Classical Oscillator Model Research Articles

Structural Evolution and Microwave Dielectric Properties of Li(3−3x)M4xNb(1−x)O4 (M=Mg,Zn; 0≤x≤0.9)

Structural evolution of Li(3−3x)M4xNb(1−x)O4 (M=Mg,Zn; 0≤x≤0.9) and microwave dielectric properties of Li(3−3x)Mg4xNb(1−x)O4 have been studied by X-ray diffraction, scanning electron microscopy, Raman spectra, infrared reflectivity (IR) fitting, and microwave resonant measurement in this work. The crystal symmetry changed from the ordered cubic Li3NbO4 (I-43m, x=0) into disordered cubic phase (Fm3m) when 0.01≤x 1/3 compositions, and its content increased with the further increase of x. Short-range cation ordering was confirmed to be present in the cubic phase by Raman analysis. Mixture of Li3NbO4 and ZnO phases was observed in the whole composition range for the ZnO-added samples. For the Mg-doped samples, the dielectric constant increased slightly with x increasing up to x=1/3 and decreased with the further increase of x. The Q×f value increased greatly with the increasing x and saturated within the composition range of 0.1≤x<1/3. Further increasing x resulted in a decrease in Q×f value. All samples exhibited negative τf value. Minimum τf value of −22 ppm/°C was obtained at x=1/3. The IR reflection spectra of the x=0, 0.2, and 1/3 samples were analyzed by Kramers–Kroning analysis and classical oscillator model simulation. The dielectric properties were extrapolated down to the microwave range using the classical oscillator model for fitting the dielectric function. The calculated dielectric constants were in agreement with the experimental ones, whereas, the calculated Q×f values showed a reverse varying trend compared with the experimental data.

MICROWAVE DIELECTRIC PROPERTIES AND RAMAN SPECTROSCOPY OF SCHEELITE SOLID SOLUTION [(Li0.5Bi0.5)1-xCax]MoO4 CERAMICS WITH ULTRA-LOW SINTERING TEMPERATURES

A Scheelite solid solution was formed based on [( Li0.5Bi0.5 )1-x Ca x] MoO 4 ceramics and prepared via a solid state reaction method in the range 0.0 ≤ x ≤ 1.0. High performance microwave dielectric properties were obtained in the [(Li0.5Bi0.5)0.15Ca0.85]MoO4 ceramic sintered at 760°C with a relative permittivity of 14.1, a Qf value of 24,000 GHz (at 10.0 GHz), and a temperature coefficient value of +10.7 ppm/°C and the [(Li0.5Bi0.5)0.1Ca0.9]MoO4 ceramic sintered at 850°C with a relative permittivity of 12.7, a Qf value of 41,300 GHz (at 10.3 GHz), and a temperature coefficient value of -16.5 ppm/°C. X-ray diffraction, Raman spectroscopy and the classical damped oscillator model were applied to study the relationship between the microwave dielectric properties and structures.

Light-induced dynamics in the Lorentz oscillator model with magnetic forces

The classical Lorentz oscillator model of bound electron motion ordinarily excludes magnetic forces at nonrelativistic intensities for the simple reason that their magnitude is small. However, perturbative and numerical results show that when the $\mathrm{vP\vec}\ifmmode\times\else\texttimes\fi{}\mathrm{BP\vec}$ term is retained, dynamically enhanced terms give rise to large amplitude, magnetically induced charge displacements at zero frequency and at twice the driving frequency in the Cartesian laboratory frame. Numerical simulations of electron motion are in accord with the predictions of perturbative theory for steady-state motion in the classical picture. Direct integration shows that magnetic response which is comparable to electric dipole response can arise in transparent dielectrics at optical frequencies. Parametric instability in the equations of motion is implicated as the source of rapid energy transfer from electric to magnetic motions by reduction of the equations to a complex Mathieu equation.

Polarizable empirical force field for sulfur-containing compounds based on the classical Drude oscillator model.

Condensed-phase computational studies of molecules using molecular mechanics approaches require the use of force fields to describe the energetics of the systems as a function of structure. The advantage of polarizable force fields over nonpolarizable (or additive) models lies in their ability to vary their electronic distribution as a function of the environment. Toward development of a polarizable force field for biological molecules, parameters for a series of sulfur-containing molecules are presented. Parameter optimization was performed to reproduce quantum mechanical and experimental data for gas phase properties including geometries, conformational energies, vibrational spectra, and dipole moments as well as for condensed phase properties such as heats of vaporization, molecular volumes, and free energies of hydration. Compounds in the training set include methanethiol, ethanethiol, propanethiol, ethyl methyl sulfide, and dimethyl disulfide. The molecular volumes and heats of vaporization are in good accordance with experimental values, with the polarizable model performing better than the CHARMM22 nonpolarizable force field. Improvements with the polarizable model were also obtained for molecular dipole moments and in the treatment of intermolecular interactions as a function of orientation, in part due to the presence of lone pairs and anisotropic atomic polarizability on the sulfur atoms. Significant advantage of the polarizable model was reflected in calculation of the dielectric constants, a property that CHARMM22 systematically underestimates. The ability of this polarizable model to accurately describe a range of gas and condensed phase properties paves the way for more accurate simulation studies of sulfur-containing molecules including cysteine and methionine residues in proteins.

A modified wake oscillator model for vortex-induced vibration of circular cylinders for a wide range of mass-damping ratio

In this paper, the behavior of an elastically mounted cylinder, subjected to vortex-induced vibrations (VIV), is investigated by a low-dimensional model. The classical wake oscillator model, as a standard model, predicts the behavior of the system at high mass-damping ratios but fails in modeling the system at low mass-damping ratios. A modified wake oscillator model is introduced in order to describe the response of the system over a wide range of mass-damping ratios. The results of this new model are compared to experimental results from the literature and shown to be in good agreement. The new model can describe most of the features of vortex-induced vibration phenomenology, such as the Griffin plot and lock-in domains.

Terahertz carrier dynamics and dielectric properties of GaN epilayers with different carrier concentrations

Using terahertz time-domain spectroscopy, we measured the complex conductivity and dielectric function of n-type GaN with various carrier concentrations on sapphire substrate. The measured complex conductivity, which is due to the free carriers, is well fitted by simple Drude model. The contribution from the lattice vibration to the complex dielectric function increases with the decrease in free carrier concentration. A better fitting of the frequency-dependent complex dielectric response was obtained by considering both of the Drude and the classical damped oscillator model.

Modeling of light amplification and enhanced spontaneous emission in silicon nanocrystals

Based on coupled quantum electrodynamics the light propagation in active silicon nanocrystals was reported in this paper. The classical electron oscillator model was employed to bridge the link between the rate equations of the four-level atomic system of the active medium and the electromagnetic interaction. With the assistance of auxiliary differential equations we numerically solved the system by using the Finite-difference Time-domain (FDTD) method. Both stimulated and spontaneous emissions were taken into account in the active medium system. Light amplification characteristics due to stimulated emission were investigated under various pumping rates. To enhance the spontaneous emission, microcavities based on one-dimensional photonic crystals were designed to maximize the nonlinear interaction between the active medium and electromagnetic waves. Preliminary experimental investigation of the cavity-enhanced luminescence was performed to demonstrate the validation of the proposed simulation scheme.

Response of an Isolated Particulate Subjected to Lateral Electric Fields in a DC Glow Discharge

Isolated spheres of borosilicate glass are suspended in a dc glow discharge in neon. The isolated sphere is laterally displaced by applying a transient voltage across a pair of electrodes mounted on the wall of the discharge tube. By monitoring the response of the particulate when subjected to a step change in the voltage and to sinusoidally varying voltages of different frequencies, the charge on the suspended sphere is inferred. Unlike most previous studies, this paper considers heavier (from 16 to 42 times heavier) particulates and heavily damped conditions. Measurements are reported for 20.3- and 4.9-mum -diameter borosilicate glass spheres. It is found that lateral excitation of an isolated particulate in a dc glow discharge cannot drive the motion to classical resonance as has been observed in previous work involving axial displacements in RF plasmas. The classical forced damped oscillator model used successfully in previous work to explain experimental observations is found to be inadequate for the conditions of this paper. Rather, the base excitation (BE) model is found to exhibit good agreement with the present experimental results at frequencies exceeding the frequency at which the displacement is a maximum. Sheath polarization, neglected in previous work, is included in this paper. It is found that drag due to collisions with neutrals is insufficient to account for the total drag on the particulate under heavily damped conditions. A new means of estimating the charge from the frequency response of the particulate motion using the BE model is described. Based on this method, charge numbers of Z = 9.2 times10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sup> and Z = 1.5 times10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> are inferred for the 20.3- and 4.9-mum spheres, respectively.

Dielectric Dispersion at Microwave Frequencies of Some Low Loss Mixed Oxide Perovskites

This paper reports the dielectric permittivities of several low loss ceramics of A(B11/2B21/2)O3 mixed oxide perovskites, Ba(Mg1/3Ta2/3)O3 (BMT), Sr(Al1/2Nb1/2)O3 (SAN), Sr(Al1/2Ta1/2)O3 (SAT), Sr(Ga1/2Ta1/2)O3 (SGT), and their modified compositions 0.7Sr(Al1/2Nb1/2)O3-0.3NdGaO3 (SAN-NG) and 0.7Sr(Al1/2Ta1/2)O3-0.3NdGaO3 (SAT-NG), measured at microwave frequencies. Measurements of the frequency-dependent dielectric constant and loss tangent are reported. Their loss tangent values are on the order of 10− 4 to 10− 5, which can not be evaluated by the traditional reflection/transmission spectra or impedance measurement techniques. A parallel-plate dielectric resonance method was adopted for dielectric measurements for such low loss materials. The frequency spectra of dielectric constants and loss tangents of were investigated by the well known classical oscillator model.

Optically induced magnetization in homogeneous, undoped dielectric media

A widely held viewpoint in optics, namely, that dynamic magnetic effects are extremely weak at optical frequencies, is re-examined. Nonlinear charge motion induced by the optical magnetic field in dielectric systems is analyzed, is predicted to be resonantly enhanced, and is observed experimentally in CCl4, C6H6, and H2O at the fundamental input frequency. Excellent agreement is obtained with a classical magnetic harmonic oscillator model, which shows that the maximum dynamic magnetic dipole (MD) moment at optical frequencies is one half the electric dipole (ED) moment. As a consequence, magnetic dipole radiation generated by the optical magnetic field with an intensity one fourth that of ED radiation, as well as unanticipated nonlinear optical effects such as magnetic white-light generation, can arise in homogeneous transparent dielectrics. The mechanism of MD formation is confirmed experimentally to be second order in the input field, and the strength of the radiation is accounted for as a first-order contribution to the vector potential. Predictions are made of optical magnetic resonance, negative permeability, self-induced magnetic birefringence, and optically induced Faraday rotation.

Analysis of Infrared Reflection Spectra of (Mg1−xZnx)Al2O4 Microwave Dielectric Ceramics

Infrared reflection spectra of (Mg1−xZnx)Al2O4 ceramics were analyzed by Kramers–Kroning analysis and classical oscillator model simulation. The dielectric properties were extrapolated down to the microwave range using the classical oscillator model for fitting the dielectric function. According to structure analysis, the losses originating from bend vibration and stretch vibration of the bond between A‐site cation and oxygen anion dominated the whole dielectric losses of the spinel ceramics. The coexistence of Mg and Zn deteriorated the intrinsic dielectric properties due to the bond asymmetry thus introduced. The calculated Qf (∼105 GHz) was much higher than the measured ones (∼104 GHz), suggesting that the extrinsic loss was significant. Therefore, the microwave dielectric properties of MgAl2O4 and ZnAl2O4 could be improved much by microstructure modification, and the little superiority in their solution compared with the end‐members was due to microstructure improvement.

Motion of an Atomic Wave Packet in a Standing-Wave Cavity Field

We present an in-depth study on the behavior of an atomic wave packet which is placed in a standing wave cavity prepared in various states of light. We extract a simple classical oscillator model out of the dynamics of the quantum system. We quantitatively resolve the states of the spatially reorganized wave packet by the dressed state spatial probability distribution functions we developed. We also report a novel type of the “quantum collapse and revival” behavior of the Rabi nutation which is originated from the effect of the quantized atomic center-of-mass motion on the atomic internal motion.

Classical and Quantum Oscillator Model of an Atom in a Classical Field with Time-Dependent Damping

A quantum system with time dependent damping, which is canonically transformed from a conservative system, is dealt with. From the wave functions of the conservative system, we use a perturbative method to find the wave function of the damped quantum system under the influence of an external field. We consider the atomic optical susceptibility of the classical oscillator model with a damping function. With the wave function of the damped quantum system under the influence of the external field, we obtain the atomic optical susceptibility of the system. In both the quantum and the classical treatments, we show that the susceptibility depends on a frequency that is not the frequency of the applied field.

Terahertz time-domain studies of far-infrared dielectric response in 5 mol % MgO:LiNbO3 ferroelectric single crystal

The 5 mol % MgO:LiNbO3 ferroelectric single crystal has attracted much attention in terahertz (THz) generation and detection by parametric process or optical rectification. In this work, the dielectric properties of 5 mol % MgO:LiNbO3 ferroelectric single crystal in 0.2−2 THz frequency range has been investigated by using transmission-type THz time-domain spectroscopy. The complex refractive index and dielectric function are extracted from the measured transmittance and phase shift. The power absorption and dispersion relationship of the lowest branch of the phonon polariton are observed. The results fit well with the classical damped oscillator model, indicating that the far-infrared dielectric response of 5 mol % MgO:LiNbO3 is dominated by the lowest transverse optical mode with E(x,y) symmetry centered at 4.533 THz. The investigation presented in this work provides important considerations for optimizing THz devices in 5 mol % MgO:LiNbO3 ferroelectric single crystal.

The determination of infrared optical constants of rare earth fluorides by classical Lorentz oscillator model

Rare earth fluoride (REF3, RE = La, Ce, Pr, Sm, Er, Yb, Y) films were deposited on Ge(1 1 1) and silicon wafers in order to determine optical constants from the near infrared up to the high frequency tail of the reststrahlen band. The FT-IR transmission spectrum and the reflection spectrum were used to examine the infrared optical properties of the fluorides. The optical constants of the films in the infrared spectrum from 2 to 20 µm were calculated using the classical Lorentz oscillator model by fitting the transmission spectrum. The reflective spectrum of the fluorides on silicon was used to demonstrate the absorption difference in this region. It is found that the extinction coefficients of rare earth fluorides films with Pnma structure (REF3, RE = Y, Yb, Er) are larger than the other fluorides films with structure (REF3, RE = La, Ce, Pr, Sm) from 15 to 20 µm.

Infrared reflection spectra of Ba6−3xSm8+2xTi18O54 (x=0.5, 0.67, and 0.75) microwave dielectric ceramics

Infrared reflection spectra of the tungsten bronze-type Ba6−3xSm8+2xTi18O54 (x=0.5, 0.67, and 0.75) ceramics were measured and analyzed by a combined method using Kramers-Kroning relation and the classical oscillator model, and the selection rules and vibration modes of the tungsten bronze-type structure were investigated by a detailed group theory analysis. Microwave dielectric properties were calculated using the dispersion parameters obtained by the classical oscillator model. The error in reflectance due to the random scattering on sample surfaces indicated obvious effect on the calculated dielectric constant, but only slightly influenced the calculated Qf, and therefore, the present analysis provided a reasonable means to predict the intrinsic microwave dielectric loss. The predicted intrinsic Qf values (&amp;gt;30000GHz) were much higher than the experimental ones (∼10000GHz), and this suggested the great potential of significant improvement of Qf value in Ba6−3xSm8+2xTi18O54 ceramics by controlling the extrinsic dielectric loss.

The classical oscillator model and dielectric constants extracted from infrared reflectivity measurements

The theoretical foundation of the classical oscillator model for the dielectric response of doped semiconductors is reviewed and some errors from the literature are pointed out. Four different modifications of the plasma frequency are identified and their physical significance is given. The influence of the dielectric parameters on reflectivity is discussed. Large changes in the dielectric parameters extracted from experimental reflectivity measurements have been reported, when in fact inappropriate or inadequate reflectivity models have been applied.

Excitation of surface plasmons at aSiO2∕Aginterface by silicon quantum dots: Experiment and theory

The excitation of surface plasmons (SPs) by optically excited silicon quantum dots (QDs) located near a Ag interface is studied both experimentally and theoretically for different QD-interface separations. The Si QDs are formed in the near-surface region of an $\mathrm{Si}{\mathrm{O}}_{2}$ substrate by Si ion implantation and thermal annealing. Photoluminescence decay-rate distributions, as derived from an inverse Laplace transform of the measured decay trace, are determined for samples with and without a Ag cover layer. For the smallest, investigated Si-QDs-to-interface distance of $44\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ the average decay rate at $\ensuremath{\lambda}=750\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ is enhanced by 80% due to the proximity of the Ag-glass interface, with respect to an air-glass interface. Calculations based on a classical dipole oscillator model show that the observed decay rate enhancement is mainly due to the excitation of surface plasmons that are on the $\mathrm{Si}{\mathrm{O}}_{2}∕\mathrm{Ag}$ interface. By comparing the model calculations to the experimental data, it is determined that Si QDs have a very high internal emission quantum efficiency of $(77\ifmmode\pm\else\textpm\fi{}17)%$. At this distance they can excite surface plasmons at a rate of $(1.1\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}{10}^{4}\phantom{\rule{0.3em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$. From the model it is also predicted that by using thin metal films the excitation of surface plasmons by Si QDs can be further enhanced. Si QDs are found to preferentially excite symmetric thin-film surface plasmons.

Mechanism of coherent acoustic phonon generation under nonequilibrium conditions

We have investigated the dynamics of coherent acoustic phonons generated with ultrafast optical excitation in monoatomic Al films using femtosecond electron diffraction. Associated coherent and thermal lattice motions were measured simultaneously with sub milli-\aa{}ngstr\"om spatial resolution in real time. We show here that the phonon dynamics can be well fitted with a classical harmonic oscillator model using a driving force which includes both electronic and lattice contributions. In particular, the pressure of hot free electrons contributes significantly in driving the coherent acoustic phonons under nonequilibrium conditions when electrons and phonons are not thermalized.

Molecular Dynamics Study of Hydration in Ethanol−Water Mixtures Using a Polarizable Force Field

The abnormal physicochemical characteristics of ethanol solvation in water are commonly attributed to the phenomenon of hydrophobic hydration. To investigate the structural organization of hydrophobic hydration in water-ethanol mixtures, we use molecular dynamics simulations based on detailed atomic models. Induced polarization is incorporated into the potential function on the basis of the classical Drude oscillator model. Water-ethanol mixtures are simulated at 11 ethanol molar fractions, from 0.05 to 0.9. Although the water and ethanol models are parametrized separately to reproduce the vaporization enthalpy, static dielectric constant, and self-diffusion constant of neat liquids at ambient conditions, they also reproduce the energetic and dynamical properties of the mixtures accurately. Furthermore, the calculated dielectric constant for the various water-alcohol mixtures is in excellent agreement with experimental data. The simulations provide a detailed structural characterization of the mixtures. A depletion of water-water hydrogen bonding in the first hydration shell of ethanol is compensated by an enhancement in the second hydration shell. The structuring effect from the second solvation shell gives rise to a net positive hydrogen-bonding excess for ethanol molar fractions up to approximately 0.5. For larger molar fractions, the second hydration shell is not sufficiently populated to overcome the net H-bond depletion from the first shell.