Electric Quadrupole Contributions Research Articles

Time-resolved circular dichroism of excitonic systems: theory and experiment on an exemplary squaraine polymer.

Experimental and theoretical foundations for femtosecond time-resolved circular dichroism (TRCD) spectroscopy of excitonic systems are presented. In this method, the system is pumped with linearly polarized light and the signal is defined as the difference between the transient absorption spectrum probed with left and with right circularly polarized light. We present a new experimental setup with a polarization grating as key element to generate circularly polarized pulses. Herein the positive (negative) first order of the diffracted light is left-(right-)circularly polarized and serves as a probe pulse in a TRCD experiment. The grating is capable of transferring ultrashort broadband pulses ranging from 470 nm to 720 nm into two separate beams with opposite ellipticity. By applying a specific chopping scheme we can switch between left and right circular polarizations and detect transient absorption (TA) and TRCD spectra on a shot-to-shot basis simultaneously. We perform experiments on a squaraine polymer, investigating excitonic dynamics, and we develop a general theory for TRCD experiments of excitonically coupled systems that we then apply to describe the experimental data in this particular example. At a magic angle of 54.7° between the pump-pulse polarization and the propagation direction of the probe pulse, the TRCD and TA signals become particularly simple to analyze, since the orientational average over random orientations of complexes factorizes into that of the interaction with the pump and the probe pulse, and the intrinsic electric quadrupole contributions to the TRCD signal average to zero for isotropic samples. Application of exciton theory to linear absorption and to linear circular dichroism spectra of squaraine polymers reveals the presence of two fractions of polymer conformations, a dominant helical conformation with close interpigment distances that are suggested to lead to short-range contributions to site energy shifts and excitonic couplings of the squaraine molecules, and a fraction of unfolded random coils. Theory demonstrates that TRCD spectra of selectively excited helices can resolve state populations that are practically invisible in TA spectroscopy due to the small dipole strength of these states. A qualitative interpretation of TRCD and TA spectra in the spectral window investigated experimentally is offered. The 1 ps time component found in these spectra is related to the slow part of exciton relaxation obtained between states of the helix in the low-energy half of the exciton manifold. The dominant 140 ps time constant reflects the decay of excited states to the electronic ground state.

The quasi bound spectrum of H2

We compute the radiative ro-vibrational emission spectrum of H involving quasi-bound states via a simple numerical method of resolution of the Schrödinger equation by introducing a modified effective molecular potential. The comparison of the eigenvalues obtained with our approximation and other theoretical methods based on scattering resonance properties is excellent. Electric quadrupole and magnetic dipole contributions are calculated and we confirm the previous computations of Forrey of the electric quadrupole transition Einstein coefficients. The astrophysical relevance of such quasi-bound levels is emphasized.

Second Harmonic Scattering of Molecular Aggregates

A general model is developed to describe the polarization-resolved second harmonic scattering (SHS) response from a liquid solution of molecular aggregates. In particular, the molecular spatial order is introduced to consider the coherent contribution, also known as the retarded contribution, besides the incoherent contribution. The model is based on the description of a liquid suspension of molecular dyes represented by point-like nonlinear dipoles, locally excited by the fundamental field and radiating at the harmonic frequency. It is shown that for a non-centrosymmetrical spatial arrangement of the nonlinear dipoles, the SHS response is very similar to the purely incoherent response, and is of electric dipole origin. However, for centrosymmetrical or close to centrosymmetrical spatial arrangements of the nonlinear dipoles, the near cancellation of the incoherent contribution due to the inversion symmetry rule allows the observation of the coherent contribution of the SHS response, also known as the electric quadrupole contribution. This model is illustrated with experimental data obtained for aqueous solutions of the dye Crystal Violet (CV) in the presence of sodium dodecyl sulfate (SDS) and mixed water-methanol solutions of the dye 4-(4–dihexadecylaminostyryl)-N-methylpyridinium iodide (DiA), a cationic amphiphilic probe molecule with a strong first hyper-polarizability; both CV and DiA form molecular aggregates in these conditions. The quantitative determination of a retardation parameter opens a window into the spatial arrangements of the dyes in the aggregates, despite the small nanoscale dimensions of the latter.

Revisiting the basic theory of sum-frequency generation.

The basic theory of sum-frequency generation (SFG) is revisited. A rigorous derivation showing that linear optical transmission and reflection at an interface result from the interference of the incident wave and induced radiation wave in a medium is presented. The derivation is extended to SFG in a medium with a finite interface layer to see how SFG evolves. Detailed description on interface vs bulk and electric dipole (ED) vs electric quadrupole (EQ) contribution to SFG are provided with essentially no model dependence, putting the theory of SFG on a solid ground and removing possible existing confusions. Electric-quadrupole contributions to SFG from the interface and bulk are discussed. It is seen that there is a relevant bulk EQ contribution intrinsically inseparable in measurement from the interface ED contribution but plays a major role among all EQ contributions; its importance relative to the ED part can only be judged by referring to the established reference cases.

Observation of a ferro-rotational order coupled with second-order nonlinear optical fields

Ferroic orders can be classified by the symmetry of their order parameters, and ferroelectric, ferromagnetic and ferro-toroidal orders have already been observed. The ferro-rotational order1–3, whose order parameter is an axial vector invariant under both time-reversal and spatial-inversion operations, is the final ferroic to be identified and has a vector order parameter. This order is closely related to a number of phenomena such as polar vortices4, giant magnetoelectric coupling5 and spin-helicity-driven ferroelectricity6, but it has received little attention so far. Here, using high-sensitivity rotational-anisotropy second-harmonic generation, we have exploited the electric quadrupole contribution to the second-harmonic generation to directly couple to this centrosymmetric ferro-rotational order in an archetype of type-II multiferroics, RbFe(MoO4)2. We found that two domain states with opposite ferro-rotational vectors emerge with distinct populations at the critical temperature Tc ≈ 195 K and gradually evolve to reach an even ratio at lower temperatures. Moreover, we have identified the ferro-rotational order phase transition as weakly first order and have revealed its coupling field as a unique combination of the induced electric quadrupole second-harmonic generation and the incident fundamental electric fields. The authors use optical spectroscopy to show that RbFe(MoO4)2 hosts a ferro-rotational phase. This is the final form of ferroic order to be observed.

Magnetic mirror metasurface based on the in-phase excitation of magnetic dipole and electric quadrupole resonances

We consider the design of magnetic mirrors that consist of a layer of two-dimensional high-refractive-index dielectric particles. The central idea is to search for conditions for which the electric field of the light backscattered by a single particle has a zero phase difference with respect to the incident field. Employing physical arguments, we conclude that this can occur when the electric dipolar contribution vanishes. Optimizing the form of the cross section, we find a situation in which the vanishing of the dipolar contribution coincides with an in-phase condition for the magnetic dipole and the electric quadrupole contributions. The resulting scattering pattern of the particle resembles that of an electric dipole, with the difference that the forward and backscattered electric fields have opposite signs. Based on these results, we design a metasurface reflector that behaves as a magnetic mirror at a specific wavelength within a wideband spectral response. Subsequently, we extend the results to the design of supported structures where a magnetic mirror condition at a single wavelength is similarly found.

Ideal magnetic dipole resonances with metal-dielectric-metal hybridized nanodisks.

Magnetic resonances generated with nonmagnetic nanostructures have been widely used to design various functional nanophotonic devices, and it is important to realize pure magnetic dipole scattering for the unambiguous study of magnetic light-matter interactions. However, the magnetic responses often spectrally overlapping with other multipoles, which is the main obstacle to achieve ideal magnetic dipole resonances. This study proposes and theoretically demonstrates that an ideal magnetic dipole resonance can be excited with metal-dielectric-metal hybridized nanodisks. It is shown that although the generated magnetic dipole scattering around the bonding resonance of the hybridized nanodisk is spectrally overlapping with strong electric dipole and electric quadrupole contributions, an almost perfect current loop can be generated by adjusting the geometry parameters and the refractive index of the dielectric layer, thereby leading to the suppressing of the overlapping multipoles and the formation of an ideal magnetic dipole scattering. What's more important is that both electric and magnetic near-fields are enhanced simultaneously with the increasing of the refractive index of the dielectric layer, which makes the hybridized nanodisk a promising platform for enhanced magnetic light-matter interactions.

Electric dipole and quadrupole contributions to valence electron binding in a charge-screening environment

We make a multipole expansion of the atomic/molecular electrostatic charge distribution as seen by the valence electron up to the quadrupole term. The Tridiagonal Representation Approach (TRA) is used to obtain an exact bound state solution associated with an effective quadrupole moment and assuming that the electron-molecule interaction is screened by suborbital electrons. We show that the number of states available for binding the electron is finite forcing an energy jump in its transition to the continuum that could be detected experimentally in some favorable settings. We expect that our solution gives an alternative, viable and simple description of the binding of valence electron(s) in atoms/molecules with electric dipole and quadrupole moments. We also ascertain that our model implies that a pure quadrupole-bound anion cannot exist in such a charge-screening environment.

Structure of the charge density wave in cuprate superconductors: Lessons from NMR

Using a mix of numerical and analytic methods, we show that recent NMR $^{17}$O measurements provide detailed information about the structure of the charge-density wave (CDW) phase in underdoped YBa$_2$Cu$_3$O$_{6+x}$. We perform Bogoliubov-de Gennes (BdG) calculations of both the local density of states and the orbitally resolved charge density, which are closely related to the magnetic and electric quadrupole contributions to the NMR spectrum, using a microscopic model that was shown previously to agree closely with x-ray experiments. The BdG results reproduce qualitative features of the experimental spectrum extremely well. These results are interpreted in terms of a generic "hotspot" model that allows one to trace the origins of the NMR lineshapes. We find that four quantities---the orbital character of the Fermi surface at the hotspots, the Fermi surface curvature at the hotspots, the CDW correlation length, and the magnitude of the subdominant CDW component---are key in determining the lineshapes.

Resolving enantiomers using the optical angular momentum of twisted light.

Circular dichroism and optical rotation are crucial for the characterization of chiral molecules and are of importance to the study of pharmaceutical drugs, proteins, DNA, and many others. These techniques are based on the different interactions of enantiomers with circularly polarized components of plane wave light that carries spin angular momentum (SAM). For light carrying orbital angular momentum (OAM), for example, twisted or helical light, the consensus is that it cannot engage with the chirality of a molecular system as previous studies failed to demonstrate an interaction between optical OAM and chiral molecules. Using unique nanoparticle aggregates, we prove that optical OAM can engage with materials' chirality and discriminate between enantiomers. Further, theoretical results show that compared to circular dichroism, mainly based on magnetic dipole contributions, the OAM analog helical dichroism (HD) is critically dependent on fundamentally different chiral electric quadrupole contributions. Our work opens new venues to study chirality and can find application in sensing and chiral spectroscopy.

Multimodal Nonlinear Optical Imaging of Live Cells Using Plasmon-Coupled DNA-Mediated Gold Nanoprism Assembly.

Multiphoton excitation microscopy techniques are the emerging nonlinear optical (NLO) imaging methods to watch the biological world due its ability to penetrate deep into living tissues. Driven by the need to develop multimodal NLO imaging probe, current article reports the design of DNA-mediated gold nanoprisms assembly based optical antennas to enhance multiphoton imaging capability in biological II window. Reported experimental data show a unique way to enhance second harmonic generation (SHG) and two-photon fluorescence (TPF) properties by several orders of magnitudes via plasmon coupled organization into gold nanoprism assembly structures. Experimental and theoretical modeling data using finite difference time domain (FDTD) simulations indicate that huge enhancement of SHG and TPF properties are mainly due to the electric quadrupole contribution and electric field enhancement. Using 1100 nm biological II window light, reported results demonstrated that antibody conjugated assembly structures are capable of exhibiting highly selective and very bright multimodal SHG and TPF imaging of human Hep G2 liver cancer cells.

Mid-infrared gyrotropy in split-ring resonators measured by Mueller matrix ellipsometry

Understanding gyrotropic effects in the mid-infrared (MIR) spectral range is of high technological interest because it is the fingerprint region of many metamaterials and organic compounds. We present experimental and simulated ellipsometric measurements of gyrotropy in the MIR region upon reflection from an ordered array of split-ring resonators, which are inherently non-chiral. We use the symmetry properties of the Mueller matrix for interpretation of the ellipsometric measurements and to identify gyrotropy. When the plane of incidence coincides with the low-symmetry optical axis, we observe gyrotropy at oblique incidence. The origin of the gyrotropy is explained by considering not only the electric dipole–magnetic dipole interaction, as in natural optical activity, but by retaining the electric dipole–electric quadrupole contributions. In isotropic systems these average to zero, however they are significant in ordered systems such as crystals and metamaterials.

The Photon Polarization Parameter of 2H(n, γ)3H reaction with Inclusion of the Electric Quadrupole Contribution

We use effective field theory (EFT) for the calculation of neutron—deuteron radiative capture at very low energies. We present here the use of EFT to calculate a low-energy photo-nuclear observable in three-body systems, the photon polarization parameter and fore—aft asymmetry at thermal neutron energies up to next-to-next to leading order (N2LO), with inclusion of the electric quadrupole contribution. The photon polarization parameter in total is found to be Rc = −0.421 ± 0.003 and is in good agreement with the other modern theoretical calculations based on modern nucleon—nucleon potentials. In comparison with our previous work, a satisfactory agreement with the available experimental data is found by inclusion of the electric quadrupole contribution.

Near-Field Mapping of Optical Modes on All-Dielectric Silicon Nanodisks

We measure, for the first time to our knowledge, the near-field amplitudes and phases of localized optical modes of high-index all-dielectric nanoparticles using apertureless near-field optical microscopy. For individual silicon nanodisks, we observe a four-lobed mode pattern and the formation of deep-subwavelength hot-spots. Our numerical calculations of the optical near-fields of the nanodisks in combination with a multipole expansion of the scattered field based on vector spherical harmonics reveal that the observed modes are dominated by electric quadrupole contributions. The observed mode is of particular interest for the design of low-loss all-dielectric metasurfaces and nanoantennas for a broad range of applications, such as directional and complex-polarization controlled emission, light extraction from multipolar atomic transitions, and coherent multiple-emitter-nanocavity interactions.

Angular dependence of resonant inelastic x-ray scattering: a spherical tensor expansion

AbstractA spherical tensor expansion is carried out to express the resonant inelastic scattering cross-section as a sum of products of fundamental spectra with tensors involving wavevectors and polarization vectors of incident and scattered photons. The expression presented in this paper differs from that of the influential article by Carra et al. (Phys. Rev. Lett. 74, 3700, 1995) because it does not omit interference terms between electric dipole and quadrupole contributions when coupling each photon to itself. Some specific cases of the spherical tensor expansion are discussed. For example the case of isotropic samples is considered and the cross-section is expressed as a combination of only three fundamental spectra for the situation where electric dipole or electric quadrupole transitions in the absorption process are followed by electric dipole transitions in the emission. This situation includes the case of untextured powder samples, which corresponds to the most frequent situation met experimentally. Finally, it is predicted that some circular dichroism may be observed on isotropic samples provided that the circular polarization of the scattered beam can be detected.

Absorption intensities of rovibronic transitions in the A-band of 16O2: Analysis and calculation of magnetic dipole and electric quadrupole contributions

The recently measured magnetic dipole (M1) absorption intensities of rovibronic transitions in the A-band (bΣg+1−XΣg−3, 030 band) of 16O2 are theoretically analyzed employing a model in which the bΣg+1:XΣg−3 mutual perturbations are treated to a sufficient degree of accuracy. Effects of rotational perturbations became manifest in the data analysis and rovibronic correction parameters are needed to reconcile theory and experiment. At a subtle level there is evidence of Herman–Wallis (HW) type effect arising from vibration–rotation interaction in the b and X states. The functional form for the HW correction factor is arrived at from first principles. The final calculations reproduce the measured intensities to fraction of a percent, well within the measurement accuracy. The present analysis leads to the value 〈M1〉0,0=0.02679(4)μB for the M1 transition moment, and the spontaneous emission rate (Einstein-A coefficient) Γ0,0=0.0874s−1. For the sake of completeness, the electric quadrupole (E2) contribution to the observed intensities is also quantitatively assessed.

Second-harmonic Generation of Treated-STO Surface

In order to investigate the surface SHG, (110) pure STO single crystals were exposed to a reducing atmosphere to induce the reduction of the Ti ion and the release of oxygen from the lattice compensating the reduction of the Ti ions. The anisotropy and asymmetry of SHG intensity explains a slight shrinkage. The incoming fundamental wave was polarized either in the p-in or s-in to the plane of incidence for the reflection geometry. The SH polarization diagram could be described by the electric dipole and/or quadrupole contribution of reduced STO single crystal surface.

Simulating Picosecond Iron K-Edge X-ray Absorption Spectra by ab Initio Methods To Study Photoinduced Changes in the Electronic Structure of Fe(II) Spin Crossover Complexes

Recent time-resolved X-ray absorption experiments probing the low-spin to high-spin photoconversion in Fe(II) complexes have monitored the complex interplay between electronic and structural degrees of freedom on an ultrafast time scale. In this study, we use transition potential (TP) and time-dependent (TD) DFT to simulate the picosecond time-resolved iron K-edge X-ray absorption spectrum of the spin crossover (SCO) complex, [Fe(tren(py)(3))](2+). This is achieved by simulating the X-ray absorption spectrum of [Fe(tren(py)(3))](2+) in its low-spin (LS), (1)A(1), ground state and its high-spin (HS), (5)T(2), excited state. These results are compared with the X-ray absorption spectrum of the high-spin analogue (HSA), [Fe(tren(6-Me-py)(3))](2+), which has a (5)T(2) ground state. We show that the TP-DFT methodology can simulate a 40 eV range of the iron K-edge XANES spectrum reproducing all of the major features observed in the static and transient spectra of the LS, HS, and HSA complexes. The pre-edge region of the K-edge spectrum, simulated by TD-DFT, is shown to be highly sensitive to metal-ligand bonding. Changes in the intensity of the pre-edge region are shown to be sensitive to both symmetry and π-backbonding by analysis of relative electric dipole and quadrupole contributions to the transition moments. We generate a spectroscopic map of the iron 3d orbitals from our TD-DFT results and determine ligand field splitting energies of 1.55 and 1.35 eV for the HS and HSA complexes, respectively. We investigate the use of different functionals finding that hybrid functionals (such as PBE0) produce the best results. Finally, we provide a detailed comparison of our results with theoretical methods that have been previously used to interpret Fe K-edge spectroscopy of equilibrium and time-resolved SCO complexes.

Electric quadrupole contribution to the nonresonant background of sum frequency generation at air/liquid interfaces

We study an electric quadrupole contribution to sum frequency generation (SFG) at air∕liquid interfaces in an electronically and vibrationally nonresonant condition. Heterodyne-detected electronic sum frequency generation spectroscopy of air∕liquid interfaces reveals that nonresonant χ((2)) (second-order nonlinear susceptibility) has a negative sign and nearly the same value for all eight liquids studied. This result is rationalized on the basis of the theoretical expressions of χ((2)) with an electric quadrupole contribution taken into account. It is concluded that the nonresonant background of SFG is predominantly due to interfacial nonlinear polarization having a quadrupole contribution. Although this nonlinear polarization is localized at the interface, it depends on quadrupolar χ((2)) in the bulk as well as that at the interface. It means that the sign of nonresonant χ((2)) bears no relation to the "up" versus "down" alignment of interfacial molecules, because nonresonant χ((2)) has a quadrupolar origin.

Contribution of the electric quadrupole resonance in optical metamaterials

Optical metamaterials can exhibit negative index of refraction when both the effective permittivity and permeability are negative. The negative permeability is usually considered to be associated with a magnetic dipole resonance and the contribution from electric quadrupoles is neglected. Here, we show by simulation that the electric quadrupole contribution is actually comparable to that from magnetic dipoles. We propose an experimental scheme to determine the relative contributions from the electric dipole, magnetic dipole, and electric quadrupole of a metallic nanostructure. This can be important in the design of metamaterials.