Enantioselective interactions of chiral molecules include distinct absorptions to opposite-handed circularly polarized light, known as chiral absorption. Traditionally, chiral absorption has been primarily attributed to electric dipole and magnetic dipole interaction with molecular chirality. However, this approach falls short for large molecules that support high-order multipolar components, such as electric quadrupole moment. Here, we introduce a theoretical model to study the chiral absorption of large molecules in the presence of plasmonic nanostructures. This model considers both electric dipole-magnetic dipole interaction and electric dipole-electric quadrupole interaction enhanced by a resonant structure. We numerically study such interactions of the chiral molecular solution in the vicinity of a nonchiral plasmonic nano-resonator. Our results show the distinct spectral information of the chiral media on- and off-resonance of the resonator.
We study the dispersions of plasmonic bands that arise from the coupling of electric quadrupole resonances in three dimensional photonic crystals (PCs) consisting of plasmonic spheres. Through analytical derivation, we show that two branches of quadrupole bands in simple cubic PCs with a small lattice constant possess negative group velocities. Distinct from double negative media in which the negative responses originates from the coupling of electric and magnetic responses (P and M), the negative dispersion induced by quadrupole resonance is an intrinsic property of quadrupole that does not r…
The possibility to use surface plasmon polaritons for enhancement of weak magnetic dipole transitions is analyzed theoretically and demonstrated experimentally for simple flat geometry and sine-wave profile modulated plasmonic films. Spontaneous emission of Eu3+ in organic matrices deposited onto plasmonic surfaces demonstrates specific angular and polarization patterns at both electric and magnetic dipole transitions with a well-defined maximum at the plasmon decoupling conditions manifesting the character and magnitude of the effect.
Quadrupole topological insulator is a symmetry-protected higher-order topological phase with intriguing topology of Wannier bands, which, however, has not yet been realized in plasmonic metamaterials. Here, we propose a lattice of plasmon-polaritonic nanocavities which can realize quadrupole topological insulators by exploiting the geometry-dependent sign-reversal of the couplings between the daisy-like nanocavities. The designed system exhibits various topological and trivial phases as characterized by the nested Wannier bands and the topological quadrupole moment which can be controlled by t…
Recently, there is a great interest in studying ultrasensitive detection and characterization of biomolecules using plasmonic particles, because they are of considerable importance in biomedical science and pharmaceutics. So far, all the theories on plasmoninduced circular dichroism (CD) are based on the dipole approximation, the electric quadrupolar contribution is generally considered to be relatively small and neglected. Here we demonstrate that the electric quadrupolar contribution not only cannot be ignored, but also plays a key role in many cases. Particularly, for the chiral medium that…
Collective resonances in plasmonic nanoparticle arrays with electric dipole moment oriented along the lattice wave propagation are theoretically investigated. The role of electric quadrupole (EQ) and magnetic dipole (MD) moments of gold nanoparticles in the resonant features of the arrays is analyzed. We perform both semi-analytical calculations of coupled multipole equations and rigorous numerical simulations varying contributions of the electric and magnetic multipoles by changing particle size and shape (spheres and disks). The arrays in homogeneous and non-homogeneous environments are cons…
We develop a theoretical formalism for collectively responding point scatterers where the radiating electromagnetic fields from each emitter are considered in the electric dipole, magnetic dipole, and electric quadrupole approximation. The contributions of the electric quadrupole moment to electromagnetically-mediated interactions between the scatterers are derived in detail for a system where each scatterer represents a linear $RLC$ circuit resonator, representing common metamaterial resonators in radiofrequency, microwave, and optical regimes. The resulting theory includes a closed set of eq…
We show that the surface plasmon polariton (SPP) radiation patterns of point-dipole emitters in the vicinity of a metal-dielectric interface are generally asymmetric with respect to the location of the emitter. In particular rotating dipoles, which emit elliptically polarized light, produce highly asymmetric SPP radiation fields that include unidirectional emission. Asymmetric SPP radiation patterns also result when a dipole oscillates tilted with respect to the plane of the interface and optical losses or gains are present in the materials. These effects can be used to directionally control S…
We present a rigorous finite element method to calculate circular dichroism (CD) in various systems consisting of nanostructures and oriented chiral molecules with electric quadrupole transitions. The interaction between oriented molecule materials, which are regarded as anisotropic chiral media, and metallic nanostructures has been investigated. Our results show that the plasmon-induced CD is sensitive to the orientations of the molecules. In many cases, the contribution of molecular electric quadrupole transitions to the total CD signal can play a key role. More interesting, we have demonstr…
We demonstrate both analytically and numerically the existence of optical pulling forces acting on particles located near plasmonic interfaces. Two main factors contribute to the appearance of this negative reaction force. The interference between the incident and reflected waves induces a rotating dipole with an asymmetric scattering pattern while the directional excitation of surface plasmon polaritons (SPP) enhances the linear momentum of scattered light. The strongly asymmetric SPP excitation is determined by spin-orbit coupling of the rotating dipole and surface plasmon polariton. As a re…
Here the multipole approach [13], in combination with the density matrix formalism is used for establishing of the model for MMs with gain. This approach allows us to investigate analytically or semi-analytically the interplay between gain and magnetic properties of the MMs, the influence of internally unstable operation mode for spasers (MAs coupled with emitters, which the MMs consist of) on the propagation characteristics, and finally to optimize MM design. Moreover, the presented model is in line with the previously presented approach [16] (actually is its natural extension on the problem …
We study theoretically the dispersion of plasmonic honeycomb lattices and find Dirac spectra for both dipole and quadrupole modes. Zigzag edge states derived from Dirac points are found in ribbons of these honeycomb plasmonic lattices. The zigzag edge states for out-of-plane dipole modes are closely analogous to the electronic ones in graphene nanoribbons. The edge states for in-plane dipole modes and quadrupole modes, however, have rather unique characters due to the vector nature of the plasmonic excitations. The conditions for the existence of plasmonic edge states are derived analytically.
Optically-induced magnetic resonances in non-magnetic media have unlocked magnetic light-matter interactions and led to new technologies in many research fields. Previous proposals for the levitation of nanoscale particles without structured illumination have worked on the basis of epsilon-near-zero surfaces or anisotropic materials but these carry with them significant fabrication difficulties. We report the optical levitation of a magnetic dipole over a wide range of realistic materials, including bulk metals, thereby relieving these difficulties. The repulsion is independent of surface loss…
Within the context of spin-related optical phenomena, the near-field directionality is generally understood from the quantum spin Hall effect of light, according to which the transverse spin of surface or guided modes is locked to the propagation direction. So far, most previous works have been focused on the spin properties of circularly polarized dipolar sources. However, in near-field optics, higher-order multipole sources (e.g., quadrupole, octupole, and so on) might become relevant, so a more in-depth formulation would be highly valuable. Building on the angular spectrum representation, w…
Crystals of plasmonic metal nanoparticles have intriguing optical properties. They reach the regimes of ultrastrong and deep strong light-matter coupling, where the photonic states need to be included in the simulation of material properties. We propose a quantum description of the plasmon polaritons in supercrystals that starts from the dipole and quadrupole excitations of the nanoparticle building blocks and their coupling to photons. Our model excellently reproduces results of finite difference time domain simulations. It provides detailed insight into the emergence of the polariton states.…
The plasmon oscillations of a metallic triaxial ellipsoid nanoparticle have been studied within the framework of the quasistatic approximation. A general method has been proposed for finding the analytical expressions describing the potential and frequencies of the plasmon oscillations of an arbitrary multipolarity order. The analytical expressions have been derived for an electric potential and plasmon oscillation frequencies of the first 24 modes. Other higher orders plasmon modes are investigated numerically.
The paper analyses the SEHR spectra of symmetrical molecules on the base of the dipole-quadrupole SEHRS theory. Existence of the bands, caused by vibrations transforming after the unit irreducible representations of corresponding symmetry groups is demonstrated. As it follows from the theoretical group analysis, these bands are forbidden in phenazine, pyrazine and in usual HRS in molecules belonging to a large number of groups (Cnh, D and higher symmetry groups for example). Their appearance strongly confirms the dipole-quadrupole SEHRS theory, which is able to explain other features of the SE…
The paper presents main aspects of the Dipole-Quadrupole theory of Surface Enhanced Infrared Absorption (SEIRA). It is pointed out the possibility of appearance of the lines, caused by totally symmetric vibrations transforming after the unit irreducible representation, which are forbidden in usual infrared absorption spectra in molecules with sufficiently high symmetry. Observation of such lines in the SEIRA spectra of diprotonated and ethylene, adsorbed on and on mordenites is pointed out. The results well agree with our ideas about surface enhanced optical processes, based on the conception …
Plasmonic chirality exhibits great potential for novel nanooptical devices due to the generation of a strong chiroptical response. Previous reports on plasmonic chirality explanations are mainly based on phase retardation and coupling. We propose a quantitative model similar to the chiral molecules for explaining the mechanism of the intrinsic plasmonic chirality quantitatively based on the interplay and mixing of electric and magnetic dipole modes, which forms a mixed electric and magnetic polarizability. The analysis method is also suitable for small chiral object down to quasi-static limit …
We present a practical scheme to separate the contributions of the electric quadrupole-like and the magnetic dipole-like effects to the forbidden second order optical nonlinear response of graphene, and give analytic expressions for the second order op- tical conductivities, calculated from the independent particle approximation, with relaxation described in a phenomenological way. We predict strong second order nonlinear effects, including second harmonic generation, photon drag, and difference fre- quency generation. We discuss in detail the controllability of these effects by tuning the che…
Plasmons are usually described in terms of macroscopic quantities such as electric fields and currents. However as fundamental excitations of metals they are also quantum objects with internal structure. We demonstrate that this can induce an intrinsic dipole moment which is tied to the quantum geometry of the Hilbert space of plasmon states. This {\it quantum geometric dipole} offers a unique handle for manipulation of plasmon dynamics, via density modulations and electric fields. As a concrete example we demonstrate that scattering of plasmons with non-vanishing quantum geometric dipole from…
The review is devoted to explanation of SERS in terms of the dipole and quadrupole light-molecule interactions arising in surface fields strongly varying in space in the region of the strongly irregular surface roughness. The main SERS characteristics, the theory of electromagnetic fields near some model kinds of rough surfaces and some other systems, the theory of SERS Raman tensor for arbitrary and symmetrical molecules, selection rules and analysis of the SER spectra, some anomalies in the SER spectra of symmetrical molecules for some specific conditions, electrodynamic forbiddance of the q…
This theoretical study, deals with the effect of bi-particle interaction on the surface plasmon resonance (SPR) in a dimer which includes two identical metal nanoparticles (NPs). Considering the dipole-dipole interaction in a Drude-like model, an appropriate equation is derived for the permittivity of each NP. The restoration force related to the classical confinement originating from the finite size of NPs is considered and an appropriate adjustment coefficient is considered for this term through analyzing experimental data. Two different polarizations are considered for the laser beam electr…
On chip exciting electric modes in individual plasmonic nanostructures are realized widely; nevertheless, the excitation of their magnetic counterparts is seldom reported. Here, we propose a highly efficient on chip excitation approach of the magnetic dipole mode of an individual split ring resonator (SRR) by integrating it onto a photonic crystal nanocavity (PCNC). A high excitation efficiency of up to 58% is realized through the resonant coupling between the modes of the SRR and PCNC. A further fine adjustment of the excited magnetic dipole mode is demonstrated by tuning the relative positio…
Dipole-quadrupole model and multipole analysis of resonant membrane metasurfaces
Leibniz University Hannover（汉诺威莱布尼茨大学）；Hannover Centre for Optical Technologies, Leibniz University Hannover（汉诺威光学技术中心，汉诺威莱布尼茨大学）；Institute of Transport and Automation Technology, Leibniz University Hannover（交通与自动化技术研究所，汉诺威莱布尼茨大学）；Cluster of Excellence PhoenixD, Leibniz University Hannover（PhoenixD卓越集群，汉诺威莱布尼茨大学）；Institute of Quantum Optics, Leibniz University Hannover（量子光学研究所，汉诺威莱布尼茨大学）
We study the topological photonic states in one-dimensional (1-D) lattices analogue to the Su-Schrieffer-Heeger (SSH) model beyond the dipole approximation. The electromagnetic resonances of the lattices supported by near-field interactions between the plasmonic nanoparticles are studied analytically with coupled dipole--quadrupole method. The topological phase transition in the bipartite lattices is determined by the change of Zak phase. Our results reveal the contribution of quadrupole moments to the near-field interactions and the band topology. It is found that the topological edge states …
In electron energy-loss spectroscopy (EELS) of individual silver nanoparticles encapsulated in silicon nitride, we observe besides the usual dipole resonance an additional surface plasmon (SP) resonance corresponding to higher angular momenta. We even observe both resonances for nanoparticle radii as small as 4 nm, where previously only the dipole resonance was assumed to play a role. Electron beams positioned outside of the particles mostly excite the dipole mode, but the higher-order resonance can even dominate the dipole peak when exciting at the particle surface, the usual choice for maxim…
The plasmonic chirality has drawn a lot of attention because of the tunable circular dichroism (CD) and the enhancement for the signal of chiral molecules. Different mechanisms have been proposed for explaining the plasmonic CD, however, a quantitative one like ab initio mechanism in chiral molecules is still unavailable. In this work, a mechanism similar to the chiral molecules is analyzed. The giant extrinsic circular dichroism of plasmonic splitting rectangle ring is quantitatively investigated theoretically. The interplay of electric and magnetic modes of the meta-structure is proposed to …
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 4fn 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 strengt…
We consider plasmonic metasurfaces constituted by an arbitrary periodic arrangement of spherical metallic nanoparticles. Each nanoparticle supports three degenerate dipolar localized surface plasmon (LSP) resonances. In the regime where the interparticle distance is much smaller than the optical or near-infrared wavelength associated with the LSPs, the latter couple through the dipole-dipole interaction and form collective plasmonic modes which extend over the whole metasurface. Within a Hamiltonian model which we solve exactly, we derive general expressions which enable us to extract analytic…
The paper demonstrates possibility of giant enhancement of Surface Enhanced Hyper Raman Scattering on the base of qualitative consideration of electromagnetic field near some models of rough metal surfaces and of some features of the dipole and quadrupole light-molecule interaction, such as it was made in the dipole-quadrupole SERS theory. Consideration of symmetrical molecules allows to obtain selection rules for their SEHR spectra and establish such regularity as appearance of the bands, caused by the totally symmetric vibrations, transforming after the unitary irreducible representation in …
The paper demonstrates possibility of giant enhancement of Surface Enhanced Hyper Raman Scattering on the base of qualitative consideration of electromagnetic field near some models of rough metal surfaces and of some features of the dipole and quadrupole light-molecule interaction, such as it was made in the dipole-quadrupole SERS theory. Consideration of symmetrical molecules allows to obtain selection rules for their SEHR spectra and establish such regularity as appearance of the lines, caused by totally symmetric vibrations, transforming after the unit irreducible representation in molecul…
We calculate the A and B hyperfine constants for the low-lying states of 229Th3+ using a high-precision relativistic all-order approach. By combining these calculations with measurements of the 6d and 5f hyperfine constants [C. J. Campbell et al., Phys. Rev. Lett. 106, 223001 (2011)], we determine the magnetic dipole μ=0.360(7)μ_B and the electric-quadrupole Q=3.11(6) eb moments of the 229Th nucleus. Our value for μis five times more accurate and is 22% smaller than the best previous value μ=0.46(4) μ_B [S. Gerstenkorn et al., J. Phys. (Paris) 35, 483 (1974)], while our value for Q is the same…
