Phase Diffusion Model Research Articles

Features of Metalorganic Chemical Vapor Deposition Selective Area Epitaxy of AlzGa1−zAs (0 ≤ z ≤ 0.3) Layers in Arrays of Ultrawide Windows

AlzGa1−zAs layers of various compositions were grown using metalorganic chemical vapor deposition on a GaAs substrate with a pattern of alternating SiO2 mask/window stripes, each 100 µm wide. Microphotoluminescence maps and thickness profiles of AlzGa1−zAs layers that demonstrated the distribution of the growth rate and z in the window were experimentally studied. It was shown that the layer growth rate and the AlAs mole fraction increased continuously from the center to the edge of the window. It was experimentally shown that for a fixed growth time of 10 min, as z increased from 0 to 0.3, the layer thickness difference between the center of the window and the edge increased from 700 Å to 1100 Å, and the maximum change in z between the center of the window and the edge reached Δz 0.016, respectively. Within the framework of the vapor -phase diffusion model, simulations of the spatial distribution of the layer thickness and z across the window were carried out. It was shown that the simulation results were in good agreement with the experimental results for the effective diffusion length D/k: Ga—85 µm, Al—50 µm.

Numerical studies of atomic three-step photoionization processes with non-monochromatic laser fields

The atomic selective multi-step photoionization process is a critical step in laser isotope separation. In this work, we study three-step photoionization processes with non-monochromatic laser fields theoretically based on the semi-classical theory. Firstly, three bandwidth models, including the chaotic field model, de-correlation model, and phase diffusion model, are introduced into the density matrix equations. The numerical results are compared with each other comprehensively. The phase diffusion model is selected for further simulations in terms of the correspondence degree to physical practice. Subsequently, numerical calculations are carried out to identify the influences of systematic parameters, including laser parameters (Rabi frequency, bandwidth, relative time delay, frequency detuning) and atomic Doppler broadening, on photoionization processes. In order to determine the optimal match among different systematic parameters, the ionization yield of resonant isotope, and selectivity factor are adopted as evaluation indexes to guide the design and optimization process. The results in this work can provide a rewarding reference for laser isotope separation.

Phase diffusion model of a one-dimensional superradiance lattice and its application as a controllable high-frequency light reflector

We study the effect of quantum phase fluctuation (QPF) on a one-dimensional superradiance lattice (1DSL) and its application as a controllable high-frequency light reflector. In electromagnetically induced transparency (EIT)-based 1DSL [Phys. Rev. Lett. 114, 043602 (2015)PRLTAO0031-900710.1103/PhysRevLett.114.043602], counter-propagating control laser fields are responsible for the hopping of electrons from the i th to the j th atom, where n 1 and n 2 coupling photons are required for forward and backward modes, respectively. In the limit of n 1 , n 2 ≫ 1 , the role of QPF becomes significant, and, therefore, the phase diffusion model of 1DSL needs to be considered. We show that in the presence of QPF a perfect 1DSL can be realized due to the fact that EIT vanishes at the resonance condition when probe detuning is zero. It leads to a reasonably high (around 60%) reflectivity of the incident probe field at resonance condition. For the off resonant case, the reflectivity reduces due to the phase diffusion; however, it can be overcome via manipulation of the control fields.

Transition between optical turbulence and dissipative solitons in a complex Ginzburg-Landau equation with quasi-cw noise

Noise-induced phase transition between chaos and ordered states plays an important role in the self-organization of dissipative structures. Here, we numerically simulate the phase transitions between statistically stationary regimes in a laser cavity by using a stochastic complex cubic-quintic Ginzburg-Landau equation with a phase-diffusion model. Depending on the linear and nonlinear gains, the dissipative system converges from the initial noise floor to different regimes, including continuous wave, phase turbulence, amplitude turbulence (AT), and stable soliton structure. Around the regime boundaries, we found that only certain phase noise can cause the instability of phase turbulence. The defects formed due to the noise will continue to spread out and self-organize to form AT or stabilize the soliton structure in the defect area. Our results are helpful in understanding the dynamics of the buildup of mode locking and noiselike pulses in passively mode-locked lasers.

Physics-based fractional-order model with simplified solid phase diffusion of lithium-ion battery

Abstract Solid phase diffusion plays an important role in the long-term performances of lithium-ion batteries. Current mechanistic model for describing the solid phase diffusion has low computational efficiency and obscure physical meanings. A simple but effective physics-based solid phase diffusion model is of great significance for the impedance characterization and aging diagnosis of lithium-ion batteries. In this paper, a physics-based fractional-order model is established by simplifying the solid phase diffusion process through Pade approximation. A full-cell fractional-order model is constructed by combining the medium-high frequency dynamic model. The proposed model has a clear physical meaning and can be used to characterize full-cell performances. Furthermore, this paper provides solutions to identifying the parameters of the full-cell fractional-order model by decoupling the dynamics in frequency and spatial domain. The established full-cell fractional-order model is validated under various working loads. The results show that the proposed physics-based fractional-order model with simplified solid phase diffusion improves the computational efficiency with little loss of accuracy, indicating that the proposed model is an appropriate candidate for online applications.

Diffusion stress analysis of spherical shell electrode

Lithium-ion batteries have a wide range of applications in the field of electronics. It is necessary to conduct in-depth study of the impact of diffusion-induced stress to enhance the performance of lithium-ion batteries. In this study, the diffusion-induced stress of spherical shell electrode is investigated. The effect of initial concentration of lithium ions and the size of electrode on the diffusion stress under constant voltage charge and discharge conditions are analysed by employing single phase diffusion model. In this paper, the evolution of the lithium ion concentration in the spherical shell electrode is calculated by controlling the initial concentration of lithium ions, and then the size of the electrode material is changed to explore the radial and circumferential stress of the spherical shell electrode material. It is found that the lower initial concentration of lithium ions can effectively reduce the diffusion stress. The stress variation of the right peak point of spherical shell electrode with lithium ion concentration is further studied. The results show that the smaller the electrode material size, the smaller the diffusion stress.

Quantum Brownian Motion at Strong Dissipation Probed by Superconducting Tunnel Junctions.

We have investigated the phase dynamics of a superconducting tunnel junction at ultralow temperatures in the presence of high damping, where the interaction with environmental degrees of freedom represents the leading energy scale. In this regime, theory predicts the dynamics to follow a generalization of the classical Smoluchowski description, the quantum Smoluchowski equation, thus, exhibiting overdamped quantum Brownian motion characteristics. For this purpose, we have performed current-biased measurements on the small-capacitance Josephson junction of a scanning tunneling microscope placed in a low impedance environment at milli-Kelvin temperatures. We can describe our experimental findings with high accuracy by using a quantum phase diffusion model based on the quantum Smoluchowski equation. In this way we experimentally demonstrate that overdamped quantum systems follow quasiclassical dynamics with significant quantum effects as the leading corrections.

Easy method for measurement of environmental impedance and superconducting phase fluctuations in one-dimensional arrays of Josephson junctions

We conduct microwave impedance measurements on a one-dimensional (1D) array of Josephson junctions to experimentally determine the Josephson inductance and shunt resistance of the constituent junctions. The effective Josephson energy provides an estimate of the environmental impedance, which is greatly increased due to phase fluctuations in the neighboring junctions. This enhancement is attributed to the charge solitons in the 1D system. In general, the environmental impedance is dominated by the junction’s normal resistance in the superconducting phase coherent regime, but overwhelmed by zero-bias resistance and differential resistance, respectively, in the Coulomb blockaded regime and in the phase fluctuating regime. The change in phase fluctuations owing to a dc bias agrees with the finite temperature phase diffusion model.

Mask effect in nano-selective- area-growth by MOCVD on thickness enhancement, indium incorporation, and emission of InGaN nanostructures on AlN-buffered Si(111) substrates

In this paper, we studied the effect of temperature and mask margin size on optical emission and growth rate enhancement (GRE) of InGaN grown by metal organic chemical vapor deposition (MOCVD) and nano-selective-area growth (NSAG) on AlN-buffered Si(111). For all mask geometries and temperatures, NSAG produced 90% single-crystal InGaN nanopyramids with smooth facets, perfect selectivity, and 1.2 times the indium composition enhancement (23% and 33% for 800 °C and 780 °C NSAG, respectively) as found in non-NSAG planar growth at the same conditions. The vapor phase diffusion model was found to be insufficient to predict NSAG GRE, and we propose an explanation combining mechanisms from the vapor phase diffusion with surface migration models. A two-peak emission was noted for all NSAG. The total and relative intensities of the two peaks was found to be strongly dependent upon both temperature and local indium precursor concentration during growth, the latter of which varies based on mask margin size. In NSAG grown at lower temperature and with higher local indium precursor concentration, the bluer of the two peaks was more dominant and the overall emission intensity was higher. InGaN nanopyramids were chemically uniform, ruling out phase separation as origin of the double-peak. We propose an explanation based on the sudden transition from strained to relaxed growth moderated by temperature and local indium precursor concentration.

Cellular automata modeling of nitriding in nanocrystalline metals

Severe plastic deformation has made it possible to alter the grain size of metal surface to nanoscale. With refined nanograins, the grain boundary effect on diffusion and phase transformation cannot be neglected. Consequently, the widely used conventional 1D nitriding model is not applicable. In this study, a 2D model considering grain boundary diffusion has been developed to investigate nanocrystalline nitriding. As a multi-physical process, both phase transition and diffusion are modeled. Cellular automata method was used to integrate the two models, and more importantly to deal with the moving 2D interface induced by grain boundaries. The phase transition model and diffusion model were validated with experimental data and the Maxwell–Garnett effective diffusion model, respectively. After validation, nitriding of nanocrystalline iron at low temperature (300°C) was simulated and compared with nitriding of coarse-grained (μm level) iron. In addition, the growth kinetic, composition and spatial distribution of the nitride layer in nanocrystalline nitriding, with different temperatures, surface nitrogen concentrations and different grain sizes, were studied. It has been found that these parameters could significantly affect the growth rate as well as the composition of the nitrided layers. The results also demonstrated that the presence of nanoscale grain can not only decrease nitriding temperature and nitriding duration making low temperature nitriding possible, but also increase the volume fraction of ∊ and γ′ phases in the nitride layer and therefore a better nitriding quality.

Stochastic noise amplification of partially coherent CW beam in the region of minimum GVD in lossless Kerr media with delayed response

Motivated by experimental evidences of spectral broadening of partial coherent pulses emitted by a P2O5-doped Raman fiber laser in a silica fiber, we theoretically study the propagation of a partially coherent optical beam through a noninstantaneous media by using extensions of the nonlinear Schrödinger equation (NLSE) including a phase-diffusion model for the partially coherent beam. The finite response time of the medium is incorporated by means of the Debye relaxation model. The dispersion relation is analytically calculated, and the gain spectra together with relevant second-order statistical quantities are numerically computed. Moreover, we provide a complete description of how these statistical properties vary as a function of the delayed nonlinear response of the medium; specifically in the regime of fast nonlinear response in which modulation instability is not expected to occur for genuine incoherent pulses.

Stochastic noise amplification in noninstantaneous Kerr media

Considering noninstantaneous Kerr nonlinearity, the propagation of a partially coherent optical beam is theoretically investigated by using extensions of the nonlinear Schrödinger equation (NLSE). In order to account for the partial coherence of the beam, a phase-diffusion model is used for the laser beam. To introduce the finite response time of the medium, a time-dependent nonlinear response is incorporated in the system of the NLSE using the Debye relaxation model. We analytically deduce the dispersion relation and numerically compute the gain spectra along with relevant second-order statistical quantities. A detailed study of how these statistical properties are influenced by the group velocity dispersion regime as well as by the delayed nonlinear response of the material is presented. The distinct features for slow and fast delayed nonlinear response are also emphasized.

Numerical simulation and optimization of pulverized coal injection with enriched oxygen into blast furnace

The combustion characteristics of pulverized coal in the blast furnace raceway is an important factor which determines the performance of injection of pulverized coal with enriched oxygen as well as the energy consumption of blast furnace. Research was carried out to investigate processes including the gas and solid flow, particle movement, drying and pyrolysis of pulverized coal and combustion of carbon residue and coke in a blast furnace with standard k–ɛ model, discrete phase model, evaporation and diffusion model, dual parallel competition model and diffusion-kinetic combustion model respectively in Fluent 6.3. The accuracy and reliability of the numerical model was verified with a semi-industrial experiment. Moreover, 7 parameters were optimized by the orthogonal experiments, taking the burnout rate as the evaluation indicator. Results show that the burnout rate under the optimal condition can be increased by 110.8% comparing to that under the standard condition. The importance of parameters influencing the evaluation indicator is found in the order which is the type of the pulverized coal, the pulverized coal injection rate, the oxygen enrichment rate, the blast temperature, the spraying gun type, the blast volume and the angle.

Frequency response of an atomic resonance driven by weak free-electron-laser fluctuating pulses

Motivated by recent experiments pertaining to the interaction of weak SASE-free-electron-laser (FEL) pulses with atoms and molecules, we investigate the conditions under which such interactions can be described in the framework of a simple phase-diffusion model with decorrelated atom–field dynamics. The nature of the fluctuations that are inevitably present in SASE-FEL pulses is shown to play a pivotal role in the success of the decorrelation. Our analysis is performed in connection with specific recent experimental results from FLASH in the soft x-ray regime.

Growth rate and composition of InGaN during InGaN/GaN quantum wells selective area metal-organic vapor phase epitaxy considering surface diffusion

Film growth rate and composition variation were numerically analyzed during the selective area growth of InGaN on both GaN triangular stripe and hexagonal pyramid microfacets. To obtain the In composition of the film, concentration of In and Ga atoms due to the surface diffusion was added to the concentration determined from the Laplace equation that governs the gas phase diffusion. When the surface diffusion is considered, the In composition and resulting wavelength increased compared to the results obtained from the vapor phase diffusion model. The In content also increased according to the increasing mask width.

Least Squares Galvanostatic Intermittent Titration Technique (LS-GITT) for Accurate Solid Phase Diffusivity Measurement

Solid phase diffusivity Ds is a key parameter in Lithium-Ion cell models because solid phase diffusion typically dominates the voltage transients. The Galvanostatic Intermittent Titration Technique (GITT) is easy to implement and universally accepted as the standard for diffusivity measurement, but the accuracy of GITT diffusivity measurement is unknown. This paper develops a Least Squares GITT (LS-GITT) that uses all of the voltage data from a GITT test to optimally tune the diffusivity in a reduced order solid phase diffusion model. The accuracies of the GITT and LS-GITT diffusivity measurements are evaluated using the RMS error between the model predicted and experimentally measured voltages. Based on experimental results from a NCM half cell, LS-GITT is more accurate than GITT, often by an order of magnitude. The GITT test overestimates Ds because the underlying model neglects the effects of bulk capacity on the voltage transients. LS-GITT gives results accurate to 1 mV RMS from 15%–100% SOC where GITT provides the same level of accuracy over less than half that SOC range. Neither technique provides accurate Ds measurements below 10% SOC.

A semiclassical optics derivation of Einstein’s rate equations

We provide a semiclassical optics derivation of Einstein’s rate equations (ERE) for a two-level system illuminated by a broadband light field, setting a limit on their validity that depends on the spectral properties of the light field. Starting from the optical Bloch equations for individual atoms, the ensemble averaged atomic inversion is shown to follow ERE under two concurrent hypotheses: (i) the decorrelation of the inversion at a given time from the field at later times and (ii) a Markov approximation owing to the short correlation time of the light field. When the latter hypothesis is relaxed, we find effective Bloch equations for the ensemble average in which the atomic polarization decay rate is increased by an amount equal to the width of the light spectrum, which allows its adiabatic elimination for a large enough spectral width. The use of a phase-diffusion model of light allows us to check our results and hypotheses using numerical simulations of the corresponding stochastic differential equations. We take into account both light bandwidth and atomic linewidth, which allows us to discuss the differences existing between rate equations in the limits of large light bandwidth or large atomic linewidth. Only in the former case does one obtain ERE with the correct expression for Einstein’s B coefficient.

Single-qubit lasing in the strong-coupling regime

Motivated by recent ``circuit QED'' experiments we study the lasing transition and spectral properties of single-qubit lasers. In the strong coupling, low-temperature regime quantum fluctuations dominate over thermal noise and strongly influence the linewidth of the laser. When the qubit and the resonator are detuned, amplitude and phase fluctuations of the radiation field are coupled, and the phase diffusion model, commonly used to describe conventional lasers, fails. We predict pronounced effects near the lasing transition, with an enhanced linewidth and non-exponential decay of the correlation functions. We cover a wide range of parameters by using two complementary approaches, one based on the Liouville equation in a Fock state basis, covering arbitrarily strong coupling but limited to low photon numbers, the other based on the coherent-state representation, covering large photon numbers but restricted to weak or intermediate coupling.

Modelling of heavy metal adsorption into activated carbon from apricot stones in fluidized bed

The purpose of the present study is to investigate the behaviour of activated carbon from apricot stones (ACAS) in a closed circuit fluidized bed (CCFB) for removal of Pb, Cu, Cd and Zn ions from aqueous solution. The expansion characteristics of the bed are studied. A homogeneous solid phase diffusion model was used to describe the mass transfer inside the adsorbent particles. A piston-dispersion model was applied for the liquid phase in the bed and compared to the calculations, assuming perfect mixing conditions in the whole CCFB adsorber. The close correspondence between the experimentally determined adsorption in batch and fluidized bed operation modes support the observation that the CCFB can be described by a stirred batch adsorption model. The concentration profile at the bed exit is satisfactorily predicted by the model, thus confirming the equilibrium and kinetic parameters, determined from the laboratory batch adsorption runs.

A growth model of cubic GaN microstripes grown by MOVPE: Vapour phase diffusion model including surface migration effects

AbstractGrowth features of c‐GaN stripes grown by selective area metalorganic vapour phase epitaxy (SA‐MOVPE) on GaAs (001) substrates with stripe patterns aligned along [110] direction were analysed by vapour phase diffusion (VPD) model including surface migration effects from (111) facets. An addition of surface migration effects was found to improve the correlation between the simulation and experiment for the fill factors smaller than 0.5. The effects of the surface migration length (L) and the weight of surface migration contribution on the surface profile and the growth rate of the c‐GaN stripes were also analysed. An increase of L was found to strongly enhance the growth rate at the centre of c‐GaN stripes, while increasing the weight of contribution leads to the growth rate enhancement at the edges of the stripes. Our simulation demonstrated that the most probable values of L and the weight of contribution were 0.8 µm and 0.13, respectively. According to our simulation, mechanism of cubic‐to‐hexagonal structural phase transition is suggested as an incentive of the surface concentration profiles.