Multipole Effects Research Articles

Extraordinary Multipole Modes and Ultra-Enhanced Optical Lateral Force by Chirality.

Strong mode coupling and Fano resonances arisen from exceptional interaction between resonant modes in single nanostructures have raised much attention for their advantages in nonlinear optics, sensing, etc. Individual electromagnetic multipole modes such as quadrupoles, octupoles, and their counterparts from mode coupling (toroidal dipole and nonradiating anapole mode) have been well investigated in isolated or coupled nanostructures with access to high Q factors in bound states in the continuum. Albeit the extensive study on ordinary dielectric particles, intriguing aspects of light-matter interactions in single chiral nanostructures is lacking. Here, we unveil that extraordinary multipoles can be simultaneously superpositioned in a chiral nanocylinder, such as two toroidal dipoles with opposite moments, and electric and magnetic sextupoles. The induced optical lateral forces and their scattering cross sections can thus be either significantly enhanced in the presence of those multipoles with high-Q factors, or suppressed by the bound states in the continuum. This work for the first time reveals the complex correlation between multipolar effects, chiral coupling, and optical lateral force, providing a distinct way for advanced optical manipulation.

Magic-intensity trapping of the Mg lattice clock with light shift suppressed below 10−19

Progress in atomic optical clocks with total uncertainty of $10^{-18}$ or below requires a precise estimation of multipolar and higher-order effects due to atom-field interactions. Magnesium is an attractive candidate for optical lattice clocks because it is insensitive to blackbody radiation and has a large quality factor. We employ a combined method of the Dirac-Fock plus core polarization and the relativistic configuration interaction to calculate the dynamic multipolar polarizabilities and the hyperpolarizabilities of the atomic Mg clock. The lattice light shift against variation of the laser detuning and trap depth is also investigated. We find that there exists a distinctive operational magic lattice intensity of $5.33(2)E_R$ ($E_R$ is the lattice photon recoil energy) that reduces the total light shift below $1\times 10^{-19}$ over 14\% of the trap depth variation, which will pave the way for the development of a new time-frequency standard of the Mg lattice clock.

Forward and Backward Switching of Nonlinear Unidirectional Emission from GaAs Nanoantennas.

High-index III-V semiconductor nanoantennas have gained great attention for enhanced nonlinear light-matter interactions, in the past few years. However, the complexity of nonlinear emission profiles imposes severe constraints on practical applications, such as in optical communications and integrated optoelectronic devices. These complexities include the lack of unidirectional nonlinear emission and the severe challenges in switching between forward and backward emissions, due to the structure of the susceptibility tensor of the III-V nanoantennas. Here, we propose a solution to both issues via engineering the nonlinear tensor of the nanoantennas. The special nonlinear tensorial properties of zinc-blende material can be used to engineer the nonlinear characteristics via growing the nanoantennas along different crystalline orientations. Based on the nonlinear multipolar effect, we have designed and fabricated (110)-grown GaAs nanoantennas, with engineered tensorial properties, embedded in a transparent low-index material. Our technique provides an approach not only for unidirectional second-harmonic generation (SHG) forward or backward emission but also for switching from one to another. Importantly, switching the SHG emission directionality is obtained only by rotating the polarization of the incident light, without the need for physical variation of the antennas or the environment. This characteristic is an advantage, as compared to other nonlinear nanoantennas, including (100)- and (111)-grown III-V counterparts or silicon and germanium nanoantennas. Indeed, (110)-GaAs nanoantennas allow for engineering the nonlinear nanophotonic systems including nonlinear "Huygens metasurfaces" and offer exciting opportunities for various nonlinear nanophotonics technologies, such as nanoscale light routing and light sources, as well as multifunctional flat optical elements.

Dynamic multipolar polarizabilities and hyperpolarizabilities of the Sr lattice clock

The progress in optical clock with uncertainty at a level of $10^{-18}$ requires unprecedented precision in estimating the contribution of multipolar and higher-order effects of atom-field interactions. Current theoretical and experimental results of dynamic multipolar polarizabilities and hyperpolarizabilities at the magic wavelength for the Sr clock differ substantially. We develop a combined approach of the Dirac-Fock plus core polarization (DFCP) and relativistic configuration interaction (RCI) methods to calculate dynamic multipolar polarizabilities and hyperpolarizabilities of the Sr atom. Our differential dynamic hyperpolarizability at the magic wavelength is $-2.09(43)\times10^{7}$ a.u., which is consistent with the existing theoretical and experimental results. Our differential multipolar polarizability is $2.68(94)\times 10^{-5}$ a.u., which validates independently the theoretical work of Porsev {\em et al.} [Phys. Rev. Lett. 120, 063204 (2018)], but different from recent measurement of Ushijima {\em et al.} [Phys. Rev. Lett. 121, 263202 (2018)].

Realization of color tunable via energy transfer in Ba1.2Ca0.8SiO4:Tb3+, Mn2+ phosphor

A detailed investigation on photoluminescence properties and energy transfer mechanism of Tb3+/Mn2+ singly doped and co-doped T-phase orthosilicate Ba1.2Ca0.8SiO4 (BCS) phosphors, synthesized by conventional solid state reaction, is provided. All the samples were investigated by X-ray diffraction (XRD), photoluminescence spectroscopy and fluorescence decay curve. The Mn2+ emission intensity of BCS:Tb3+, Mn2+ is 28 times stronger than that of BCS:Mn2+. In addition, the emission color of BCS:Tb3+, Mn2+ phosphors can be tuned from green to orange-red by varying Mn2+ concentration. The efficient energy transfer from Tb3+ to Mn2+ is responsible for these phenomena. By employing the Inokuti–Hirayama model and Dexter's energy transfer theory, the dipole–dipole interaction is confirmed as the predominant multipolar effect in controlling this energy transfer process.

Influence of multipole effects on the cross section and alignment following inner-shell ionization of atoms by a linearly polarized photon

On the basis of the fully relativistic Dirac-Fock treatment of single ionization by a linearly polarized photon with regard to the E1, M1, E2, M2, and E3 multipoles of the radiative field as well as their interference, we have assessed the influence of multipole effects on the cross sections and alignment parameters A20 and A22 of the residual ions, taking the 3p3/2 and 3d3/2 vacancies of selected Zn and Zn-like Kr6+, Cd18+, and Xe24+ ions as examples. Starting from the most general method of density matrix theory, we carried out specific analytic expressions in terms of the reduced matrix elements of multipole fields, corresponding to different ion-core states. It is shown that the multipole contributions to the photoionization cross sections can be considerable, the character of which becomes more evident as the incident energy and/or atomic number increases. These dramatic influences also lead to a remarkable increase in the alignment parameter A20 of the residual ions, yet virtually independent of the nuclear charge for A22. The present results in Coulomb gauge and Babushkin gauge excellently agreed with each other, suggesting that there is a high degree of convergence achieved in this study. Comparison of our results with experimental data and other theoretical predictions, when available, is made.

Analytical model of resonant electromagnetic dipole-quadrupole coupling in nanoparticle arrays

An analytical model for investigations of multipole coupling effects in the finite and infinite nanoparticle arrays supporting electromagnetic resonances is presented and discussed. This model considers the contributions of both electric and magnetic modes excited in the nanoparticles, including electric and magnetic dipoles and electric and magnetic quadrupoles. The magnetic quadrupole propagator (Green's tensor) that describes the electromagnetic field generated by a point magnetic quadrupole source in all wave zones is derived. As an example, we apply the developed model to study infinite two-dimensional rectangular periodic arrays of spherical silicon nanoparticles supporting the dipole and quadrupole resonant responses. The correctness and accuracy of the analytical model are confirmed by the agreement of its results with the results of full-wave numerical simulations. Using the developed model, we show the electromagnetic coupling between electric dipole and magnetic quadrupole moments as well as between magnetic dipole and electric quadrupole moments even for the case of an infinite rectangular periodic array of spherical nanoparticles. The strong suppression of the dipole or quadrupole moment due to the coupling effects is demonstrated and discussed for spherical nanoparticle arrays. The analytical expressions for the reflection and transmission coefficients written with the effective dipole and quadrupole polarizabilities are derived for normal light incidences and zero-order diffraction. The derived expressions are applied to explain the lattice anapole (invisibility) states when the incident light is transmitted unperturbed through the silicon nanoparticle array. The important role of dipole and quadrupole excitations in scattering compensation resulting in the lattice anapole effect is explicitly demonstrated. The presented approach can be used for designing metasurfaces and further utilizing them in developing ultrathin functional optical elements.

Analytical calculation of optical forces on spherical particles in optical tweezers: tutorial

Arthur Ashkin was awarded the 2018 Nobel prize in physics for the invention of optical tweezers. Since the first publication in 1986 Optical Tweezers have been used as a tool to measure forces and rheological properties of microscopic systems. For the calibration of these measurements, the knowledge of the forces is fundamental. However, it is still common to deduce the optical forces from assumptions based on the particle size with respect to the trapping laser wavelength. This show the necessity to develop a complete and accurate electromagnetic model that does not depend on early approximations of the force model. Furthermore, the model we developed has several advantages, such as morphology--dependent resonances, size dependence for large spheres, and multipole effects from smaller particles, just to name a few. In this tutorial, we review and discuss the physical modeling of optical forces in optical tweezers, which are the resultant forces exerted by a trapping beam on a sphere of any size and composition.

Evaluation of the polar contribution in the SAFT-VR Mie equation of state for simultaneous correlation of condensed-phase density, condensed-phase speed of sound, saturated density and saturated pressure of pure polar fluids

Polar forces affect significantly the thermodynamic properties and phase equilibria of pure fluids. In this work, the original SAFT-VR Mie equation of state was modified by the introduction of an explicit term to account for multipolar effects. Two approaches were evaluated: the Polar SAFT-VR Mie (PSAFT-VR Mie) and the Truncated Polar SAFT-VR Mie (tPSAFT-VR Mie). For non-associating molecules the agreement between experimental data and model predictions are very good. The tPSAFT-VR Mie equation of state presented better results than the SAFT-VR Mie and PSAFT-VR Mie models correlating condensed-phase density, condensed-phase speed of sound, saturated density and saturated pressure with lower deviations. For associating molecules the results obtained with the tPSAFT-VR Mie model were equivalent to the ones obtained with the SAFT-VR Mie equation of state. In order to the tPSAFT-VR Mie model better predict second-derivative thermodynamic properties, such as the speed of sound and the isobaric heat capacity, some information about this type of property must be used in the pure components parameters regression. All evaluated models predicted similar values for the second virial coefficient.

Luminescence and Energy Transfer between Ce3+ and Pr3+ in BaY2Si3O10 under VUV-vis and X-ray Excitation.

A detailed investigation on photoluminescence properties and energy transfer (ET) dynamics of Ce3+, Pr3+-doped BaY2Si3O10 is provided along with the potential X-ray excited luminescence application. The luminescence properties of Pr3+ are studied in VUV-UV-vis spectral range at low temperature, and the spectral profiles of Pr3+3P0 and 1D2 emission lines are determined using time-resolved emission spectra. Upon 230 nm excitation, the electron population from Pr3+ 4f5d state to its 4f2 excited state is discussed in detail. As Pr3+ concentration rises, Pr3+3P0 and 1D2 luminescence possess different concentration-related properties. The incorporation of Ce3+ in the codoped sample produces the strong Ce3+ luminescence under 230 nm excitation, which is the combined result of Pr3+ 4f5d → Ce3+ 5d ET and Ce3+ intrinsic excitation. On the other hand, the increasingly strong ET of Ce3+ 5d → Pr3+ 4f2 results in the decrease of Ce3+ emission intensity and the gradual deviation of Ce3+ luminescence decay from the single exponential in the system. By employing the Inokuti-Hirayama model, the dipole-dipole interaction is confirmed as the predominant multipolar effect in controlling this ET process, and the value of C DA is determined to be 9.97 × 10-47 m6·s-1. Finally, the relatively low scintillation light yield of Ce3+-doped BaY2Si3O10 material impedes its application potential in the scintillator field, and the cosubstitution of Pr3+ results in the observable decline of scintillation performance.

Nanofocusing of structured light for quadrupolar light-matter interactions

The spatial structure of an electromagnetic field can determine the characteristics of light-matter interactions. A strong gradient of light in the near field can excite dipole-forbidden atomic transitions, e.g., electric quadrupole transitions, which are rarely observed under plane-wave far-field illumination. Structured light with a higher-order orbital angular momentum state may also modulate the selection rules in which an atom can absorb two quanta of angular momentum: one from the spin and another from the spatial structure of the beam. Here, we numerically demonstrate a strong focusing of structured light with a higher-order orbital angular momentum state in the near field. A quadrupole field was confined within a gap region of several tens of nanometres in a plasmonic tetramer structure. A plasmonic crystal surrounding the tetramer structure provides a robust antenna effect, where the incident structured light can be strongly coupled to the quadrupole field in the gap region with a larger alignment tolerance. The proposed system is expected to provide a platform for light-matter interactions with strong multipolar effects.

Multipolar Kondo effect in a S01−P23 mixture of Yb173 atoms

Whereas in the familiar Kondo effect the exchange interaction is dipolar, it can also be multipolar, as has been realized in a recent experiment. Here we study multipolar Kondo effect in a Fermi gas of cold $^{173}$Yb atoms. Making use of different AC polarizability of the electronic ground state Yb($^{1}$S$_{0}$) and the long-lived metastable state Yb$^{*}$($^{3}$P$_{2}$), it is suggested that the latter atoms can be localized and serve as a dilute concentration of magnetic impurities while the former ones remain itinerant. The exchange mechanism between the itinerant Yb and the localized Yb$^{*}$ atoms is analyzed and shown to be antiferromagnetic. The quadruple and octuple interactions act to enhance the Kondo temperature $T_K$ that is found to be experimentally accessible. The bare exchange Hamiltonian needs to be decomposed into dipole ($d$), quadruple ($q$) and octuple ($o$) interactions in order to retain its form under renormalization group (RG) analysis, in which the corresponding exchange constants ($\lambda_{\mathrm{d}}$, $\lambda_{\mathrm{q}}$ and $\lambda_{\mathrm{o}}$) flow independently. Numerical solution of the RG scaling equations reveals a few finite fixed points, indicating an over-screening, which suggests a non-Fermi liquid phase. The impurity contribution to the magnetic susceptibility is calculated in the weak coupling regime (${T}\gg{T}_{K}$).

Optical response of hybrid semiconductor quantum dot-metal nanoparticle system: Beyond the dipole approximation

We study the response of a semiconductor quantum dot-metal nanoparticle system to an external field E0 cos (ωt). The borders between Fano, double peaks, weak transition, strong transition, and bistability regions of the phase diagram move considerably as one regards the multipole effects. The exciton-induced transparency is an artifact of the dipole approximation. The absorption of the nanoparticle, the population inversion of the quantum dot, the upper and lower limits of intensity where bistability occurs, the characteristic time to reach the steady state, and other features of the hybrid system change due to the multipole effects. The phase diagrams corresponding to the fields parallel and perpendicular to the axis of system are quite distinguishable. Thus, both the intensity and the polarization of the incident field can be used to control the system. In particular, the incident polarization can be used to switch on and switch off the bistable behavior. For applications such as miniaturized bistable devices and nanosensors sensitive to variations of the dielectric constant of the surrounding medium, multipole effects must be considered.

Multipole effects in the photoionization processes of Mg isoelectronic series with Z = 12–22

In this paper, we calculate relativistic photoionization parameters for Mg and Mg-like ions for photon energies between 10 eV and 30 keV using Dirac–Fock initial discrete-state wave functions and final central-field continuum wave functions. By taking multipole contributions into account, we achieve results that are in good agreement with both experimental data and theoretical results for neutral Mg atoms, and are within 5% of the experimental data for photon energies above 1 keV. We also find that, in relativistic photoionization calculations, the magnetic quadrupole transition tends to be more important than the magnetic dipole transition. The effect of multipoles is studied in detail by considering the contribution of the electric dipole transition to the full multipole calculation.

Partial-wave analysis and multipole transition interferences in the breakup of 6Li on 152Sm target

We have performed a detailed partial-wave analysis in order to analyze each partial-wave contribution to the breakup cross-sections as well as multipole interference effects in the [Formula: see text] breakup reaction. The results show that [Formula: see text]-waves contribute up to 67.03% of the overall integrated total breakup cross-section, distributed as follows: 10.43% for the [Formula: see text] partial-wave, 21.94% for the [Formula: see text] partial-wave and 34.66% for the [Formula: see text] partial-wave. A similar trend is observed for both Coulomb and nuclear breakup cross-sections. The importance of [Formula: see text]-waves over the non-[Formula: see text]-waves in the breakup process is mainly due to the higher-order multipole interferences. It is also obtained that the combination of [Formula: see text]-waves and [Formula: see text]-waves accounts for 84.77%, 89.95% and 73.58% of the total, Coulomb and nuclear breakup cross-sections, respectively. Considering the results obtained for the [Formula: see text] and [Formula: see text] partial-waves, we conclude that the [Formula: see text] and [Formula: see text] resonant breakup cross-sections, which can be obtained by integrating over the resonant energy range, could not be negligible compare to the [Formula: see text] resonant breakup cross-section. As far as this reaction is concerned, we can conclude that in the sequential breakup of [Formula: see text], excitations to all its three resonant states should be considered for a fair description of such process.

Nonlinear optical higher-order effects in an optical lattice clock

The development of optical frequency standards with a relative uncertainty of reproducing the time and frequency units at a level as low as 10−17–10−18 calls for an unprecedented accuracy in estimating the role of higher orders of optical nonlinearity, caused by the influence of the optical lattice on the frequency shift of the ‘clock transition’. This paper presents a systematic calculation of the contributions of multipole nonlinear anharmonic effects to the error of clocks based on optical lattices for alkaline-earth-like Sr, Yb, and Hg atoms.

Multipolar interference effects in nanophotonics.

Scattering of electromagnetic waves by an arbitrary nanoscale object can be characterized by a multipole decomposition of the electromagnetic field that allows one to describe the scattering intensity and radiation pattern through interferences of dominating multipole modes excited. In modern nanophotonics, both generation and interference of multipole modes start to play an indispensable role, and they enable nanoscale manipulation of light with many related applications. Here, we review the multipolar interference effects in metallic, metal-dielectric and dielectric nanostructures, and suggest a comprehensive view on many phenomena involving the interferences of electric, magnetic and toroidal multipoles, which drive a number of recently discussed effects in nanophotonics such as unidirectional scattering, effective optical antiferromagnetism, generalized Kerker scattering with controlled angular patterns, generalized Brewster angle, and non-radiating optical anapoles. We further discuss other types of possible multipolar interference effects not yet exploited in the literature and envisage the prospect of achieving more flexible and advanced nanoscale control of light relying on the concepts of multipolar interference through full phase and amplitude engineering.This article is part of the themed issue 'New horizons for nanophotonics'.

Higher-order effects on uncertainties of clocks of Mg atoms in an optical lattice

Multipole, nonlinear and anharmonic effects on the optical-lattice-based clocks of Mg atoms are evaluated theoretically. Dipole polarizabilities, hyperpolarizabilities and multipolar polarizabilities for Mg atoms are calculated in the single-electron approximation with the use of analytical presentations for the wave and Green’s functions in the modified model-potential approach. For comparison, the data are also given for atoms of the group IIb elements (Zn, Cd, Hg).

Resonant optical gradient force interaction for nano-imaging and -spectroscopy

The optical gradient force provides optomechanical interactions, for particle trapping and manipulation, as well as for near-field optical imaging in scanning probe microscopy. Based on recent spectroscopic experiments, its extension and use for a novel form of chemical scanning probe nano-imaging was proposed. Here, we provide the theoretical basis in terms of spectral behavior, resonant enhancement, and distance dependence of the optical gradient force from numerical simulations in a coupled nanoparticle model geometry. We predict an asymmetric line shape of the optical gradient force for molecular electronic or vibrational resonances, corresponding to the real part of the dielectric function of the sample materials. Yet the line shape can become symmetric and absorptive for collective polaritonic excitations. The corresponding magnitudes of the force range from fN to pN, respectively. The distance dependence scales considerably less steeply than simple point dipole model predictions due to multipole effects. The combination of these characteristics of the optical gradient force offers the chance to experimentally distinguish it from competing processes such as thermal expansion induced forces. In addition we provide a perspective for further resonant enhancement and control of optical forces.

Higher-order effects on the precision of clocks of neutral atoms in optical lattices

The recent progress in designing optical lattice clocks with fractional uncertainties below ${10}^{\ensuremath{-}17}$ requires unprecedented precision in estimating the role of higher-order effects of atom-lattice interactions. In this paper, we present results of systematic theoretical evaluations of the multipole, nonlinear, and anharmonic effects on the optical-lattice-based clocks of alkaline-earth-like atoms. Modifications of the model-potential approach are introduced to minimize discrepancies of theoretical evaluations from the most reliable experimental data. Dipole polarizabilities, hyperpolarizabilities, and multipolar polarizabilities for neutral Ca, Sr, Yb, Zn, Cd, and Hg atoms are calculated in the modified approach.