Nonlinear Dipole Research Articles

Tailoring Second-Harmonic Generation in Single L-Shaped Plasmonic Nanoantennas from the Capacitive to Conductive Coupling Regime

We investigate the efficiency of second-harmonic generation (SHG) over the transition from capacitive to conductive coupling in orthogonal L-shaped dimer gold antennas. By tuning both the gap and antenna length, the bonding and antibonding resonances are individually addressed. Results on the intensity and polarization of SHG are compared quantitatively with microscopic numerical simulations taking into account the nanoscale nonlinear surface dipole distribution, elucidating the interplay between symmetry at macroscopic and microscopic levels and optical resonance effects. Microscopic modeling reveals strong cancellations of nonlinear dipoles by capacitive coupling in plasmonic nanogaps, resulting in only small changes in SHG efficiency despite large local field enhancement in the gap. Experimentally, irreproducible polarization properties are obtained in a range of parameters associated with strong optical near fields in the gap of the antennas, which is interpreted as a consequence of nanoscopic asymmet...

Second harmonic generation microscopy investigation of the crystalline ultrastructure of three barley starch lines affected by hydration.

Second harmonic generation (SHG) microscopy is employed to study changes in crystalline organization due to altered gene expression and hydration in barley starch granules. SHG intensity and susceptibility ratio values (R'SHG ) are obtained using reduced Stokes-Mueller polarimetric microscopy. The maximum R'SHG values occur at moderate moisture indicating the narrowest orientation distribution of nonlinear dipoles from the cylindrical axis of glucan helices. The maximum SHG intensity occurs at the highest moisture and amylopectin content. These results support the hypothesis that SHG is caused by ordered hydrogen and hydroxyl bond networks which increase with hydration of starch granules.

Mesoscopic magnetomechanical hysteresis in a magnetorheological elastomer.

Field-induced magnetostatic interaction in a pair of identical particles made of a magnetically soft ferromagnet is studied. It is shown that due to saturation of the ferromagnet magnetization, this case differs significantly from the (super)paramagnetic one. A numerical solution is given, discussed, and compared with that provided by a simpler model (nonlinear mutual dipoles). We show that for multidomain ferromagnetic particles embedded in an elastomer matrix, as for paramagnetic ones in the same environment, pair clusters may form or break by a hysteresis scenario. However, the magnetization saturation brings in important features to this effect. First, the bistability state and the hysteresis take place only in a limited region of the material parameters of the system. Second, along with the hysteresis jumps occurring under the sole influence of the field, the "latent" hysteresis is possible which realizes only if the action of the field is combined with some additional (nonmagnetic) external factor. The obtained conditions, when used to assess the possibility of clustering in real magnetorheological polymers, infer an important role of mesoscopic magnetomechanical hysteresis for the macroscopic properties of these composites.

Quantum–classical correspondence and the role of the dipole function in molecular dissociation

Abstract We consider the quantum and classical dissociation dynamics of heteronuclear diatomic molecules induced by infrared laser pulses. The field–molecule interaction is given by the product of the time-dependent electric field and the molecule permanent dipole. We investigate the influence of the dipole function in molecular dissociation. We show that the dissociation can be suppressed at certain external field frequencies for a nonlinear and finite-range dipole function. The correspondence between quantum and classical results is established by relating classical Fourier amplitudes to discrete–continuum quantum matrix elements.

Resonant second-harmonic generation in metal–insulator–metal structure

Optical second-harmonic generation (SHG) in a metal–insulator–metal (MIM) structure is investigated. The experimental results of the second-harmonic (SH) intensity profile as a function of the angle of incidence indicate that the SH light observed from the MIM structure is mainly from bulk nonlinear polarization (quadrupoles or magnetic dipoles) in the metallic layer rather than from the nonlinear electric dipoles at the metallic surface (surface SHG). This is because the SH fields from the metallic surfaces in contact with the insulator layer are canceled and the SH light from the bulk nonlinear polarization (bulk SHG) is dominantly observed. A comparison with the SH intensity from a quartz crystal used as a standard reveals that the susceptibility for the bulk nonlinear polarization is found be in the order of 102 pm/V.

Dynamic symmetry-breaking in a simple quantum model of magneto-electric rectification, optical magnetization, and harmonic generation

The state mixings necessary to mediate three new optical nonlinearities are shown to arise simultaneously and automatically in a 2-level atom with an ℓ = 0 ground state and an ℓ = 1 excited state that undergoes a sequence of electric and magnetic dipole-allowed transitions. The treatment is based on an extension of dressed state theory that includes quantized electric and magnetic field interactions. Magneto-electric rectification, transverse magnetization, and second-harmonic generation are shown to constitute a family of nonlinear effects that can take place regardless of whether inversion is a symmetry of the initial unperturbed system or not. Interactions driven jointly by the optical electric and magnetic fields produce dynamic symmetry-breaking that accounts for the frequency, the intensity dependence, and the polarization of induced magnetization in prior experiments. This strong field quantum model explains not only how a driven 2-level system may develop nonlinear dipole moments that are forbidden between or within its stationary states, but it also broadens the class of materials suitable for optical energy conversion applications and magnetic field generation with light so as to include all transparent dielectrics.

Nonlinear Surface-Plasmon Whispering-Gallery Modes in Metallic Nanowire Cavities

We demonstrate that the surface second-harmonic generation can lead to the formation of nonlinear plasmonic whispering-gallery modes (WGMs) in microcavities made of metallic nanowires. Since these WGMs are excited by induced surface nonlinear dipoles, they can be generated even when they are not coupled to the radiation continuum. Consequently, the quality factor of these nonlinear modes can be as large as the theoretical limit imposed by the optical losses in the metal. Remarkably, our theoretical analysis shows that nonlinear plasmonic WGMs are characterized by fractional azimuthal modal numbers. This suggests that the plasmonic cavities investigated here can be used to generate multicolor optical fields with fractional angular momentum. Applications to plasmonic sensors are also discussed.

Study of dipole moments of LiSr and KRb molecules by quantum Monte Carlo methods

Heteronuclear dimers are of significant interest to experiments seeking to exploit ultracold polar molecules in a number of novel ways, including precision measurement, quantum computing and quantum simulation. We calculate highly accurate Born–Oppenheimer total energies and electric dipole moments as a function of internuclear separation for two such dimers, LiSr and KRb. We apply fully correlated, high-accuracy quantum Monte Carlo methods for evaluating these molecular properties in a many-body framework. We use small-core effective potentials combined with multi-reference Slater–Jastrow trial wave functions to provide accurate nodes for the fixed-node diffusion Monte Carlo method. For reference and comparison, we calculate the same properties with Hartree–Fock and with restricted Configuration Interaction methods, and carefully assess the impact of the recovered many-body correlations on the calculated quantities. For LiSr, we find a highly non-linear dipole moment curve, which may make this molecule’s dipole moment tunable through vibrational state control.

Nonlinear estimation-based dipole source localization for artificial lateral line systems

As a flow-sensing organ, the lateral line system plays an important role in various behaviors of fish. An engineering equivalent of a biological lateral line is of great interest to the navigation and control of underwater robots and vehicles. A vibrating sphere, also known as a dipole source, can emulate the rhythmic movement of fins and body appendages, and has been widely used as a stimulus in the study of biological lateral lines. Dipole source localization has also become a benchmark problem in the development of artificial lateral lines. In this paper we present two novel iterative schemes, referred to as Gauss–Newton (GN) and Newton–Raphson (NR) algorithms, for simultaneously localizing a dipole source and estimating its vibration amplitude and orientation, based on the analytical model for a dipole-generated flow field. The performance of the GN and NR methods is first confirmed with simulation results and the Cramer–Rao bound (CRB) analysis. Experiments are further conducted on an artificial lateral line prototype, consisting of six millimeter-scale ionic polymer–metal composite sensors with intra-sensor spacing optimized with CRB analysis. Consistent with simulation results, the experimental results show that both GN and NR schemes are able to simultaneously estimate the source location, vibration amplitude and orientation with comparable precision. Specifically, the maximum localization error is less than 5% of the body length (BL) when the source is within the distance of one BL. Experimental results have also shown that the proposed schemes are superior to the beamforming method, one of the most competitive approaches reported in literature, in terms of accuracy and computational efficiency.

Comparative Study on the Effective Dielectric Constant of the Graded Composites

The effective dielectric constant of the graded composites was calculated with three different methods, namely, the nonlinear differential effective dipole approximation method (NDEDA), the Maxwell-Garnette method (MGT) and the sum rule method (Sum). In each layer of the graded composites, the distribution of the dielectric constant follows a Drude form. Our numerical results show that when the number of layers N inside the graded composites increases, a gradual transition from sharp peaks to an emerging broad continuous band is clearly obtained. Moreover, the results obtained by the MGT and sum rule methods achieve a good agreement with that by the NDEDA method when N is approaching infinity.

Electric dipole (hyper)polarizabilities of spatially confined LiH molecule

In this study we report on the electronic contributions to the linear and nonlinear static electronic electric dipole properties, namely the dipole moment (μ), the polarizability (α), and the first-hyperpolarizability (β), of spatially confined LiH molecule in its ground X (1)Σ(+) state. The finite-field technique is applied to estimate the corresponding energy and dipole moment derivatives with respect to external electric field. Various forms of confining potential, of either spherical or cylindrical symmetry, are included in the Hamiltonian in the form of one-electron operator. The computations are performed at several levels of approximation including the coupled-cluster methods as well as multi-configurational (full configuration interaction) and explicitly correlated Gaussian wavefunctions. The performance of Kohn-Sham density functional theory for the selected exchange-correlation functionals is also discussed. In general, the orbital compression effects lead to a substantial reduction in all the studied properties regardless of the symmetry of confining potential, however, the rate of this reduction varies depending on the type of applied potential. Only in the case of dipole moment under a cylindrical confinement a gradual increase of its magnitude is observed.

All-optical manipulation of light inX- andT-shaped photonic crystal waveguides with a nonlinear dipole defect

We consider light transmission in $\mathrm{X}$- and $\mathrm{T}$-shaped photonic crystal waveguides which hold nonlinear defect with two resonant dipole modes. By use of the coupled-mode theory and by numerical solution of the Maxwell equations for the transverse-magnetic (TM) light mode, we show two stable types of the solutions. The first type has no cross talk, while the second type does owe to nonlinearity of the defect. We show also that direct path transmission processes in the waveguides play an important role for breaking of symmetry.

On the Northward Motion of Midlatitude Cyclones in a Barotropic Meandering Jet

Abstract The combined effects of the deformation (horizontal stretching and shearing) and nonlinearities on the beta drift of midlatitude cyclones are studied using a barotropic quasigeostrophic model on the beta plane. It is found that, without any background flow, a cyclonic vortex moves more rapidly northward when it is initially strongly stretched along a mostly north–south direction. This meridional stretching is more efficient at forming an anticyclone to the east of the cyclone through Rossby wave radiation. The cyclone–anticyclone couple then forms a nonlinear vortex dipole that propagates mostly northward. The case of a cyclone embedded in uniformly sheared zonal flows is then studied. A cyclone evolving in an anticyclonic shear is stretched more strongly, develops a stronger anticyclone, and moves faster northward than a cyclone embedded in a cyclonic shear, which remains almost isotropic. Similar results are found in the general case of uniformly sheared nonzonal flows. The evolution of cyclones is also investigated in the case of a more realistic meandering jet whose relative vorticity gradient creates an effective beta and whose deformation field is spatially varying. A statistical study reveals a strong correlation among the cyclone’s stretching, the anticyclone strength, and the velocity toward the jet center. These different observations agree with the more idealized cases. Finally, these results provide a rationale for the existence of preferential zones for the jet-crossing phase: that is, the phase when a cyclone crosses a jet from its anticyclonic to its cyclonic side.

Generation of s-polarized surface-like electromagnetic waves during nonlinear resonant light scattering

It is shown that, under certain conditions, two inhomogeneous s-polarized electromagnetic waves can be simultaneously excited in a nonlinear dipole monolayer. These waves propagate along the monolayer at the same phase velocity and exponentially decay with increasing distance from this layer in both directions.

Nonlinear Optical Properties of Type I Collagen Fibers Studied by Polarization Dependent Second Harmonic Generation Microscopy

Collagen (type I) fibers are readily visualized with second harmonic generation (SHG) microscopy though the molecular origin of the signal has not yet been elucidated. In this study, the molecular origin of SHG from type I collagen is investigated using the time-dependent coupled perturbed Hartree-Fock calculations of the hyperpolarizibilities of glycine, proline, and hydroxyproline. Two effective nonlinear dipoles are found to orient in-the-plane of the amino acids, with one of the dipoles aligning close to the pitch orientation in the triple-helix, which provides the dominant contribution to the SHG polarization properties. The calculated hyperpolarizability tensor element ratios for the collagen triple-helix models: [(Gly3)n]3, [(Gly-Pro2)n]3, and [(Gly-Pro-Hyp)n]3, are used to predict the second-order nonlinear susceptibility ratios, χ(zzz)(2)/χ(iiz)(2) and χ(zii)(2)/χ(iiz)(2) of collagen fibers. From SHG microscopy polarization in, polarization out (PIPO) measurements of type I collagen in human lung tissue, a theoretical method is used to extract the triple-helix orientation angle with respect to the collagen fiber. The study shows the dominant role of amino acid orientation in the triple-helix for determining the polarization properties of SHG and provides a method for determining the triple-helix orientation angle in the collagen fibers.

Polarizability and hyperpolarizability of BN zigzag nanotubes calculated by the coupled perturbed Kohn-Sham scheme

Linear and nonlinear electric dipole susceptibilities are evaluated for infinite periodic zigzag BN nanotubes utilizing primarily the coupled perturbed Kohn-Sham scheme recently implemented in the crystal code. The effect of different functionals, basis set, and computational parameters is examined. Most of the calculations are done at the B3LYP/6-31G* level. For electronic linear polarizabilities, substantial differences compared to the uncoupled sum-over-states scheme are found. Much larger radii were considered than in earlier studies, thereby permitting accurate comparison with corresponding properties of the hexagonal monolayer. In addition, we confirmed the dielectric shell model for the linear polarizability, but with a significantly different shell thickness than previously thought. Vibrational (ionic) contributions to the nonlinear susceptibilities are calculated. In doing so, the finite-field--nuclear-relaxation (FF--NR) method was employed for the transverse components of the (6,0), (9,0), and (12,0) nanotubes. Aside from being computationally more efficient than other procedures, this method includes anharmonicity effects through first order and, as shown, is readily applied to key dynamic as well as static properties (and yields the static linear polarizability as well). Our calculated nonlinear vibrational susceptibilities sometimes exceed, or even greatly exceed, the corresponding static electronic susceptibility. In such cases, the relative magnitude of the vibrational contribution grows substantially with tube radius over the range considered. Future plans include extending these FF--NR calculations to large nanotubes and to the longitudinal (periodic) direction as well.

A new form of spontaneously polarized material

We report here the discovery of a new form of spontaneously polarized material. Examples of this material, in the form of films, demonstrate the property that they spontaneously harbour electric fields which may exceed 10(8) Vm(-1), achieving potentials of tens of volts on the film surface. The molecules presently identified form a diverse group, thus far of six species, with gas phase dipoles lying between 0.08 D and 0.5 D: propane (0.08 D), isopentane (0.13 D), nitrous oxide (0.167 D), isoprene (0.25 D), toluene (0.385 D) and CF(3)Cl (Freon-13; 0.5 D). Here we concentrate on an understanding of the nature of the interactions which give rise to the spontaneously polarized state, using the measured temperature dependence of the electric field in N(2)O as a diagnostic. We show that the polarized state can arise through a mechanism of non-linear dipole alignment in a single domain in which dipole alignment generates the electric field within the film and the field generates dipole alignment. Non-local interactions take place over the dimension of the thickness of the film and permeate the entire medium through the agency of the electric field. This new type of material may have wide ranging applications in devices and in nanotechnology.

Graphene and few-layer graphite probed by second-harmonic generation: Theory and experiment

We have measured second-harmonic generation (SHG) from graphene and other graphitic films, from two layers to bulk graphite, at room temperature; all samples are mounted on a 300 nm oxide layer of a Si(001) substrate. With 800 nm, 150 fs fundamental pulses, the anisotropic response was recorded for combinations of $p$-, $s$-, and diagonally polarized fundamental and second-harmonic beams as the samples were rotated about their normal. Graphene samples display SHG signatures only slightly different from that of the bare substrate which shows SHG with fourfold rotational symmetry. All other layered systems show threefold symmetry, although the ratio of isotropic to anisotropic response varies with the number of layers. A model based on linear light propagation in layered media with interface dipole and bulk quadrupole SHG sources is presented for the analysis. We show that data from all layered samples can be understood in terms of well-known linear optical properties, the SHG response of the bare substrate and four independent, complex nonlinear dipole susceptibility tensor elements of the graphene/air interface.

Molecular χ(2) gratings via electron-beam lithography

We show that the nonlinear optical activity of an organic molecule may be quenched by electron irradiation. Exploiting this effect, we inscribe periodic χ(2) patterns in the molecular films by means of a scanning electron microscope. The second harmonic diffraction efficiency of the resulting χ(2) gratings is measured. The relative intensity of the diffraction orders observed agrees with the expectations for a sheet of nonlinear dipoles with a periodic modulation. No linear diffraction is seen. The present method allows realizing any type of two-dimensional χ(2) pattern with a resolution only limited by the electron beam patterning capabilities.

Interaction-induced electric properties and cooperative effects in model systems

A detailed analysis of the interaction-induced linear and non-linear axial static electric dipole properties and the interaction energy of the model HCHO(HF)(n) (n = 1, 2) complexes is carried out using the HF SCF, MP2, CCSD and CCSD(T) levels of approximation combined with a wide range of basis sets, namely the correlation-consistent basis sets of Dunning and co-workers, the polarization-consistent basis sets of Jensen, and the recently reported polarized LPol sets. The results of this study show that even the smallest among the LPol sets, the LPol-ds and LPol-dl sets, yield interaction induced axial static electric dipole properties of an accuracy comparable to that obtained with the aug-cc-pVQZ basis set. Using the LPol-ds, the LPol-dl, and the LPol-fl sets we have estimated the induced electric properties and the interaction energy of the HCHO(HF)(n) (n = 1-9) complexes, the cooperative effects in these systems, and the two-body effects. The many-body analysis shows that the two-body contributions to the induced first hyperpolarizability are not sufficient to correctly reproduce the general tendency for the changes in the property with the elongation of the polymer chain, since already for the n = 4 complex the more-than-two-body terms become dominant.