Showing papers on "Quadrupole published in 2012"

Magnetic dipole and electric quadrupole transitions in the trivalent lanthanide series: Calculated emission rates and oscillator strengths

Abstract: Given growing interest in optical-frequency magnetic dipole transitions, we use intermediate coupling calculations to identify strong magnetic dipole emission lines that are well suited for experimental study. The energy levels for all trivalent lanthanide ions in the $4{f}^{\text{n}}$ configuration are calculated using a detailed free ion Hamiltonian, including electrostatic and spin-orbit terms as well as two-body, three-body, spin-spin, spin-other-orbit, and electrostatically correlated spin-orbit interactions. These free ion energy levels and eigenstates are then used to calculate the oscillator strengths for all ground-state magnetic dipole absorption lines and the spontaneous emission rates for all magnetic dipole emission lines including transitions between excited states. A large number of strong magnetic dipole transitions are predicted throughout the visible and near-infrared spectrum, including many at longer wavelengths that would be ideal for experimental investigation of magnetic light-matter interactions with optical metamaterials and plasmonic antennas.

Profile of the static permittivity tensor of water at interfaces: consequences for capacitance, hydration interaction and ion adsorption.

Abstract: We derive the theoretical framework to calculate the dielectric response tensor and determine its components for water adjacent to hydrophilic and hydrophobic surfaces using molecular dynamics simulations. For the nonpolarizable water model used, linear response theory is found to be applicable up to an external perpendicular field strength of ∼2 V/nm, which is well beyond the experimental dielectric breakdown threshold. The dipole contribution dominates the dielectric response parallel to the interface, whereas for the perpendicular component it is essential to keep the quadrupole and octupole terms. Including the space-dependent dielectric function in a mean-field description of the ion distribution at a single charged interface, we reproduce experimental values of the interfacial capacitance. At the same time, the dielectric function decreases the electrostatic part of the disjoining pressure between two charged surfaces, unlike previously thought. The difference in interfacial polarizability between h...

Collective resonances in metal nanoparticle arrays with dipole-quadrupole interactions

Abstract: Two-dimensional periodic arrays of metal dipole nanoparticles support excitation of narrow collective resonances, which can be used for enhanced light reflection or transmission and for sensing applications. With growing particle sizes, the width of collective dipole resonances is increased, approaching the width of localized surface plasmon resonance of a single particle. However, in systems with broad collective dipole resonances, much narrower resonances can be obtained due to higher multipole radiation coupling between particles. Here we developed a theoretical (semianalytical) approach for investigations of the collective (diffractive) coupling between dipole and quadrupole modes of isolated metal particles arranged in infinite or finite-size arrays. This approach is based on a solution of coupled dipole-quadrupole equations, where the dipole and quadrupole polarizabilities of individual particles are determined by Mie theory. The radiative quadrupole coupling between the particles is introduced by the full-wave quadrupole propagator. Extinction and scattering cross sections of nanoparticle arrays with dipole-quadrupole interactions are presented and discussed. The developed approach is applied for investigations of light transmission through two-dimensional hexagonal arrays of gold nanoparticles. It is shown that the quadrupole coupling can produce narrow collective resonances on the dipole background in the transmission spectra. Sensing properties of the quadrupole resonances are discussed.

Beyond mean-field low-lying excitations of dipolar Bose gases

Abstract: We theoretically investigate various beyond mean-field effects on Bose gases at zero temperature featuring the anisotropic and long-range dipole-dipole interaction in addition to the isotropic and short-range contact interaction. Within the realm of the Bogoliubov-de Gennes theory, we consider static properties and low-lying excitations of both homogeneous and harmonically trapped dipolar bosonic gases. For the homogeneous system, the condensate depletion, the ground-state energy, the equation of state, and the speed of sound are discussed in detail. Making use of the local density approximation, we extend these results in order to study the properties of a dipolar Bose gas in a harmonic trap and in the regime of large particle numbers. After deriving the equations of motion for the general case of a triaxial trap, we analyze the influence of quantum fluctuations on important properties of the gas, such as the equilibrium configuration and the low-lying excitations in the case of a cylinder-symmetric trap. In addition to the monopole and quadrupole oscillation modes, we also discuss the radial quadrupole mode. We find that the latter acquires a quantum correction exclusively due to the dipole-dipole interaction. As a result, we identify the radial quadrupole as a reasonably accessible source for the signature of dipolar many-body effects and stress the enhancing character that dipolar interactions have for quantum fluctuations in the other oscillation modes.

Equilibrium models of relativistic stars with a toroidal magnetic field

Abstract: We have computed models of rotating relativistic stars with a toroidal magnetic field and investigated the combined e ects of magnetic field and rotation on the apparent shape (i.e. the surface deformation), which could be relevant for the electromagnetic emission, and on the internal matter distribution (i.e. the quadrupole distortion), which could be relevant for the emission of gravitational waves. Using a sample of eight di erent cold nuclear-physics equations of state, we have computed models of maximum field strength, as well as the distortion coe cients for the surface and the quadrupolar deformations. Surprisingly, we find that nonrotating models admit arbitrary levels of magnetisation, accompanied by a growth of size and quadrupole distortion to which we could not find a limit. Rotating models, on the other hand, are subject to a mass-shedding limit at frequencies well below the corresponding ones for unmagnetised stars. Overall, the space of solutions can be split into three distinct classes for which the surface deformation and the quadrupole distortion are either: prolate and prolate, oblate and prolate, or oblate and oblate, respectively. We also derive a simple formula expressing the relativistic distortion coe cients and that allows one to compute the surface deformation and the quadrupole distortion up to significant levels of rotation and magnetisation, essentially covering all known magnetars. Such formula replaces Newtonian equivalent expressions that overestimate the quadrupole distortion by about a factor of five and are inadequate for strongly-relativistic objects like neutron stars.

The third and a half-post-Newtonian gravitational wave quadrupole mode for quasi-circular inspiralling compact binaries

Abstract: We compute the quadrupole mode of the gravitational waveform of inspiralling compact binaries at the third and half-post-Newtonian (3.5PN) approximation of general relativity. The computation is performed using the multipolar post-Newtonian formalism, and restricted to binaries without spins moving on quasi-circular orbits. The new inputs mainly include the 3.5PN terms in the mass quadrupole moment of the source, and the control of required subdominant corrections to the contributions of hereditary integrals (tails and nonlinear memory effect). The result is given in the form of the quadrupolar mode (2, 2) in a spin-weighted spherical harmonic decomposition of the waveform, and may be used for comparison with the counterpart quantity computed in numerical relativity. It is a step towards the computation of the full 3.5PN waveform, whose knowledge is expected to reduce the errors on the location parameters of the source.

Effect of surface motion on the rotational quadrupole alignment parameter of D 2 reacting on Cu(111)

Abstract: Ab initio molecular dynamics (AIMD) calculations using the specific reaction parameter approach to density functional theory are presented for the reaction of D2 on Cu(111) at high surface temperature (T(s)=925 K). The focus is on the dependence of reaction on the alignment of the molecule's angular momentum relative to the surface. For the two rovibrational states for which measured energy resolved rotational quadrupole alignment parameters are available, and for the energies for which statistically accurate rotational quadrupole alignment parameters could be computed, statistically significant results of our AIMD calculations are that, on average, (i) including the effect of the experimental surface temperature (925 K) in the AIMD simulations leads to decreased rotational quadrupole alignment parameters, and (ii) including this effect leads to increased agreement with experiment.

Near-field manipulation of spectroscopic selection rules on the nanoscale

Abstract: In conventional spectroscopy, transitions between electronic levels are governed by the electric dipole selection rule because electric quadrupole, magnetic dipole, and coupled electric dipole-magnetic dipole transitions are forbidden in a far field. We demonstrated that by using nanostructured electromagnetic fields, the selection rules of absorption spectroscopy could be fundamentally manipulated. We also show that forbidden transitions between discrete quantum levels in a semiconductor nanorod structure are allowed within the near-field of a noble metal nanoparticle. Atomistic simulations analyzed by an effective mass model reveal the breakdown of the dipolar selection rules where quadrupole and octupole transitions are allowed. Our demonstration could be generalized to the use of nanostructured near-fields for enhancing light-matter interactions that are typically weak or forbidden.

Origin-independent calculation of quadrupole intensities in X-ray spectroscopy

Abstract: For electronic excitations in the ultraviolet and visible range of the electromagnetic spectrum, the intensities are usually calculated within the dipole approximation, which assumes that the oscillating electric field is constant over the length scale of the transition. For the short wavelengths used in hard X-ray spectroscopy, the dipole approximation may not be adequate. In particular, for metal K-edge X-ray absorption spectroscopy (XAS), it becomes necessary to include higher-order contributions. In quantum-chemical approaches to X-ray spectroscopy, these so-called quadrupole intensities have so far been calculated by including contributions depending on the square of the electric-quadrupole and magnetic-dipole transition moments. However, the resulting quadrupole intensities depend on the choice of the origin of the coordinate system. Here, we show that for obtaining an origin-independent theory, one has to include all contributions that are of the same order in the wave vector consistently. This leads to two additional contributions depending on products of the electric-dipole and electric-octupole and of the electric-dipole and magnetic-quadrupole transition moments, respectively. We have implemented such an origin-independent calculation of quadrupole intensities in XAS within time-dependent density-functional theory, and demonstrate its usefulness for the calculation of metal and ligand K-edge XAS spectra of transition metal complexes.

Multipole expansion at the level of the action

Abstract: Sources of long wavelength radiation are naturally described by an effective field theory (EFT) which takes the form of a multipole expansion. Its action is given by a derivative expansion where higher order terms are suppressed by powers of the ratio of the size of the source over the wavelength. In order to determine the Wilson coefficients of the EFT, i.e. the multipole moments, one needs the mapping between a linear source term action and the multipole expansion form of the action of the EFT. In this paper we perform the multipole expansion to all orders by Taylor expanding the field in the source term and then decomposing the action into symmetric trace-free tensors which form irreducible representations of the rotation group. We work at the level of the action, and we obtain the action to all orders in the multipole expansion and the exact expressions for the multipole moments for a scalar field, electromagnetism, and linearized gravity. Our results for the latter two cases are manifestly gauge invariant. We also give expressions for the energy flux and the (gauge dependent) radiation field to all orders in the multipole expansion. The results for linearized gravity are a component of the EFT framework NRGR and will greatly simplify future calculations of gravitational wave observables in the radiation sector of NRGR.

Controlling the dynamics of quantum mechanical systems sustaining dipole-forbidden transitions via optical nanoantennas

Abstract: We suggest to excite dipole-forbidden transitions in quantum mechanical systems by using appropriately designed optical nanoantennas. The antennas are tailored such that their near field contains sufficiently strong contributions of higher-order multipole moments. The strengths of these moments exceed their free-space analogs by several orders of magnitude. The impact of such excitation enhancement is exemplarily investigated by studying the dynamics of a three-level system. It decays upon excitation by an electric quadrupole transition via two electric dipole transitions. Since one dipole transition is assumed to be radiative, the enhancement of this emission serves as a figure of merit. Such self-consistent treatment of excitation, emission, and internal dynamics as developed in this contribution is the key to predict any observable quantity. The suggested scheme may represent a blueprint for future experiments and will find many obvious spectroscopic and sensing applications.

Spin induced multipole moments for the gravitational wave amplitude from binary inspirals to 2.5 Post-Newtonian order

Abstract: Using the NRGR effective field theory formalism we calculate the remaining source multipole moments necessary to obtain the spin contributions to the gravitational wave amplitude to 2.5 Post-Newtonian (PN) order. We also reproduce the tail contribution to the waveform linear in spin at 2.5PN arising from the nonlinear interaction between the current quadrupole and the mass monopole.

Accurate van der Waals coefficients from density functional theory

Abstract: The van der Waals interaction is a weak, long-range correlation, arising from quantum electronic charge fluctuations. This interaction affects many properties of materials. A simple and yet accurate estimate of this effect will facilitate computer simulation of complex molecular materials and drug design. Here we develop a fast approach for accurate evaluation of dynamic multipole polarizabilities and van der Waals (vdW) coefficients of all orders from the electron density and static multipole polarizabilities of each atom or other spherical object, without empirical fitting. Our dynamic polarizabilities (dipole, quadrupole, octupole, etc.) are exact in the zero- and high-frequency limits, and exact at all frequencies for a metallic sphere of uniform density. Our theory predicts dynamic multipole polarizabilities in excellent agreement with more expensive many-body methods, and yields therefrom vdW coefficients C6, C8, C10 for atom pairs with a mean absolute relative error of only 3%.

Influence of internal structure on the motion of test bodies in extreme mass ratio situations

Abstract: We investigate the motion of test bodies with internal structure in general relativity. We utilize a multipolar approximation scheme along the lines of Mathisson-Papapetrou-Dixon including the quadrupolar order. The motion of pole-dipole and quadrupole test bodies is studied in the context of the Kerr geometry. For an explicit quadrupole model, which includes spin and tidal interactions, the motion in the equatorial plane is characterized by an effective potential and by the binding energy. We compare our findings to recent results for the conservative part of the self-force of bodies in extreme mass ratio situations. Possible implications for gravitational wave physics are outlined.

Spin induced multipole moments for the gravitational wave amplitude from binary inspirals to 2.5 Post-Newtonian order

Abstract: Using the NRGR effective field theory formalism we calculate the remaining source multipole moments necessary to obtain the spin contributions to the gravitational wave amplitude to 2.5 Post-Newtonian (PN) order. We also reproduce the tail contribution to the waveform linear in spin at 2.5PN arising from the nonlinear interaction between the current quadrupole and the mass monopole.

Chromatic effects in quadrupole scan emittance measurements

Abstract: A reliable transverse emittance measurement for high-brightness electron beams is of utmost importance for the successful development of fourth generation light sources and for the beam transport in plasmabased accelerators. When the beam exhibits a significant energy spread, typical quadrupole scan emittance measurements may be affected depending on the beam properties and on the quadrupoles arrangement. The emittance degradation induced by chromatic effects in measurements involving magnetic lattices is evaluated analytically for different configurations. Analytical and numerical calculations compared with measurements have been used to evaluate the consequent error on the emittance value measured for single and double quadrupole schemes and for typical operating conditions at the SPARC facility

Deformation, breakup and motion of a perfect dielectric drop in a quadrupole electric field

Abstract: A detailed nonlinear analysis of the deformation and breakup of a perfect dielectric (PD) drop, suspended in another perfect dielectric fluid, in the presence of a quadrupole electric field is presented using analytical (asymptotic) and numerical (boundary integral) methods. The quadrupole field is the simplest kind of an axisymmetric non-uniform electric field. A drop, when placed at the center of such a field, does not translate, thus allowing systematic investigation of the effect of non-uniformity of the electric field. The deformation of a drop under a quadrupole field for PD-PD systems exhibits several novel features as compared to that of a drop under a uniform electric field. The first order analysis predicts oblate deformation for a PD-PD system when the dielectric constant of the suspending medium is larger than that of the drop (Q = ei/ee < 1). This is in sharp contrast to uniform electric fields where oblate shapes are observed only in leaky dielectric systems. Prolate shapes are observed for ...

Positron scattering from O 2

Abstract: We report on recent cross section results for positron scattering from molecular oxygen (O2). Total cross sections (TCSs) were measured with a positron spectrometer in the energy range from 0.1 to 50 eV and with an energy resolution of the positron beam of ∼0.25 eV. In addition, TCSs as well as elastic and inelastic integral cross sections were computed within the independent atom model and screening corrected additivity rule approach, with both dipole and dipole plus quadrupole polarization potentials, between 1 and 1000 eV impact energy. An overall fair level of accord is found between the experimental TCS and that calculated with the model that includes the quadrupole term. Comparison to earlier measurements shows very good agreement with the present measured TCS and fair agreement with the TCS computed with our most physical model above ∼8 eV. Conversely, we find only a marginal level of accord when comparing our experimental TCS with previous computations, while the present TCS calculated with the dipole plus quadrupole potentials appears to agree reasonably well with most of the existing theoretical results above ∼100 eV.

Spin-stretching modes in anisotropic magnets: spin-wave excitations in the multiferroic Ba2CoGe2O7

Abstract: We studied spin excitations in the magnetically ordered phase of the noncentrosymmetric Ba(2)CoGe(2)O(7) in high magnetic fields up to 33 T. In the electron spin resonance and far infrared absorption spectra we found several spin excitations beyond the two conventional magnon modes expected for such a two-sublattice antiferromagnet. We show that a multiboson spin-wave theory describes these unconventional modes, including spin-stretching modes, characterized by an oscillating magnetic dipole and quadrupole moment. The lack of inversion symmetry allows each mode to become electric dipole active. We expect that the spin-stretching modes can be generally observed in inelastic neutron scattering and light absorption experiments in a broad class of ordered S > 1/2 spin systems with strong single-ion anisotropy and/or noncentrosymmetric lattice structure.

A theoretical survey of atomic structure and forbidden transitions in the 4p k and 4d k ground configurations of tungsten ions W 29+ through W 43+

Abstract: Energy levels, wavelengths and radiative decay rates have been calculated for states within the 4p k (k = 1–5) and 4d k (k = 1–9) ground configurations in highly charged tungsten ions. Magnetic dipole (M1) and electric quadrupole (E2) transition probabilities have been obtained using the fully relativistic multiconfiguration Dirac–Fock (MCDF) approach including the correlations within the n = 4 complex, some n = 4 → n � = 5 single excitations and quantum electrodynamics effects. The validity of the method is assessed through limited comparison with experimental and theoretical data previously published as well as with new relativistic Hartree–Fock calculations. The excellent agreement observed between our new MCDF A-values and those obtained using different theoretical approaches together with a detailed analysis of configuration interaction effects does not confirm the very recent GRASP2K calculations of Jonauskas et al (2012 At. Data Nucl. Data Tables 98 19) for M1 lines within the 4d k configurations, the latter results remaining in large disagreement with all other methods in many cases.

Role of nuclear quadrupole coupling on decoherence and relaxation of central spins in quantum dots.

Abstract: Strain-induced gradients of local electric fields in semiconductor quantum dots can couple to the quadrupole moments of nuclear spins We develop a theory describing the influence of this quadrupolar coupling on the spin correlators of electron and hole "central" spins localized in such dots We show that when the quadrupolar coupling strength is comparable to or larger than the hyperfine coupling strength between nuclei and the central spin, the relaxation rate of the central spin is strongly enhanced and can be exponential We demonstrate a good agreement with recent experiments on spin relaxation in hole-doped (In,Ga)As self-assembled quantum dots

Low-energy nuclear spectroscopy in a microscopic multiphonon approach

Abstract: The low-lying spectra of heavy nuclei are investigated within the quasiparticle– phonon model. This microscopic approach goes beyond the quasiparticle random-phase approximation by treating a Hamiltonian of separable form in a microscopic multiphonon basis. It is therefore able to describe the anharmonic features of collective modes as well as the multiphonon states, whose experimental evidence is continuously growing. The method can be put in close correspondence with the proton–neutron interacting boson model. By associating the microscopic isoscalar and isovector quadrupole phonons with proton–neutron symmetric and mixed-symmetry quadrupole bosons, respectively, the microscopic states can be classified, just as in the algebraic model, according to their phonon content and their symmetry. In addition, these states disclose the nuclear properties which are to be ascribed to genuine shell effects, not included in the algebraic approach. Due to its flexibility, the method can be implemented numerically for systematic studies of spectroscopic properties throughout entire regions of vibrational nuclei. The spectra and multipole transition strengths so computed are in overall good agreement with the experimental data. By exploiting the correspondence of the method with the interacting boson model, it is possible to embed the microscopic states into this algebraic frame and, therefore, face the study of nuclei far from shell closures, not directly accessible to merely microscopic approaches. Here, it is shown how this task is accomplished through systematic investigations of magnetic dipole and, especially, electric dipole modes along paths moving from the vibrational to the transitional regions. The method is very well suited to the study of well-deformed nuclei. It provides reliable descriptions of low-lying

High-precision atomic clocks with highly charged ions: Nuclear-spin-zero f 12 -shell ions

Abstract: Optical atomic clocks using highly charged ions hold an intriguing promise of metrology at the 19th significant figure Here we study transitions within the $4{f}^{12}$ ground-state electronic configuration of highly charged ions We consider isotopes lacking hyperfine structure and show that the detrimental effects of coupling of electronic quadrupole moments to the gradients of a trapping electric field can be effectively reduced by using specially chosen virtual clock transitions The estimated systematic fractional clock accuracy is shown to be below ${10}^{\ensuremath{-}19}$

Rubidium-87 Bose-Einstein condensate in an optically plugged quadrupole trap

Abstract: We describe an experiment to produce ${}^{87}$Rb Bose-Einstein condensates in an optically plugged magnetic quadrupole trap, using a blue-detuned laser. Due to the large detuning of the plug laser with respect to the atomic transition, the evaporation has to be carefully optimized in order to efficiently overcome the Majorana losses. We provide a complete theoretical and experimental study of the trapping potential at low temperatures and show that this simple model describes our data well. In particular, we demonstrate methods to reliably measure the trap oscillation frequencies and the bottom frequency, based on periodic excitation of the trapping potential and on radio-frequency spectroscopy, respectively. We show that this hybrid trap can be operated in a well-controlled regime that allows a reliable production of degenerate gases.

Quadrupole moments of spherical semi-magic nuclei within the self-consistent Theory of Finite Fermi Systems

Abstract: The quadrupole moments of odd neighbors of semi-magic lead and tin isotopes and N = 50 , N = 82 isotones are calculated within the self-consistent Theory of Finite Fermi Systems based on the Energy Density Functional by Fayans et al Two sets of published functionals are used to estimate systematic errors of the present self-consistent approach They differ by the spin-orbit and effective tensor force parameters The functional DF3-a leads to quadrupole moments in reasonable agreement with the experimental ones for most, but not all, nuclei considered

Microscopic description of quadrupole-octupole coupling in Sm and Gd isotopes with the Gogny energy density functional

Abstract: The interplay between the collective dynamics of the quadrupole and octupole deformation degree of freedom is discussed in a series of Sm and Gd isotopes both at the mean-field level and beyond, including parity symmetry restoration and configuration mixing. Physical properties such as negative-parity excitation energies and $E1$ and $E3$ transition probabilities are discussed and compared to experimental data. Other relevant intrinsic quantities such as dipole moments, ground-state quadrupole moments or correlation energies associated with symmetry restoration and configuration mixing are discussed. For the considered isotopes, the quadrupole-octupole coupling is found to be weak and most of the properties of negative-parity states can be described in terms of the octupole degree of freedom alone.

Rapid structural change in low-lying states of neutron-rich Sr and Zr isotopes

Abstract: The rapid structural change in low-lying collective excitation states of neutron-rich Sr and Zr isotopes is studied by solving a five-dimensional collective Hamiltonian with parameters determined from both relativistic mean-field and nonrelativistic Skyrme-Hartree-Fock calculations using the PC-PK1 and SLy4 forces, respectively. Pair correlations are treated in the BCS method with either a separable pairing force or a density-dependent zero-range force. The isotope shifts, excitation energies, and electric monopole and quadrupole transition strengths are calculated and compared with corresponding experimental data. The calculated results with both the PC-PK1 and the SLy4 forces exhibit a picture of spherical-oblate-prolate shape transition in neutron-rich Sr and Zr isotopes. However, compared with the experimental data, the PC-PK1 (or SLy4) force predicts a more moderate (or dramatic) change in most of the collective properties around $N=60$. The underlying microscopic mechanism responsible for the rapid transition is discussed.

Role of Nuclear Quadrupole Coupling on Decoherence and Relaxation of Central Spins in Quantum Dots

Abstract: Strain-induced gradients of local electric fields in semiconductor quantum dots can couple to the quadrupole moments of nuclear spins. We develop a theory describing the influence of this quadrupolar coupling on the spin correlators of electron and hole "central" spins localized in such dots. We show that when the quadrupolar coupling strength is comparable to or larger than the hyperfine coupling strength between nuclei and the central spin, the relaxation rate of the central spin is strongly enhanced and can be exponential. We demonstrate a good agreement with recent experiments on spin relaxation in hole-doped (In,Ga)As self-assembled quantum dots.

Shape transition and fluctuations in neutron-rich Cr isotopes around N = 40

Abstract: The spherical-to-prolate shape transition in neutron-rich Cr isotopes from N = 34 to 42 is stud- ied by solving the collective Schrodinger equation for the five-dimensional quadrupole collective Hamiltonian. The collective potential and inertial functions are microscopically derived with use of the constrained Hartree-Fock-Bogoliubov plus local quasiparticle random-phase approximation method. Nature of the quadrupole collectivity of low-lying states is discussed by evaluating exci- tation spectra and electric quadrupole moments and transition strengths. The result of calculation indicates that Cr isotopes around 64 Cr are prolately deformed but still possess transitional character; large-amplitude shape fluctuations dominate in their low-lying states.

Resonance properties of optical all-dielectric metamaterials using two-dimensional multipole expansion

Abstract: We examine the electromagnetic response of metamaterial unit elements consisting of dielectric rods embedded in a nonmagnetic background medium. We establish a theoretical framework in which the response is described through the electric and magnetic multipole moments that are simultaneously generated via the polarization currents that are excited upon the incidence of plane waves. The corresponding dipole and quadrupole polarizabilities are then calculated as a function of the Mie scattering coefficients, and their resonances are mapped for the case of dielectric cylindrical rods as a function of the geometry and the material parameters used. The results provide critical insight into the anisotropic response of two-dimensional rod-type metamaterials and can be used as a unified methodology in the calculation of exotic effective electromagnetic parameters involved in phenomena such as optical magnetism.