Electromagnetic Multipoles Research Articles

Geometric Phase-Driven Scattering Evolutions.

Conventional approaches for scattering manipulations largely rely on the technique of field expansions into spherical harmonics (electromagnetic multipoles), which nevertheless is not only nongeneric (expansion coefficients depend on the origin position of the coordinate system) but also more descriptive than predictive. Here, we explore this classical topic from a different perspective of controlled excitations and interferences of quasinormal modes (QNMs) supported by the scattering system. Scattered waves are expanded into coherent additions of QNMs, among which the relative amplitudes and phases are crucial factors to architect for scattering manipulations. Relying on the electromagnetic reciprocity, we provide full geometric representations based on the Poincaré sphere for those factors, and discover the hidden geometric phase of QNMs that drives the scattering evolutions. Further synchronous exploitations of the incident polarization-dependent geometric phase and excitation amplitudes enable efficient manipulations of both scattering intensities and polarizations. Continuous geometric phase spanning 2π is directly manifest through scattering variations, even in the rather elementary configuration of an individual particle scattering waves of varying polarizations. We have essentially established a profoundly all-encompassing framework for the calculations of geometric phase in arbitrary scattering systems that are reciprocal. Our theoretical model will greatly broaden horizons of many disciplines not only in photonics but also in general wave physics where geometric phase is generic and ubiquitous.

Hybridization of electromagnetic multipoles in a nanoscatterer in the presence of another nanoscatterer

Coupling between multipolar modes of different orders has not been investigated in depth, despite its fundamental and practical relevance in the context of optical metamaterials and metasurfaces. Here, we use an electromagnetic multipole expansion of both the scattered fields and the oscillating electric currents to reveal the multipolar excitations in a nanoparticle positioned close to another nanoparticle. The considered single-particle multipoles radically differ from multipoles excited in a pair of nanoparticles. Using the expansion, we reveal the multipole character of the electric currents and the contributions of the multipole moments to the scattering cross section of each particle, including the effect of their interaction. We find that light scattered by the particles plays the role of an inhomogeneous incident field for each of the particles, leading to hybridization of the originally independent orthogonal multipole resonances. For an incident plane wave polarized along the nanoparticle pair, the hybridization of the dipole and quadrupole resonances gives rise to a significant narrowband resonance in the spectrum of the dipole scattering, which can be of interest for various applications, e.g. in surface-enhanced fluorescence and Raman spectroscopy. In general, this work shows that the multipole-multipole interaction between nanoparticles must be treated by taking into account also such hybridized multipole resonances.

Efficient and accurate numerical-projection of electromagnetic multipoles for scattering objects

In this paper, we develop an efficient and accurate procedure of electromagnetic multipole decomposition by using the Lebedev and Gaussian quadrature methods to perform the numerical integration. Firstly, we briefly review the principles of multipole decomposition, highlighting two numerical projection methods including surface and volume integration. Secondly, we discuss the Lebedev and Gaussian quadrature methods, provide a detailed recipe to select the quadrature points and the corresponding weighting factor, and illustrate the integration accuracy and numerical efficiency (that is, with very few sampling points) using a unit sphere surface and regular tetrahedron. In the demonstrations of an isotropic dielectric nanosphere, a symmetric scatterer, and an anisotropic nanosphere, we perform multipole decomposition and validate our numerical projection procedure. The obtained results from our procedure are all consistent with those from Mie theory, symmetry constraints, and finite element simulations.Graphical

Transverse Scattering from Nanodimers Tunable with Generalized Cylindrical Vector Beams

AbstractAchieving directional control of optical antennas is critically important for the design of flexible interconnects between free‐space optics and on‐chip photonic circuitry. Here, a new concept of tunable transverse scattering of light from dielectric nanodimer antennas is suggested theoretically and demonstrated experimentally based on a selective excitation of the specific electromagnetic multipoles with the simultaneous suppression of both forward and backward scatterings. Importantly, it is revealed that the direction of the transverse scattering from nanodimers can be steered actively by varying the vectorial properties of the generalized cylindrical beams, and this new functionality in the experiment is demonstrated.

Optically transparent and flexible-assembled metasurface rasorber for infrared-microwave camouflage based on a hybrid anapole state.

Hybrid anapole state, originating from the destructive interference of more than one basic electromagnetic multipole moments with their toroidal counterparts, enables the simultaneous suppression of multiple leading scattering channels, thereby demonstrates promising applications in perfect absorption and electromagnetic camouflage. However, the formation of hybrid anapoles is challenging because a careful overlap of electromagnetic multipoles with their toroidal counterparts is required. In this study, we propose and experimentally demonstrate a transparent and flexible assembled metasurface rasorber supporting hybrid anapole states for infrared and microwave camouflage, which not only supports low IR emissivity in the range of 8-14 μm but also exhibits an absorption-transmission-absorption response in the microwave band. In addition, the conformal and tunable performances of the fabricated metasurface rasorber are experimentally demonstrated. Our study provides a new strategy for designing multispectral camouflage metasurfaces.

Emergent Magnetomultipoles and Nonlinear Responses of a Magnetic Hopfion.

The three-dimensional emergent magnetic field B^{e} of a magnetic hopfion gives rise to emergent magnetomultipoles in a similar manner to the multipoles of classical electromagnetic field. Here, we show that the nonlinear responses of a hopfion are characterized by its emergent magnetic toroidal moment T_{z}^{e}=1/2∫(r×B^{e})_{z}dV and emergent magnetic octupole component Γ^{e}=∫[(x^{2}+y^{2})B_{z}^{e}-xzB_{x}^{e}-yzB_{y}^{e}]dV. The hopfion exhibits nonreciprocal dynamics (nonlinear hopfion Hall effect) under an ac driving current applied along (perpendicular to) the direction of T_{z}^{e}. The sign of nonreciprocity and nonlinear Hall angle is determined by the polarity and chirality of hopfion. The nonlinear electrical transport induced by a magnetic hopfion is also discussed. This Letter reveals the vital roles of emergent magnetomultipoles in nonlinear hopfion dynamics and could stimulate further investigations on the dynamical responses of topological spin textures induced by emergent electromagnetic multipoles.

Optical magnetism and wavefront control by arrays of strontium atoms

By analyzing the parameters of electronic transitions, we show how bosonic Sr atoms in planar optical lattices can be engineered to exhibit optical magnetism and other higher-order electromagnetic multipoles that can be harnessed for wavefront control of incident light. Resonant $\lambda\simeq 2.6\mu$m light for the $^3D_1\rightarrow {^3}P_0$ transition mediates cooperative interactions between the atoms while the atoms are trapped in a deeply subwavelength optical lattice. The atoms then exhibit collective excitation eigenmodes, e.g., with a strong cooperative magnetic response at optical frequencies, despite individual atoms having negligible coupling to the magnetic component of light. We provide a detailed scheme to utilize excitations of such cooperative modes consisting of arrays of electromagnetic multipoles to form an atomic Huygens' surface, with complete $2\pi$ phase control of transmitted light and almost no reflection, allowing nearly arbitrary wavefront shaping. In the numerical examples, this is achieved by controlling the atomic level shifts of Sr with off-resonant ${^3P}_J\rightarrow {^3D}_1$ transitions, which results in a simultaneous excitation of arrays of electric dipoles and electric quadrupoles or magnetic dipoles. We demonstrate the wavefront engineering for a Sr array by realizing the steering of an incident beam and generation of a baby-Skyrmion texture in the transmitted light via a topologically nontrivial transition of a Gaussian beam to a Poincar\'{e} beam, which contains all possible polarizations in a single cross-section.

Multipolar expansions for scattering and optical force calculations beyond the long wavelength approximation

We review three different approaches for the calculation of electromagnetic multipoles, namely, the Cartesian primitive multipoles, the Cartesian irreducible multipoles, and the spherical multipoles. We identify the latter as the best suited to describe the scattering of electromagnetic radiation, as exemplified for an amorphous silicon sphere. These multipoles are then used to calculate the optical force acting on semiconductor, dielectric or metallic particles in a wide wavelength range, from the dipolar regime down to the Mie regime.

Flexible and transparent broadband microwave metasurface absorber based on multipolar interference engineering.

Electromagnetic multipoles enable rich electromagnetic interactions in a metasurface and offer another degree of freedom to control electromagnetic responses. In this work, we design and experimentally demonstrate an optically transparent, flexible and broadband microwave metasurface absorber based on multipolar interference engineering. Different from previous works, the designed metasurface simultaneously supports fundamental electric dipole and high-order electric quadrupole mode, whose interference satisfies the back-scattering suppression condition based on the generalized Kerker effect and thus high absorption. The measurement results indicate that the fabricated metasurface exhibits a high average absorption of 89% in the microwave band from 4 GHz to 18 GHz, together with a good optical transparency. Our study offers an alternative approach for designing broadband microwave metasurface absorber, which is potentially applicable in electromagnetic shielding, radar stealth and energy harvesting.

WS2/hBN Hetero-nanoslits with Spatially Mismatched Electromagnetic Multipoles for Directional and Enhanced Light Emission

van der Waals (vdW) heterostructures based on vertical-stacking transition metal dichalcogenides (TMDCs) with tunable excitonic energies and spin-valley properties show intriguing optical and optoelectronic applications. Additionally, vdW heterostructures with high refractive indices, exciton-induced Lorentzian dispersion, and controllable structures are ideal building blocks as optical resonators for subwavelength light confinement and effective light-matter interaction, which have not been studied. Herein, we build vdW hetero-nanoslits based on tungsten disulfide (WS2) and hexagonal boron nitride (hBN) multilayers. The multipole optical modes arise from the evolution of electromagnetic near-field distributions through engineering of refractive index and corresponding optical path differences (OPDs). More importantly, the coupling between electromagnetic multipoles with spectral and spatial overlap facilitates the directional scattering with an engineered forward-to-backward (F/B) ratio from 0.1 to 100.0 owing to generalized Kerker effects. Through further combination of WS2 monolayers and WS2/hBN hetero-nanoslits, the photoluminescence (PL) modulation in the range of 50% to 800% is achieved. The enhancement factor and modulation range are comparable to the best performances of single-element plasmonic or dielectric nanostructures. This work provides a different insight into designing nanophotonic devices in the visible range by solely relying on vdW heterostructures.

Structured light excitation of toroidal dipoles in dielectric nanodisks

Conventional electromagnetic multipoles can be completed by complementary sources of toroidal moments, opening the door to the engineering of nanophotonic devices. The main contribution of this study is comparing different light sources for enhancing the toroidal dipole response in a given system. We theoretically study the toroidal dipole excitation in an individual dielectric nanodisk by structured light illumination, including the tightly focused radially polarized beam and the focused doughnut pulse. The toroidal dipole and anapole can be excited by the interplay of the radial and longitudinal components of the incident light. As opposed to the plane wave illumination, the tightly focused radially polarized light can excite a near-ideal toroidal dipole while the contributions of the Cartesian electric dipole and other modes are significantly suppressed. We also show that the focused doughnut pulse is a promising tool for exciting a resonant toroidal response in nanophotonic systems. Furthermore, it is demonstrated that toroidal-driven field confinement leads to an enhancement of energy concentration inside the nanodisk that can potentially increase light harvesting and boost both linear and nonlinear light-matter interactions.

Single-energy partial-wave analysis for pion photoproduction with fixed- t analyticity

Experimental data for pion photoproduction including differential cross sections and various polarization observables from four reaction channels, $\gamma p \to \pi^0 p$, $\gamma p \to \pi^+n$, $\gamma n \to \pi^- p$ and $\gamma n \to \pi^0 n$ from threshold up to $W=2.2$ GeV have been used in order to perform a single-energy partial wave analysis with minimal model dependence by imposing constraints from unitarity and fixed-$t$ analyticity in an iterative procedure. Reaction models were only used as starting point in the very first iteration. We demonstrate that with this procedure partial wave amplitudes can be obtained which show only a minimal dependence on the initial model assumptions. The analysis has been obtained in full isospin, and the Watson theorem is enforced for energies below $W=1.3$ GeV but is even fulfilled up to $W\approx 1.6$ GeV in many partial waves. Electromagnetic multipoles $E_{\ell\pm}$ and $M_{\ell\pm}$ are presented and discussed for $S,P,D$ and $F$-waves.

Electromagnetic multipoles of positive parity states in 27Al by elastic and inelastic electron scattering

Nuclear structure of 27Al nucleus has been investigated using shell model with self-consistent Hartree–Fock calculations. Shell model calculations are performed with full sd model space for positive parity states. For all selected excited states, Skyrme interactions are adopted to generate from them a one-body potential in Hartrre-Fock theory to calculate the single-particle matrix elements and compared with those of the harmonic oscillator. The deduced results are discussed for the longitudinal and transverse form factors and compared with the available experimental data. It has been found that the core-polarization effects are essential in obtaining a reasonable description of the data.

Optical magnetic response without metamaterials

One of the main achievements of metamaterials research has been the development of structured matter exhibiting optical magnetism: first, in an array of microwave split-ring resonators and, soon after, in plasmonic and dielectric metamaterials at THz to visible frequencies. We show here that metamaterial structuring is not necessary to achieve optical magnetic response. Indeed, such a response is an essential characteristic of homogeneous dielectric thin films—Fabry–Pérot resonances, for example, depend on interference among electromagnetic multipoles including the magnetic dipole.

Vector-spherical-harmonics representation of vector complex source beams carrying vortices

Vectorial solutions of Maxwell's equations describing highly focused and variously polarized vector complex source vortex beams are investigated. An analytical representation of these beams in the vector-spherical basis of electromagnetic multipoles is presented. In particular, three different families of optical vector vortex beams are studied in detail. Whereas the vortical solutions derived within spherical symmetry can be represented only by electric (magnetic) multipoles, solutions derived within cylindrical and Cartesian symmetry also exhibit magnetic (electric) multipole components. We utilize the representation of the studied beams in vector-spherical harmonics to investigate their interaction with a cluster of nanoparticles.

Manipulating light scattering by nanoparticles with magnetoelectric coupling

Light scattering by nanoparticles can be well understood and manipulated in the framework of induced electromagnetic multipoles. Conventionally, the scattering properties of light by nanoparticles are considered to be a result of superposition of the radiation from the induced multipoles due to their orthogonality. Here, we reveal that the interaction between the electric and magnetic dipoles in adjacent nanoparticles can provide an additional route to manipulate light scattering. Specifically, we show that an all-dielectric dimer can support the magnetoelectric coupling effect, in which the electric/magnetic dipole in one nanoparticle can induce an additional magnetic/electric dipole in the other nanoparticle. Such additional electric and magnetic dipoles can suppress or enhance light extinction, which is determined by the phase relationship with respect to the incident field. Furthermore, the magnetoelectric coupling induced dipoles can modify the far-field scattering pattern and even realize unidirectional forward scattering. As a proof-of-principle demonstration, experimental measurements at microwave frequency were performed, and the results are in good agreement with the theoretical ones. Our results may pave the way for manipulating light scattering and novel wave phenomena with magnetoelectric coupling.

Direct detection of vector dark matter through electromagnetic multipoles

Dark matter particles, even if they are electrically neutral, could interact with the Standard Model particles via their electromagnetic multipole moments. In this paper, we focus on the electromagnetic properties of the complex vector dark matter candidate, which can be described by means of seven form factors. We calculate the differential scattering cross-section with nuclei due to the interactions of the dark matter and nuclear multipole moments, and we derive upper limits on the former from the non-observation of dark matter signals in direct detection experiments. We also present a model where the dark matter particle is a gauge boson of a dark SU(2) symmetry, and which contains heavy new fermions, charged both under the dark SU(2) symmetry and under the electromagnetic U(1) symmetry. The new fermions induce at the one loop level electromagnetic multipole moments, which could lead to detectable signals in direct detection experiments.

Electromagnetic Multipoles: Line Singularities and Hopf Indices of Electromagnetic Multipoles (Laser Photonics Rev. 14(7)/2020)

In article number 2000049 by Weijin Chen, Yuntian Chen, and Wei Liu, topological morphologies of electromagnetic multipoles of general complex vectorial forms are explored, and are portrayed through line fields with singularities of half-integer Hopf indices. With this topological insight, the hidden dimension of radiative circularly polarized Bloch modes is further unveiled, revealing their line singularity origins and establishing equivalences between their topological charges and multipolar Hopf indices.

Line Singularities and Hopf Indices of Electromagnetic Multipoles

AbstractElectromagnetic multipoles serve as one of the most ubiquitous languages in photonics, forming a complete expansion basis for radiations of arbitrary types. Electromagnetic multipoles from the perspective of line fields and singularities are explored. It is then discovered that, for arbitrary finite sources in a homogeneous background, there have to be isolated directions along which the radiation is either zero or circularly polarized. For such singular directions, half‐integer Hopf indices can be assigned and the index sum has to be a global invariant of 2. With this topological insight, the hidden dimensions of radiative circularly polarized Bloch modes of photonic crystal slabs are unveiled, revealing their topological origins of line singularities and indices. This work has established subtle connections between three seemingly unrelated but sweeping physical entities (line singularities of Hopf indices, electromagnetic multipoles, and Bloch modes), which can nourish new frames of visions and applications fertilizing many related fields.

Bound States in the Continuum in One-Dimensional Dimerized Plasmonic Gratings**Supported by the National Natural Science Foundation of China (Grant Nos. 11804288 and 91750102) and the Projects of President Foundation of Chongqing University (Grant No. 2019CDXZWL002).

A simple one-dimensional subwavelength plasmonic grating can support symmetry protected bound states in the continuum (BICs), but not necessarily for the non-symmetry protected BICs. By dimerizing the lattice, non-symmetry protected BIC can be supported on the dimerized grating and can be tuned readily. The mechanism for the BICs in the dimerized grating is interpreted in the viewpoint of interference between the electromagnetic multipoles.