Excited States

A refined calculation that accounts for molecular polarizabilities, crystal reaction fields and resulting field induced moments in polar molecular crystals allows excited-state dipole moments and polarizabilities to be derived from optically determined Stark splitting versus applied electric field results. The determination of these excited-state properties in a dipolar lattice is particularly dependent on the evaluation of the local field at a molecular site. For this case, the local field is evaluated by introduction of an ellipsoidal cavity approximation and by using the Ewald-Kornfeld lattice summation method for dipolar arrays. The dipolar benzophenone crystal was chosen to demonstrate this method. The dipole moments of the lowest 1nπ* and 3nπ* states of benzophenone have been determined and are 1.23 D and 1.72 D, respectively; these are the zero field values and refer to the benzophenone molecules in the absence of the crystal environment. The polarizabilities of benzophenone in its ground, 1nπ* and 3nπ* states are, in units of 10−23 cm3, 0.532, 0.898, and 0.56, respectively. The excited-state moments are nearly parallel to the ground state moment in the crystal environment and the benzophenone dipole does not reverse direction in going from the ground to the lowest singlet and triplet states.