Higher Order Multipoles Research Articles

Giant intrinsic chiro-optical activity in planar dielectric nanostructures

The strong optical chirality arising from certain synthetic metamaterials has important and widespread applications in polarization optics, stereochemistry and spintronics. However, these intrinsically chiral metamaterials are restricted to a complicated three-dimensional (3D) geometry, which leads to significant fabrication challenges, particularly at visible wavelengths. Their planar two-dimensional (2D) counterparts are limited by symmetry considerations to operation at oblique angles (extrinsic chirality) and possess significantly weaker chiro-optical responses close to normal incidence. Here, we address the challenge of realizing strong intrinsic chirality from thin, planar dielectric nanostructures. Most notably, we experimentally achieve near-unity circular dichroism with ~90% of the light with the chosen helicity being transmitted at a wavelength of 540 nm. This is the highest value demonstrated to date for any geometry in the visible spectrum. We interpret this result within the charge-current multipole expansion framework and show that the excitation of higher-order multipoles is responsible for the giant circular dichroism. These experimental results enable the realization of high-performance miniaturized chiro-optical components in a scalable manner at optical frequencies.

Enhancement of low-frequency sound emission by metamaterial enclosures

Emission of low-frequency sound by a source is limited by the size of the source relative to sound wavelength. We propose to place the source in a subwavelength enclosure of anisotropic metamaterials which enhances the emission around Mie resonant frequencies of that enclosure [J. Zhao, L. Zhao, and Y. Wu, J. Acoust. Soc. Am. 142(1), EL24–29, July 2017]. The enclosure has a relatively small sound speed along the radiation direction, enabling the resonances to occur at low frequencies. Our numerical simulations provide evidence of the proposed low-frequency enhancement for both monopole and multipole sources. The common Mie resonant frequencies increase with the order of the multipoles. Here, we introduce an extreme anisotropy in the azimuth of the enclosure to degenerate the resonant frequencies of higher-order multipoles down to the same frequencies as the lower-order multipoles. The degeneracy associated with the anisotropy of the enclosure is theoretically analyzed. The results guide the experimental realization of the enclosure for low-frequency enhancement.

On the projected mass distribution around galaxy clusters

Gravitational lensing allows to quantify the angular distribution of the convergence field around clusters of galaxies to constrain their connectivity to the cosmic web. We describe in this paper the corresponding theory in Lagrangian space where analytical results can be obtained by identifying clusters to peaks in the initial field. We derive the three-point Gaussian statistics of a two-dimensional field and its first and second derivatives. The formalism allows us to study the statistics of the field in a shell around a central peak, in particular its multipolar decomposition. The peak condition is shown to significantly remove power from the dipolar contribution and to modify the monopole and quadrupole. As expected, higher order multipoles are not significantly modified by the constraint. Analytical predictions are successfully checked against measurements in Gaussian random fields. The effect of substructures and radial weighting is shown to be small and does not change the qualitative picture. The non-linear evolution is shown to induce a non-linear bias of all multipoles proportional to the cluster mass.We predict the Gaussian and weakly non-Gaussian statistics of multipolar moments of a two-dimensional field around a peak as a proxy for the azimuthal distribution of the convergence field around a cluster of galaxies. A quantitative estimate of this multipolar decomposition of the convergence field around clusters in numerical simulations of structure formation and in observations will be presented in two forthcoming papers.

Multipolar electromagnetic fields around neutron stars: general-relativistic vacuum solutions

Magnetic fields inside and around neutron stars are at the heart of pulsar magnetospheric activity. Strong magnetic fields are responsible for quantum effects, an essential ingredient to produce leptonic pairs and the subsequent broadband radiation. The variety of electromagnetic field topologies could lead to the observed diversity of neutron star classes. Thus it is important to include multipolar components to a presumably dominant dipolar magnetic field. Exact analytical solutions for these multipoles in Newtonian gravity have been computed in recent literature. However, flat spacetime is not adequate to describe physics in the immediate surrounding of neutron stars. We generalize the multipole expressions to the strong gravity regime by using a slowly rotating metric approximation such as the one expected around neutron stars. Approximate formulas for the electromagnetic field including frame dragging are computed from which we estimate the Poynting flux and the braking index. Corrections to leading order in compactness and spin parameter are presented. As far as spindown luminosity is concerned, it is shown that frame dragging remains irrelevant. For high order multipoles starting from the quadrupole, the electric part can radiate more efficiently than the magnetic part. Both analytical and numerical tools are employed.

A multipole expansion technique for predicting en-route aircraft noise

This study investigates the noise emitted by aircraft overflights. A multipole expansion method is used to model the noise source generated by propeller-driven aircrafts. Indeed, the multipole expansion method is frequently used in the study of electromagnetic wave propagation in which the far-field potential due to a localized charge distribution is approximated. This same technique is equally applicable in acoustics where the directivity of the aircraft noise source is modeled by summing a series of multipoles. For instance, the zero, first and second moment represent a monopole, dipole, and quadrupole, respectively. The first moment term is omni-directional and high order multipole terms have shown increasingly strong dependency on the receiver’s angular positions. The multipole expansion method leads to a more accurate model for evaluating the directivity effect due to aircraft flyovers. In the current study, precise (comprehensive) experimental data were used to determine the strength of each multipo...

Dark Mode Driven Extra-narrow and Multiband Absorber

Recently, metamaterial absorbers have received tremendous amount of interest because of their remarkable ability to manipulate the amplitude, phase, and polarization of light. However, most absorbers rely on the direct coupling of electric or magnetic field with external excitation, which lead to inevitable energy leakage to the surrounding environment and depress the quality factor of the structure. In this work, we investigate the multiband absorption property by exciting dark plasmonic modes in reflective symmetric and asymmetric metamaterials. Theoretically, the existence of dark plasmonic modes in asymmetric metamaterials is unambiguously illustrated by the improved eigen-mode theory. With the introduction of asymmetry, dark modes in metamaterials can be easily excited by normal incident plane wave. Moreover, we also directly excite the dark modes in symmetric absorber with oblique incidence. The dark modes splitting mechanism is also clarified with the excitation of designer surface plasmon. Dominated by magnetic dipole or higher-order multipole, these dark modes possess high quality factors (Q). Numerical results indicate that the metamaterial absorber maintains high absorbance within a wide-angle incidence (0~50°). The high Q asymmetric metamaterial absorber can be an excellent candidate for multiband plasmonic sensor.

Design and testing of a four rod crab cavity for High Luminosity LHC

A 4-rod deflecting structure is proposed as a possible crab cavity design for the LHC high luminosity upgrade. Crab cavities are required for the LHC luminosity upgrade to provide a greater bunch overlap in the presence of a crossing angle, but must fit in the existing limited space. The structure has two parallel sections consisting of two longitudinally opposing quarter-wave rods, where each rod has the opposite charge from each of its nearest neighbors. The structure is transversely compact because the frequency is dependent on the rod lengths rather than the cavity radius. Simulations were undertaken to investigate the effect of rod shape on surface fields, higher order multipole terms and induced wakefields in order to obtain the optimal rod shape. The simulation results presented show that the addition of focus electrodes or by shaping the rods the sextupole contribution of the cavity voltage can be negated; the sextupole contribution is 321.57 mTm/m2, Epeak=27.7 MV/m and Bpeak=63.9 mT at the design voltage of 3 MV. The damping requirements for the LHC are critical and suitable couplers to damp all modes but the operating mode are presented. The results of various testing cycles of the first SRF 4 rod prototype cavity are presented and show that the cavity has reached the required transverse voltage of 3 MV.

Long term dynamics of the high luminosity Large Hadron Collider with crab cavities

The High Luminosity upgrade of the Large Hadron Collider (HL-LHC) aims to achieve an integrated luminosity of 200-300 fb(-1) per year, including the contribution from the upgrade of the injector chain. For the HL-LHC the larger crossing angle together with a smaller beta function at the collision point would result in more than 70% luminosity loss due to the incomplete geometric overlap of colliding bunches. To recover head-on collisions at the high-luminosity particle-physics detectors ATLAS and CMS and benefit from the very low beta* provided by the Achromatic Telescopic Squeezing (ATS) optics, a local crab cavity scheme provides transverse kicks to the proton bunches. The tight space constraints at the location of these cavities leads to designs which are axially non-symmetric, giving rise to high order multipoles components of the main deflecting mode and, since these kicks are harmonic in time, we expand them in a series of multipoles in a similar fashion as is done for static field magnets. In this work we calculate, for the first time, the higher order multipoles and their impact on beam dynamics for three different crab cavity prototypes. Different approaches to calculate the multipoles are presented. Furthermore, we perform the first calculation of their impact on the long term stability of the machine using the concept of dynamic aperture.

Impact of Quadrupolar Electrostatics on Atoms Adjacent to the Sigma-Hole in Condensed-Phase Simulations.

Halogenation is one of the cases for which advanced molecular simulation methods are mandatory for quantitative and predictive studies. The present work provides a systematic investigation of the importance of higher-order multipoles on specific sites of halobenzenes, other than the halogen, for static and dynamic properties in condensed-phase simulations. For that purpose, solute-solvent interactions using point charge (PC), multipole (MTP), and hybrid point charge/multipole (HYB) electrostatic models are analyzed in regions of halogen bonding and extended to regions of π orbitals of phenyl carbons. Using molecular dynamics simulations and quantum chemical methods, it is found that the sigma-hole does not only affect the halogen and the carbon bound to it but its effect extends to the carbons adjacent to the CX bond. This effect increases with the magnitude of the positive potential of the sigma-hole. With the MTP and HYB3 models, all hydration free energies of the PhX compounds are reproduced within 0.1 kcal/mol. Analysis of pair distribution functions and hydration free energies of halogenated benzenes provides a microscopic explanation why "point charge"-based representations with off-site charges fail in reproducing thermodynamic properties of the sigma-hole. Application of the hybrid models to study protein-ligand binding demonstrates both their accuracy and computational efficiency.

Shaping the Radiation Pattern of Second-Harmonic Generation from AlGaAs Dielectric Nanoantennas

We study the manipulation of the radiation pattern of second-harmonic generation from AlGaAs all-dielectric nanoantennas exhibiting electric and magnetic resonances. We show the importance of the interference of different higher order multipoles in the nonlinear response of dielectric antennas for shaping of their second-harmonic radiation pattern. In particular, we show how such multipolar interference can be engineered in AlGaAs nanodisks by manipulating the pump beam polarization, incidence angle, and disk geometry. In this way we demonstrate the shaping of the radiation pattern in order to increase the second-harmonic power by a factor of 8 when measured in experiment through a finite numerical aperture microscope objective.

The Sensitivity of the Distance Dependent Plasmonic Coupling between Two Nanocubes to their Orientation: Edge-to-Edge versus Face-to-Face

Using DDA calculations, the electromagnetic field distribution and polarization vector plots were calculated as functions of the separation distance between a pair of 42-nm Ag nanocube dimers oriented in either an edge-to-edge or face-to-face configuration. We found that, as the separation distance of the nanocube dimer is decreased, the orientation of the dimer dramatically affects its near-field coupling behavior. The expected dipole–dipole exponential coupling behavior between the surfaces of the two nanocubes was found to fail at a separation distance of 6 nm for the face–to-face configuration and 14 nm for the edge-to-edge arrangement. The failure of the dipole–dipole coupling mechanism results from an increased contribution from the higher-order multipoles (e.g., quadrupole–dipole). Because this failure occurs at a larger separation distance for the edge-to-edge orientation, the relative ratio of the multipole to the dipole moment generated by the edge-to-edge dimer must be larger than the ratio for...

SELF-TRAPPING OF DISKOSEISMIC CORRUGATION MODES IN NEUTRON STAR SPACETIMES

ABSTRACT We examine the effects of higher-order multipole contributions of rotating neutron star (NS) spacetimes on the propagation of corrugation (c-)modes within a thin accretion disk. We find that the Lense–Thirring precession frequency, which determines the propagation region of the low-frequency fundamental corrugation modes, can experience a turnover allowing for c-modes to become self-trapped for sufficiently high dimensionless spin j and quadrupole rotational deformability α. If such self-trapping c-modes can be detected, e.g., through phase-resolved spectroscopy of the iron line for a high-spin low-mass accreting neutron star, this could potentially constrain the spin-induced NS quadrupole and the NS equation of state.

Developments in magnet modeling and beam optics for the ARIS separator at FRIB

A description is given on the methods used for field analysis of magnets and the extracted parameters used for accurate beam simulations of the fragment separator. For the strong focusing magnets, Fourier decomposition is used in order to extract induced fields associated with higher order multipoles. For dipoles, a 2D field map model is used instead in order to emulate complex field distributions. The theory of the models and the techniques chosen are described, along with results from Monte Carlo beam simulations up to 5th order. The n=6 multipole induced by the quadrupole is the most significant component. The effects on separator performance with and without this component in the model are demonstrated.

Discrete dipole approximation for black carbon-containing aerosols in arbitrary mixing state: A hybrid discretization scheme

An accurate and efficient simulation of light scattering by an atmospheric black carbon (BC)-containing aerosol—a fractal-like cluster of hundreds of carbon monomers that is internally mixed with other aerosol compounds such as sulfates, organics, and water—remains challenging owing to the enormous diversities of such aerosols׳ size, shape, and mixing state. Although the discrete dipole approximation (DDA) is theoretically an exact numerical method that is applicable to arbitrary non-spherical inhomogeneous targets, in practice, it suffers from severe granularity-induced error and degradation of computational efficiency for such extremely complex targets. To solve this drawback, we propose herein a hybrid DDA method designed for arbitrary BC-containing aerosols: the monomer-dipole assumption is applied to a cluster of carbon monomers, whereas the efficient cubic-lattice discretization is applied to the remaining particle volume consisting of other materials. The hybrid DDA is free from the error induced by the surface granularity of carbon monomers that occurs in conventional cubic-lattice DDA. In the hybrid DDA, we successfully mitigate the artifact of neglecting the higher-order multipoles in the monomer-dipole assumption by incorporating the magnetic dipole in addition to the electric dipole into our DDA formulations. Our numerical experiments show that the hybrid DDA method is an efficient light-scattering solver for BC-containing aerosols in arbitrary mixing states. The hybrid DDA could be also useful for a cluster of metallic nanospheres associated with other dielectric materials.

The consequences of improperly describing oscillator strengths beyond the electric dipole approximation.

The interaction between a quantum mechanical system and plane wave light is usually modeled within the electric dipole approximation. This assumes that the intensity of the incident field is constant over the length of the system and transition probabilities are described in terms of the electric dipole transition moment. For short wavelength spectroscopies, such as X-ray absorption, the electric dipole approximation often breaks down. Higher order multipoles are then included to describe transition probabilities. The square of the magnetic dipole and electric quadrupole are often included, but this results in an origin-dependent expression for the oscillator strength. The oscillator strength can be made origin-independent if all terms through the same order in the wave vector are retained. We will show the consequences and potential pitfalls of using either of these two expressions. It is shown that the origin-dependent expression may violate the Thomas-Reiche-Kuhn sum rule and the origin-independent expression can result in negative transition probabilities.

Disposable Plasmonics: Plastic Templated Plasmonic Metamaterials with Tunable Chirality.

Development of low-cost disposable plasmonic substrates is vital for the applicability of plasmonic sensing. Such devices can be made using injection-molded templates to create plasmonic films. The elements of these plasmonic films are hybrid nanostructures composed of inverse and solid structures. Tuning the modal coupling between the two allows optimization of the optical properties for nanophotonic applications.

Development of an AMOEBA water model using GEM distributed multipoles

Distributed multipoles obtained from the Gaussian electrostatic model (GEM) have been previously shown to be amenable for use in the AMOEBA force field [JCTC(2012) 12, 5072]. GEM distributed multipoles (GEM-DM) were determined for several systems including water. This previous AMOEBA water model with GEM-DM included only monopoles on the hydrogens and multipoles up to quadrupoles on the oxygen. This model showed good agreement with experiment for several properties at room temperature, but not at higher temperatures. In this contribution, we present the development of an AMOEBA water model using GEM-DM with distributed multipoles for each atomic site up to the quadrupole level. Quantum mechanical energy decomposition analysis has been employed to compare each term of the force field for parametrization. The inclusion of higher-order multipoles on hydrogen atoms is shown to provide better agreement with experiment on a number of properties including liquid density ( $$\rho$$ ), enthalpy of vaporization ( $$\Delta H_\mathrm{vap}$$ ), heat capacity ( $$C_{p}$$ ), and self-diffusion coefficient (D) for a range of temperatures.

Analytical expressions for fringe fields in multipole magnets

Fringe fields in multipole magnets can have a variety of effects on the linear and nonlinear dynamics of particles moving along an accelerator beam line. An accurate model of an accelerator must include realistic models of the magnet fringe fields. Fringe fields for dipoles are well understood and can be modeled at an early stage of accelerator design in such codes as mad8, madx, gpt or elegant. Existing techniques for quadrupole and higher order multipoles rely either on the use of a numerical field map, or on a description of the field in the form of a series expansion about a chosen axis. Usually, it is not until the later stages of a design project that such descriptions (based on magnet modeling or measurement) become available. Furthermore, series expansions rely on the assumption that the beam travels more or less on axis throughout the beam line; but in some types of machines (for example, Fixed Field Alternating Gradients or FFAGs) this is not a good assumption. Furthermore, some tracking codes, such as gpt, use methods for including space charge effects that require fields to vary smoothly and continuously along a beam line: in such cases, realistic fringe field models are of significant importance. In this paper, a method for constructing analytical expressions for multipole fringe fields is presented. Such expressions allow fringe field effects to be included in beam dynamics simulations from the start of an accelerator design project, even before detailed magnet design work has been undertaken. The magnetostatic Maxwell equations are solved analytically and a solution that fits all orders of multipoles is derived. Quadrupole fringe fields are considered in detail as these are the ones that give the strongest effects. The analytic expressions for quadrupole fringe fields are compared with data obtained from numerical modeling codes in two cases: a magnet in the high luminosity upgrade of the Large Hadron Collider inner triplet, and a magnet in the nonscaling FFAG EMMA. In both examples, the analytical expressions provide a good approximation to the numerical field maps.

Temperature dependences of N2-broadening and shift coefficients in the ν6 perpendicular band of 12CH3D

The temperature-dependences of line broadening and shift parameters for many 12CH3D transitions have been determined using six high-resolution, high signal-to-noise ratio, room-temperature CH3D (98% purity) and CH3D-N2 spectra recorded with 25cm path length ( at 0.01cm−1 unapodized resolution) using the McMath−Pierce FTS located on Kitt Peak, Arizona, and 17 additional high quality, pure CH3D (99% purity) and CH3D-N2 spectra recorded between 79 and 296K with the 20.38cm path coolable cell (at 0.0056cm−1 unapodized resolution) with the Bruker 125HR FTS at the Jet Propulsion Laboratory (JPL), Pasadena, California. The spectra have been fitted simultaneously applying a multispectrum nonlinear least-squares technique. In the analysis, the Lorentzian N2-broadened half-width coefficients and the corresponding pressure-shift coefficients as well as their temperature dependences are extracted for about 400 transitions (0≤J″≤19, K″≤16) in the perpendicular (ΔK=±1) ν6 band. At 296K, the measured N2-broadened half-width coefficients range from 0.0209 to 0.0782cm−1atm−1 whereas the majority of the associated N2-induced shift coefficients are negative, and the values are between -0.016 and 0.005cm−1atm−1. The temperature dependence exponents for N2-broadened half-widths range between 0.264 and 0.924, whereas the temperature dependence coefficients for N2-induced shifts are between 0 and 0.00011cm−1atm−1K−1. The N2-broadened half-width coefficients have been also calculated using a semi-classical approach based on a rigorous treatment of the active molecule as a symmetric top, a model intermolecular potential comprising both short- and long-range interactions, and exact classical trajectories. The role of the various high-order multipoles in the line-broadening at low, middle and high values of the rotational quantum number J″ has been investigated and the main features of the K-dependences analyzed. The calculations performed for 296, 240 and 190K have allowed to deduce the half-width temperature-dependence exponents, completing the general comparison of our new experimental results with those which are available in the literature.

Towards an optical far-field measurement of higher-order multipole contributions to the scattering response of nanoparticles

We experimentally show an all-optical multipolar decomposition of the lowest-order eigenmodes of a single gold nanoprism using azimuthally and radially polarized cylindrical vector beams. By scanning the particle through these tailored field distributions, the multipolar character of the eigenmodes gets encoded into 2D-scanning intensity maps even for higher-order contributions to the eigenmode that are too weak to be discerned in the direct far-field scattering response. This method enables a detailed optical mode analysis of individual nanoparticles.