Electrostatic Approximation Research Articles

Designed Synthesis of Solid and Hollow Cu2–xTe Nanocrystals with Tunable Near-Infrared Localized Surface Plasmon Resonance

Solid and hollow structures of Cu2–xTe nanocrystals are synthesized by the injection of a Te–TOP solution at different reaction times. Both types of Cu2–xTe nanocrystals exhibit an intense absorption peak (localized surface plasmon resonance (LSPR)) in the near-infrared region, arising from excess holes in the valence band, and high molar extinction coefficients of 2.6 × 107 M–1 cm–1 at 1150 nm and 8.1 × 107 M–1 cm–1 at 1200 nm are demonstrated for the solid-type and hollow-type Cu2–xTe nanocrystals, respectively. The experimentally observed extinction spectra and calculated extinction spectra based on the electrostatic approximation are studied. The LSPR responses in the near-infrared (NIR) region for both solid and hollow Cu2–xTe nanocrystals are affected by the refractive index of the medium, whereas the NIR resonance shift is more obvious in the hollow-type Cu2–xTe nanocrystals. Furthermore, the localized surface plasmon band of the Cu2–xTe nanostructures can be tuned by post processing via oxidation ...

Calculation and measurement of radiation corrections for plasmon resonances in nanoparticles

The problem of plasmon resonances in metallic nanoparticles can be formulated as an eigenvalue problem under the condition that the wavelengths of the incident radiation are much larger than the particle dimensions. As the nanoparticle size increases, the quasistatic condition is no longer valid. For this reason, the accuracy of the electrostatic approximation may be compromised and appropriate radiation corrections for the calculation of resonance permittivities and resonance wavelengths are needed. In this paper, we present the radiation corrections in the framework of the eigenvalue method for plasmon mode analysis and demonstrate that the computational results accurately match analytical solutions (for nanospheres) and experimental data (for nanorings and nanocubes). We also demonstrate that the optical spectra of silver nanocube suspensions can be fully assigned to dipole-type resonance modes when radiation corrections are introduced. Finally, our method is used to predict the resonance wavelengths for face-to-face silver nanocube dimers on glass substrates. These results may be useful for the indirect measurements of the gaps in the dimers from extinction cross-section observations.

The Dark Side of Plasmonics

Plasmonic dark modes are pure near-field modes that can arise from the plasmon hybridization in a set of interacting nanoparticles. When compared to bright modes, dark modes have longer lifetimes due to their lack of a net dipole moment, making them attractive for a number of applications. We demonstrate the excitation and optical detection of a collective dark plasmonic mode from individual plasmonic trimers. The trimers consist of triangular arrangements of gold nanorods, and due to this symmetry, the lowest-energy dark plasmonic mode can interact with radially polarized light. The experimental data presented confirm the excitation of this mode, and its assignment is supported with an electrostatic approximation wherein these dark modes are described in terms of plasmon hybridization. The strong confinement of energy in these modes and their associated near fields hold great promise for achieving strong coupling to single photon emitters.

Electrodynamics of semiconductor-coated noble metal nanoshells

The full Maxwell equations for a system of concentric shells of a noble metal and a semiconductor, with a very sharp excitonic resonance with a bare frequency in the gap between the bare plasmonic resonant frequency branches and having a strong oscillator strength, are solved. The plasmon-exciton coupling model is verified to produce for this dressed plexcition a spectrum that consists of a splitting of the bare excitonic resonance into two daughters and a shift in the plasmonic resonances from their bare values. The spectral region separating the excitonic daughters exhibits the features characteristic of induced transparency and slow light propagation. Furthermore, I show that the eigenvalues of this coupled system as herein are computed to significantly differ from those obtained in the electrostatic approximation where retardation and radiation reaction terms are neglected.

Eigenmodes of coupled plasmons–excitons in a system of adjoining spherical metallic-J-aggregate nanoshells

Using the spherical modes of the full-Maxwell equations, I compute the eigenfrequencies of the complex consisting of concentric passive inner core, a metallic nanoshell, molecular J-aggregate adsorped to the surface of the metal, immersed in a passive solution. The coupling of the plasmons of the metal to the excitons of the J-aggregate is incorporated in the formalism through the continuity conditions for the tangential components of the electric field and magnetic flux density at the materials interfaces. Comparison with results obtained using the electrostatic approximation shows deviations in both the values of the resonance frequencies and their decay-rates.

Gyrokinetic TEM stability calculations for quasi-isodynamic stellarators

Recent theoretical findings suggest that in perfectly quasi-isodynamic stellarators, the trapped-particle instability as well as the ordinary electron-density-gradient-driven trapped-electron mode are stable in the electrostatic and collisionless approximation. In these configurations contours of constant magnetic field strength B are poloidally closed, the second adiabatic invariant J is constant on flux surfaces and peaks in the centre. It follows that the diamagnetic drift frequency ω*α and the bounce-averaged magnetic drift frequency are in opposite directions, 0, everywhere on the flux surface. This is the signature of average "good curvature" for trapped particles and, thanks to this property, particles that bounce faster than the frequency of any unstable mode must draw energy from it near marginal stability. Consequently, the point of marginal stability cannot exist for the collisionless trapped-particle mode, and hence this mode will be absent. By a similar argument, the ordinary trapped-electron mode is also stable. Because perfect quasi-isodynamicity can never be reached, it is necessary to test configurations approaching quasi-isodynamicity numerically in order to probe their resilience against trapped-particle modes. Progress has been made to extend gyrokinetic simulations to stellarator geometries, enabling us to perform the first linear gyrokinetic simulations of density-gradient-driven modes in stellarator configurations approaching quasi-isodynamicity, such as Wendelstein 7-X and more recently found configurations. These simulations appear to confirm the analytical predictions.

Drastically increased absorption in vertical semiconductor nanowire arrays: A non-absorbing dielectric shell makes the difference

Enhanced absorption of especially long wavelength light is needed to enable the full potential of semiconductor nanowire (NW) arrays for optoelectronic applications. We show both experimentally and theoretically that a transparent dielectric shell (Al2O3 coating) can drastically improve the absorption of light in InAs NW arrays. With an appropriate thickness of the Al2O3 shell, we achieve four times stronger absorption in the NWs compared to uncoated NWs and twice as good absorption as when the dielectric completely fills the space between the NWs. We provide detailed theoretical analysis from a combination of full electrodynamic modeling and intuitive electrostatic approximations. This reveals how the incident light penetrates better into the absorbing NW core with increasing thickness of the dielectric shell until a resonant shell thickness is reached. We provide a simple description of how to reach this strongly absorbing resonance condition, making our results easy to apply for a broad wavelength range and a multifold of semiconductor and dielectric coating material combinations.

Fragment Molecular Orbital Molecular Dynamics with the Fully Analytic Energy Gradient.

Fragment molecular orbital molecular dynamics (FMO-MD) with periodic boundary conditions is performed on liquid water using the analytic energy gradient, the electrostatic potential point charge approximation, and the electrostatic dimer approximation. Compared to previous FMO-MD simulations of water that used an approximate energy gradient, inclusion of the response terms to provide a fully analytic energy gradient results in better energy conservation in the NVE ensemble for liquid water. An FMO-MD simulation that includes the fully analytic energy gradient and two body corrections (FMO2) gives improved energy conservation compared with a previously calculated FMO-MD simulation with an approximate energy gradient and including up to three body corrections (FMO3).

A periodic charge-dipole electrostatic model: Parametrization for silver slabs

We present an extension of the charge-dipole model for the description of periodic systems. This periodic charge-dipole electrostatic model (PCDEM) allows one to describe the linear response of periodic structures in terms of charge- and dipole-type gaussian basis functions. The long-range electrostatic interaction is efficiently described by means of the continuous fast multipole method. As a first application, the PCDEM method is applied to describe the polarizability of silver slabs. We find that for a correct description of the polarizability of the slabs both charges and dipoles are required. However a continuum set of parametrizations, i.e., different values of the width of charge- and dipole-type gaussians, leads to an equivalent and accurate description of the slabs polarizability but a completely unphysical description of induced charge-density inside the slab. We introduced the integral squared density measure which allows one to obtain a unique parametrization which accurately describes both the polarizability and the induced density profile inside the slab. Finally the limits of the electrostatic approximations are also pointed out.

One Dimensional Modeling of Radio Frequency Electric Field Penetration into Magnetized Plasmas

Full penetration of RF electric fields into magnetized plasmas is expected in order to realize the Lissajous helicon plasma accelerator (LHPA). We study the electric field penetration in bulk plasma in one-dimensional electrostatic approximation using two analytical models: the matrix sheath model and the vacuum gap model. An identical formula for the electric field is obtained from the models. The formula is benchmarked by particle-in-cell (PIC) simulations. The full penetration of the electric field is realized when the relation (q ≪0.01) is satisfied, where q is the measure of the degree of the shielding effect due to plasma density and electron magnetization.

Plasmonic Core–Shell Nanowires for Enhanced Second-Harmonic Generation

We demonstrate the synthesis and characterization of core–shell nanowires consisting of a non-centrosymmetric KNbO3 core and a gold shell. This type of nanostructure combines the nonlinear optical properties of the core and the plasmonic resonance of the shell in the near infrared spectral range. We report successful spectroscopic measurements on coated single wires to characterize the resonant behavior of the gold shell. We present a theoretical model based on the electrostatic approximation to estimate the enhancement of second-harmonic generation in a nanowire due to the shell. It suggests a possible enhancement factor of up to 4,000 for a system with a nanoshell of 16 nm thickness at a wavelength of 900 nm.

Integral equation for electrostatic waves generated by a point source in a spatially homogeneous magnetized plasma

The electric field generated by a time varying point charge in a three-dimensional, unbounded, spatially homogeneous plasma with a uniform background magnetic field and a uniform (static) flow velocity is studied in the electrostatic approximation which is often valid in the near field. For plasmas characterized by Maxwell distribution functions with isotropic temperatures, the linearized Vlasov-Poisson equations may be formulated in terms of an equivalent integral equation in the time domain. The kernel of the integral equation has a relatively simple mathematical form consisting of elementary functions such as exponential and trigonometric functions (sines and cosines), and contains no infinite sums of Bessel functions. Consequently, the integral equation is amenable to numerical solutions and may be useful for the study of the impulse response of magnetized plasmas and, more generally, the response to arbitrary waveforms.

Analytic gradient for the embedding potential with approximations in the fragment molecular orbital method

The first analytic derivative with respect to nuclear coordinates is derived for the fragment molecular orbital method used with electrostatic approximations. It is shown how response contributions due to the coupling between the electronic state of fragments and the embedding potential can be accurately and efficiently calculated. The accuracy of the analytic gradient is shown in comparison to the numerical gradient for a polypeptide and water clusters. For the largest system the overall speedup of about 4.9 is observed when approximations are used in FMO.

The van der Waals interaction of an atom with the convex surface of a nanocylinder*

In this work, the van der Waals interaction between an atom and the convex surface of both metal and dielectric nanocylinders is analyzed. We obtain closed analytical equations for the van der Waals interaction potential in the electrostatic approximation and compare this with the case of the atom interaction with a flat surface. We show that the strength of the van der Waals interaction for the nanocylinder differs significantly from that of the flat surface. This is especially visible at distances of the order of a cylinder radius from the surface, where the nanocylinder potential reduces to half that of the flat surface potential. We also note that a weakening of the van der Waals potential for a cylindrical surface as compared with that for a flat surface can be important when considering schemes for trapping atoms around nanofibers.

The electrostatic approximation in the problem of diffraction of a plane wave by a group of coaxial small scatterers

The modified null-field method (MNFM) is applied to solve an electrostatic problem for a group of coaxial bodies of revolution. A modification of the MNFM is proposed for strongly prolate or strongly oblate bodies. Dependences of scattering and absorption cross sections on various parameters of the problem are obtained. The method is tested for an electrostatic problem for a single strongly prolate or strongly oblate spheroid used as an example.

Study on Helicon Plasma Lissajous Acceleration for Electrodeless Electric Propulsion

(Received June 27th, 2011) In order to realize a long lifetime of an electric propulsion system, we have been investigating various electrodeless electric propulsion concepts utilizing a helicon plasma source. In one of our concepts, helicon plasma is electromagnetically accelerated using a rotating electric field in the presence of a diverging static magnetic field. This acceleration concept is called the Lissajous acceleration. Plasma acceleration experiments have been conducted and plasma acceleration was evaluated using a Mach probe. Although the experiments showed some features of the electromagnetic acceleration, most increment of the plasma velocity is caused by the increment of the electron temperature. The thrust (4.95 μN) did not reach feasible values for real applications, and therefore, it is important to find a better operational condition with the aid of a theoretical thrust model. We have developed a theoretical thrust model which consists of a trajectory analysis and an electric field penetration model in the electrostatic approximation. The model shows that experimental parameters are off from an optimum operational condition which provides the maximum thrust.

A new static calculation of the streamer region for long spark gaps

Different electrostatic approximations have been proposed to calculate the streamer region without going in deep details of the behavior of density of particles under the effect of high electric fi ...

Electrostatic solution and rayleigh approximation for small nonspherical particles in a spheroidal basis

The electrostatic problem for the case of axially symmetric particles is analyzed in a spheroidal basis. In this case, the wavenumber is zero and Maxwell’s equations are reduced to the Laplace equation for scalar potentials. An alternative approach involves solving integral equations that are similar to those obtained within the framework of the extended boundary conditions method. The scalar potentials are represented as expansions in terms of eigenfunctions of the Laplace equation in a spheroidal frame of reference, and unknown expansion coefficients are determined from an infinite set of linear algebraic equations (the separation of variables method). These two approaches yield exact solutions of the problem in the case of axially symmetric particles, which coincide with known solutions in particular cases. Investigation of infinite systems allowed finding the boundaries where these algorithms are valid. Numerical calculations showed that, for spheroidal Chebyshev particles (i.e., perturbed spheroids), the Rayleigh approximation based on the electrostatic solution is applicable in a wide range of the problem parameters and is in fair agreement with the results obtained using the discrete dipole approximation.

Comparison of polarizable continuum model and quantum mechanics/molecular mechanics solute electronic polarization: Study of the optical and magnetic properties of diazines in water

A combination of the polarizable continuum model (PCM) and the hybrid quantum mechanics/molecular mechanics (QM/MM) methodology, PCM-MM/QM, is used to include the solute electronic polarization and then study the solvent effects on the low-lying n→π(∗) excitation energy and the (15)N nuclear magnetic shielding of pyrazine and pyridazine in aqueous environment. The results obtained with PCM-MM/QM are compared with two other procedures, i.e., the conventional PCM and the iterative and sequential QM/MM (I-QM/MM). The QM calculations are made using density functional theory in the three procedures. For the excitation energies, the time-dependent B3LYP/6-311+G(d) model is used. For the magnetic shielding, the B3LYP/aug-pcS2(N)/pcS2(C,O,H) is used with the gauge-including atomic orbitals. In both cases, i.e., PCM-MM/QM and I-QM/MM, that use a discrete model of the solvent, the solute is surrounded by a first shell of explicit water molecules embedded by an electrostatic field of point charges for the outer shells. The best results are obtained including 28 explicit water molecules for the spectral calculations and 9 explicit water molecules for the magnetic shielding. Using the PCM-MM/QM methodology the results for the n→π(∗) excitation energies of pyridazine and pyrazine are 32,070 ± 80 cm(-1) and 32,675 ± 60 cm(-1), respectively, in good agreement with the corresponding I-MM/QM results of 32,540 ± 80 cm(-1) and 32,710 ± 60 cm(-1) and the experimental results of 33,450-33,580 cm(-1) and 32,700-33,300 cm(-1). For the (15)N magnetic shielding, the corresponding numbers for the gas-water shifts obtained with PCM-MM/QM are 47.4 ± 1.3 ppm for pyridazine and 19.7 ± 1.1 ppm for pyrazine, compared with the I-QM/MM values of 53.4 ± 1.3 ppm and 19.5 ± 1.2 ppm and the experimental results of 42-54 ppm and 17-22 ppm, respectively. The agreement between the two procedures is found to be very good and both are in agreement with the experimental values. PCM-MM/QM approach gives a good solute polarization and could be considered in obtaining reliable results within the expected QM/MM accuracy. With this electronic polarization, the solvent effects on the electronic absorption spectra and the (15)N magnetic shielding of the diazines in water are well described by using only an electrostatic approximation. Finally, it is remarked that the experimental and theoretical results suggest that the (15)N nuclear magnetic shielding of any diazine has a clear dependence with the solvent polarity but not directly with the solute-solvent hydrogen bonds.

Fabrication and characterization of electrostatic oscillators based on CNT bundles

Fabrication and characterization of electrostatic oscillators based on carbon nanotube (CNT) bundles have been demonstrated. Experimentally, different sizes of CNT bundles have been transferred from as-fabricated, vertically aligned CNT forests on the growth substrate onto the tip of metallic probes by a “pick, stick and break” process. When placed under an electrostatic field generated by a fixed DC bias, these CNT bundles moved laterally in the direction of the electrical field. Under AC excitations, CNT bundles vibrated back and forth following the driving frequencies. Analytically, the static deformation-voltage behavior of these electrostatic oscillators has been modeled by electrostatic bending approximation. These CNT bundles could function as oscillators for various applications in the general field of NEMS (Nanoelectromechanical Systems).