Dependent Rate Equations Research Articles

Prompt Analysis and Design for Passively Mode-Locked Solid-State Lasers with Semiconductor Saturable Absorbers

The critical pump power for achieving passively continuous-wave mode-locking in a solid-state laser is analytically derived from the spatially dependent rate equations and the criterion for the intracavity pulse energy. A prompt way is proposed to straightforwardly design the cavity for passively mode-locked solid-state lasers. Complete experiments are performed to demonstrate the proposed cavity design and, simultaneously, to verify the theoretical model for the critical pump powers. It is interestingly observed that even though a larger modulation depth causes a higher critical pump power, it can generate a shorter pulse width in return.

Quadratic Zeeman spectral diffusion of thulium ion population in an yttrium gallium garnet crystal

The creation of well understood structures using spectral hole burning is an important task in the use of technologies based on rare earth ion doped crystals. We apply a series of different techniques to model and improve the frequency dependent population change in the atomic level structure of Thulium Yttrium Gallium Garnet (Tm:YGG). In particular we demonstrate that at zero applied magnetic field, numerical solutions to frequency dependent three-level rate equations show good agreement with spectral hole burning results. This allows predicting spectral structures given a specific hole burning sequence, the underpinning spectroscopic material properties, and the relevant laser parameters. This enables us to largely eliminate power dependent hole broadening through the use of adiabatic hole-burning pulses. Though this system of rate equations shows good agreement at zero field, the addition of a magnetic field results in unexpected spectral diffusion proportional to the induced Tm ion magnetic dipole moment and average magnetic field strength, which, through the quadratic Zeeman effect, dominates the optical spectrum over long time scales. Our results allow optimization of the preparation process for spectral structures in a large variety of rare earth ion doped materials for quantum memories and other applications.

The study on the gain of signal pulse in gain fibers and its application in simulation of mode-locked fiber lasers

The effect of the signal pulse on the population densities of upper-level particles of doped ions in gain fibers is studied. The population densities of upper-level particles decrease gradually after encountering the signal pulse in both the two-level system and the three-level system, and the decreasing degree is related to the power of the pulse. Since the power of the signal will change greatly in a short time in a pulsed laser, the time dependent rate equations are more suitable for describing the interaction between the pulse signal and doped particles than the steady state rate equations. Based on this, a simulation method of passively mode-locked fiber lasers, in which the gain of the signal is calculated by time dependent rate equations, is proposed. An erbium doped mode-locked fiber laser at 1564nm is simulated as an example, and the pulse width and spectral width in the simulation results are close to the experimental results. By adding noise to the initial pulse, the stability of the model is verified, and the mode competition between different modes in the process of mode locking can be studied. This method can not only provide a reference for building mode-locked fiber lasers, but also provide a method for studying the mechanism of mode locking.

Nd:YAG end-pumped zigzag multi-pass slab amplifier optimization: numerical and experimental study regarding the saturation effects.

A numerical modeling of Nd:YAG end-pumped zigzag multi-pass slab amplifier is developed. Spatial dependent rate equations have been solved taking into consideration the pump and laser beam saturation effects with regard to overlap correction of the signal path through gain medium. Based on our results, efficient amplifier structure with optimized output power could be designed with respect to the change in the number of signal beam-pass, doping concentration and slab length. In order to verify our modeling an experimental setup is designed.

Characterization of creep constraint effect for brazed joint specimens at crack tip by new constraint parameter As

In this study, a new creep constraint parameter As of brazed joint was proposed based on existing constraint parameters R* and Ac. The proposed parameter As is superior than R* and Ac because the constraint parameter As is not affected by the selection of creep steady time and distance from crack tip. And the load independence of constraint parameter As for different constraint levels are all superior than that of parameter R* and Ac. Based on the relationships between creep crack growth (CCG) rate and constraint parameter predicted by single-material method, the superiority to characterize constraint effect of constraint parameter As is clarified. The CCG rate equation dependent constraint of brazed joints is established based on the defined parameter. The CCG data predicted by established constraint dependent CCG rate equation have a good accordance with experiment. The established CCG rate equation dependent constraint can predict the CCG rate at different constraint levels very well.

A more Accurate Constraint Parameter to Characterize the Creep Constraint Effect at Crack Tip of Cr-Mo-V Steel

A suitable constraint parameter is a key to quantify the creep crack tip constraint levels. In this study, a new more accurate creep constraint parameter As of brazed joint was proposed based on the existing constraint parameters R* and Ac. The CCG rate equation of Cr-Mo-V steel related to the constraint parameter As is obtained. The results show that the constraint parameter As is basically unchanged with the increase of creep time. The crack growth data predicted by the constraint dependent CCG rate equation are in good agreement with the experimental data. The established constraint dependent CCG rate equation can predict the CCG rate at other constraint levels very well.

Strong light illumination on gain-switched semiconductor lasers helps the eavesdropper in practical quantum key distribution systems

The temperature of the semiconductor diode increases under strong light illumination whether thermoelectric cooler is installed or not, which changes the output wavelength of the laser (Lee et al., 2017). However, other characteristics also vary as temperature increases. These variations may help the eavesdropper in practical quantum key distribution systems. We study the effects of temperature increase on gain-switched semiconductor lasers by simulating temperature dependent rate equations. The results show that temperature increase may cause large intensity fluctuation, decrease the output intensity and lead the signal state and decoy state distinguishable. We also propose a modified photon number splitting attack by exploiting the effects of temperature increase. Countermeasures are also proposed.

Temporal evolution of electron beam generated Argon plasma in pasotron device

The plasma- assisted slow wave oscillator (PASOTRON) is a high power microwave source in which the electron beam in the interaction region is confined by the background plasma. The plasma is generated by impact ionization of background gas with the electron beam. A model has been developed for temporal evolution of Argon plasma in pasotron device. In this model, we consider electron beam of energy E interacting with Argon gas. The resulting ionization creates quasi neutral argon plasma composed of argon Ar atoms, singly ionized ions Ar+1and electrons having energy from 0 to E. Electron impact excitation, ionization, radiative decay, radiative recombination and three body recombination processes are considered in this model. Population of ground and excited states of argon atom, ground state of argon ion as well as the population of electron energy groups is calculated by solving time dependent rate equations. Temporal evolution of electron beam generated plasma is given.

A Microscopic Capacitor Model of Voltage Coupling in Membrane Proteins: Gating Charge Fluctuations in Ci-VSD

The voltage sensitivity of membrane proteins is reflected in the response of the voltage sensing domains (VSDs) to the changes in membrane potential. This response is implicated in the displacement of positively charged residues, associated with the conformational changes of VSDs. The displaced charges generate nonlinear (i.e., voltage-dependent) capacitance current called the gating current (and its corresponding gating charge), which is a key experimental quantity that characterizes voltage activation in VSMP. However, the relevant theoretical/computational approaches, aimed to correlate the structural information on VSMP to electrophysiological measurements, have been rather limited, posing a broad challenge in computer simulations of VSMP. Concomitant with the development of our coarse-graining (CG) model of voltage coupling, we apply our theoretical framework for the treatments of voltage effects in membrane proteins to modeling the VSMP activation, taking the VSDs (Ci-VSD) derived from the Ciona intestinalis voltage sensitive phosphatase (Ci-VSP) as a model system. Our CG model reproduces the observed gating charge of Ci-VSD activation in several different perspectives. In particular, a new closed-form expression of the gating charge is evaluated in both nonequilibrium and equilibrium ways, while considering the fluctuation-dissipation relation that connects a nonequilibrium measurement of the gating charge to an equilibrium measurement of charge fluctuations (i.e., the voltage-independent linear component of membrane capacitance). In turn, the expression uncovers a novel link that connects an equilibrium measurement of the voltage-independent linear capacitance to a nonequilibrium measurement of the voltage-dependent nonlinear capacitance (whose integral over voltage is equal to the gating charge). In addition, our CG model yields capacitor-like voltage dependent free energy parabolas, resulting in the free energy difference and the free energy barrier for the Ci-VSD activation at "zero" (depolarization) membrane potential. Significantly, the resultant voltage dependent energetics enables a direct evaluation of capacitance-voltage relationship (C-V curve) as well as charge-voltage relationship (Q-V curve) that is in a good agreement with the observed measurement of Ci-VSD voltage activation. Importantly, an extension of our kinetic/thermodynamic model of voltage dependent activation in VSMP allows for novel derivations of voltage-dependent rate constants, whose parameters are expressed by the intrinsic properties of VSMP. These novel closed-form expressions offer a physicochemical foundation for the semiempirical Eyring-type voltage dependent rate equations that have been the cornerstone for the phenomenological (kinetic) descriptions of gating and membrane currents in the mechanistic study of ion channels and transporters. Our extended theoretical framework developed in the present study has potential implications on the roles played by gating charge fluctuations for the spike generations in nerve cells within the framework of the Hodgkin-Huxley-type model.

Study of spectral linewidth in Ne-like Se x-ray laser.

Based on the modeling of the geometrically dependent gain coefficient (GDGC) and rate equations, this theoretical study explains the spectral linewidth behavior in an Se x-ray laser operating at 206.4Å. The study used the reported experimental measurements for an Se target of 6.3cm in length for the analysis. To obtain a finite value for the amplified spontaneous emission (ASE) intrinsic linewidth that initiates at the threshold length, we subtracted the ASE intensity background from the calculated ASE intensity to derive the corresponding FWHM. For homogeneously and Doppler broadened linewidths of 14mÅ and 36mÅ, we calculated the ASE Voigt profile linewidth to be 44mÅ, initiated at the threshold length of 0.13cm. The interaction is rather insensitive to the collision broadening; for the homogeneously broadened linewidth up to 21 mÅ, we could still explain the linewidth measurements. In this case, we calculated the related Voigt profile linewidth to be 48.5mÅ. The current GDGC modeling approach greatly simplified the ASE analyses of these lasers.

Measuring the Elevated Temperature Dependence of Up-Conversion in Nd:YAG

We present the measurement of the energy transfer upconversion coefficient temperature-dependence from the main upper laser level (4F3/2) of 1at.% doped Nd:YAG. This is achieved by a very simple method employing the z-scan technique, through monitoring the transmitted power of a probe laser tuned to the main absorption peak at 808 nm. In addition, to fully develop a simple model to support the measurements, we have accurately measured the temperature dependent absorption coefficient for this absorption band, covering the range from 300-450K. The spatially dependent two-level rate equation model is described, which simulates the relationship between the incident pump irradiance and power transmitted by the crystal, in function of its temperature. By comparing the experimental results with the model, we obtain a value for the energy transfer upconversion coefficient of 5.1±0.4 ×10-17 cm3/s, at room temperature, decreasing to 2.0 ×10-17 cm3/s at 450 K.

Theory of suppressing avalanche process of carrier in short pulse laser irradiated dielectrics

A theory for controlling avalanche process of carrier during short pulse laser irradiation is proposed. We show that avalanche process of conduction band electrons (CBEs) is determined by the occupation number of phonons in dielectrics. The theory provides a way to suppress avalanche process and a direct judgment for the contribution of avalanche process and photon ionization process to the generation of CBEs. The obtained temperature dependent rate equation shows that the laser induced damage threshold of dielectrics, e.g., fused silica, increase nonlinearly with the decreases of temperature. Present theory predicts a new approach to improve the laser induced damage threshold of dielectrics.

Development of a finite strain two-network model for shape memory polymers using QR decomposition

The aim of this paper is to develop a thermodynamically consistent finite deformation continuum model to simulate the thermomechanical response of shape memory polymers (SMPs). The SMP is modeled as a thermoviscoelastic material whose response in a thermomechanical cycle is modeled as a combination of a rubbery (viscoelastic) and a glassy (elastic) network in series. The activation criterion for the breakage of temporary network junctions is governed by a temperature dependent rate equation (akin to a thermal Bauschinger effect). We further show how the decomposition of the deformation gradient into an upper triangular matrix and a rotation (the QR) decomposition can be used instead of the more traditional polar (RU) decomposition in the development of models for such materials with persistent configurational changes. Such a decomposition has both physical meaning as well as computational advantages due to their convenient structure. Using these assumptions, we propose a specific form for the Helmholtz potential and the rate of dissipation. The model is simple (deliberately ignoring some aspects such as anisotropy that affect the quantitative but not the qualitative response features) and is able to capture the major phenomena of interest in SMPs. The efficacy of the resulting model, which is in a state evolution form, is demonstrated by comparing with published experimental data for simple shear. We study the response of the SMP model for monotonic shear deformation, different deformation rates as well as cyclic shear deformation at different temperatures. Comparisons with experiments show good agreement. Finally, we implement the thermomechanical cycle under shear deformations and study the behavior of the model.

Time-dependent radiative transfer calculations for supernovae

In previous papers we discussed results from fully time-dependent radiative transfer models for core-collapse supernova (SN) ejecta, including the Type II-peculiar SN 1987A, the more "generic" SN II-Plateau, and more recently Type IIb/Ib/Ic SNe. Here we describe the modifications to our radiative modeling code, CMFGEN, which allowed those studies to be undertaken. The changes allow for time-dependent radiative transfer of SN ejecta in homologous expansion. In the modeling we treat the entire SN ejecta, from the innermost layer that does not fall back on the compact remnant out to the progenitor surface layers. From our non-LTE time-dependent line-blanketed synthetic spectra, we compute the bolometric and multi-band light curves: light curves and spectra are thus calculated simultaneously using the same physical processes and numerics. These upgrades, in conjunction with our previous modifications which allow the solution of the time dependent rate equations, will improve the modeling of SN spectra and light curves, and hence facilitate new insights into SN ejecta properties, the SN progenitors and the explosion mechanism(s). CMFGEN can now be applied to the modeling of all SN types

Strain dependent rate equation to predict elevated temperature flow behavior of modified 9Cr-1Mo (P91) steel

True stress–strain data from isothermal hot compression tests on modified 9Cr-1Mo steel over a wide range of temperature (1173–1373K) and strain rate (0.001–100s−1) were employed for constitutive analysis following the sine-hyperbolic Arrhenius equation. The correction for shear modulus and diffusivity in the constitutive equation showed a clear deviation from power-law at higher stresses and this was accounted for by considering the contribution from pipe diffusion. The stress dependence was found to obey rate equation of the form ε˙/DL =constant [sinh(αLσ/G)]nh, where DL is lattice diffusivity, G is shear modulus and, αL and nh are constants. After incorporating the influence of strain on material constants, the developed constitutive equation could predict flow stress in the strain rate range 0.1–100s−1 at all temperatures with very good correlation and generalization. Though deviation in prediction was observed at lower strain rates 0.001 and 0.01s−1, a higher correlation coefficient (R=0.99) and a lower average absolute relative error (7.3%) for the entire investigated hot working domain revealed that the prediction of flow stress was satisfactory.

Orange and IR to violet up-conversion processes in Nd:ZBLAN glasses

In this work we investigate, compare and discuss UV and violet emission behaviour under pulsed, multi-photon orange and infra-red excitation in Nd 3+ doped ZBLAN samples of different concentrations ranging from 0.3 to 5 mol.%. Supported by the obtained spectroscopic results, orange and IR excitation schemes were proposed and verified by time dependent rate equation model, which has been employed to confirm the nature of observed processes. Proposed model returns fitting results which qualitatively reflect the experimentally obtained fluorescence decays.

Ultraviolet emission excitation in RE 3+ activated fluoride fibers

Short-wavelength (∼280–410 nm) fluorescence in Er 3+, Tm 3+, Nd 3+ and Ho 3+ doped ZBLAN glasses was studied experimentally and attributed to transitions from the 2P 3/2, 1I 6 and 1D 2, 4D 3/2, 3D 3 states, respectively. Properties of these high-lying metastable levels, such as state energies, transition wavelengths, lifetimes, emission branching ratios and cross-sections, which are important for laser action analysis, were determined. In particular, up-conversion UV emission excitation schemes for Nd 3+ and Ho 3+ doped ZBLAN were studied experimentally and modeled by time dependent rate equations. Violet and ultraviolet laser operation in Nd 3+ and Ho 3+ doped ZBLAN fibers under up-conversion pumping was studied theoretically basing on measured spectroscopic parameters.

A multi-scale method for the calculation of charge transfer rates through the Π-stack of DNA: application to DNA dynamics

We describe an ultra-fast, multi-scale method for calculating charge transfer rates through the pi-stack of DNA using a simple charge hopping model in conjunction with the Marcus equation. The calculation of the parameters required as input to the Marcus equation, such as the electronic coupling and the driving force, are calculated with a combination of quantum mechanical methods and conformations sampled from classical molecular dynamics (MD) simulations. The resulting set of time dependent rate equations are then solved stochastically using Monte Carlo (MC) methods. We have applied this model to investigate the importance of thermal fluctuations in DNA conformation over picosecond and nanosecond timescales, and have identified the timescales of most relevance to hole transfer through DNA.

Influences of the Current Transverse Profile on the Transverse Mode Competition of VCSELs Diodes

A spatially independent model of vertical-cavity surface-emitting lasers (VCSELs) is derived by integrating the spatially dependent rate equations over the cross section of the cavity of a VCSEL. The angular and radial non-uniformities of the injection current are taken into account. The well-known LP modes of a weakly-guiding cylindrical waveguide are employed to describe the transverse modal structure in the VCSEL cavity. This model is solved in a self-consistent way by using the 4th order Runge-Kutta method. The dependence of transverse mode competition on the current intensity, the angular and radial non-uniformities of the injection current, and the geometrical parameters of the electrical contact are thoroughly investigated and analyzed. The results are useful to the optimum design of the optical transverse modal structure of VCSELs.

Effect of tritium reduction in determining energy gain by using R-matrix method direct laser fusion in D-T reaction

The laser fusion criterion is known as the ρ R-Criterion, also called high-gain condition. This parameter is temperature dependent and can be calculated by R-matrix method. This method is applied for determining improved fusion cross-section for the reactions T(d,n) 4He, 3He(d,p) 4He, D(d,p)T, D(d,n) 3He. In this paper the time dependent reaction rate equations for fusion reaction T(d,n) 4He are solved and by using the obtained results we computed the fusion power density, energy gain versus temperature and ρ R-parameter. The obtained results show that a suitable combination may be a deuterium fraction f D=0.65 and f r=0.35 which would lead 30% reduction in the tritium content of the fuel mixture, and this choice would not change the energy gain value very much. Finally, the obtained energy gain for D-T reaction by using R-matrix is in good agreement with other theories.