Conventional Rate Equations Research Articles

Carrier Dynamics in Strain Induced Quantum Dots Modeled by Rate Equations and Gaussian Excitation Beam Distribution

Strain induced quantum dots are investigated by time resolved and continuous wave photoluminescence spectroscopy. Carrier dynamics is modeled with rate equations taking into account also the Gaussian intensity distribution of the excitation beam. It is shown that the Gaussian distribution has a clear effect on the saturation behaviour of the quantum dot peak intensities. The calculated intensities agree better with the measured luminescence intensities than results from the conventional rate equation approach.

Modeling of three-dimensional photonic crystal lasers in a frequency domain: A scattering matrix solution

We derive a light-intensity-dependent dielectric constant for a gain medium based on the conventional rate equation model. A scattering-matrix method in conjunction with an efficient iteration procedure is proposed to simulate photonic crystal lasers (PCLs). The light output vs pumping (L-I) curve, lasing mode profile, and chirping effect of the lasing wavelength {lambda}{sub L} can be calculated. We check our method in a one dimensional distributed Bragg reflector laser and simulate a complex three dimensional woodpile PCL to test the capabilities of our model. We found that PCLs with a more uniform field distribution in the gain media will have higher L-I slope efficiencies as well as more stable lasing wavelengths {lambda}{sub L}.

Effect of temperature dependence of electrical resistivity on the cooling performance of a single thermoelectric element

The coefficients of performance (COP) φ 0 and φ for a single thermoelectric (TE) element welded with two metal plates were calculated as functions of temperature difference (Δ T) and thermoelectric figure of merit ( ZT) from the conventional thermal rate equations and the new thermal rate ones proposed here, respectively. We made an attempt to take the differences in the Seebeck coefficient α, electrical resistivity ρ and thermal conductivity κ of TE materials at the hot and cold sides of a TE element into the thermal rate equations on the assumption that their TE properties change linearly with temperature. However, the difference in κ was neglected even in the new thermal rate equations because its temperature dependence was too small when φ was applied to the high-performance Bi–Te alloys. The normalized temperature dependences at 300 K of α and ρ were denoted by A and B, respectively. The term of A in the thermal rate equations was canceled out by the Thomson coefficient, but that of B remained. When B > 0 K −1, φ/ φ 0 is enhanced more significantly with an increase of B at larger Δ T and lower ZT, and it reached about 1.20 at Δ T = 80 K for Bi–Te alloys with B ≈ 5 × 10 −3 K −1. It was thus found that the COP of a cooling module is also affected strongly by B as well as ZT.

CaF2 doped with Tm3+: A cluster model

Experimental evidence of ion clustering is studied in Tm3+:CaF2 using the spectroscopic signature given by the quenching of the 1.45 μm fluorescence. A model, based on rate equations, and taking into account the probabilities of the different states for clusters, is proposed. The agreement with experimental data appears better with a pair model than with a conventional rate equation model analysis.

Long-time kinetics of the excited-state association–dissociation reaction with differentlifetimes

We consider the long-time behaviour of the reversible diffusion-influenced reaction when A and C are immobile electronically excited states andB particles arein excess. A andC have differentlifetimes. When C decays faster than A, the two leading terms of the asymptotic behaviour are obtained analytically by mappingthis problem onto an effective irreversible reaction. The first term is exponential, and itcoincides with that obtained from conventional rate equations with steady-statediffusion-influenced rate constants. The second term in the exponent is , as in the Smoluchowski irreversible kinetics.

加圧雰囲気下での溶鋼への窒素溶解挙動

High nitrogen stainless steels have got a lot of attention recently because of its high material performance. In order to produce steels with nitrogen contents above atmospheric pressure solubility, melting process under pressurized process have been developed. Though nitrogen content in the steels shall be important for the operation, behavior of nitrogen dissolution into molten steel under pressurized atmosphere have not been cleared. Therefore, investigation has done by the use of pressurized induction furnace. The results are follows: (1) Nitrogen solubility under pressurized atmosphere showed good correlation between observed and calculated value except for high Cr-high N alloy. (2) The rate of nitrogen dissolution under pressurized atmosphere is expressed by conventional rate equation, and the rate is not associated with atmospheric pressure.

Theory of Intersubband Raman Laser in Modulation-doped Asymmetric Coupled Double Quantum Wells

A microscopic theory is developed for the laser gain due to stimulated intersubband electronic Raman scattering pumped by CO 2 laser in modulation-doped GaAs/AlGaAs asymmetric coupled double quantum wells (ACDQWs). Based on the charge-density-excitation (CDE) mechanism, the formula for electronic Raman scattering cross-section is given, taking into account the coupling between intersubband plasmon and optical phonons including GaAs confined LO phonons and interface phonons. Stimulated Raman gain factor is then derived from the cross-section. The optimization of Raman gain, the gain saturation and threshold condition are also discussed. Numerical analysis for temporal variation of stimulated Stokes photon density, subband populations and output Raman laser power is carried out by using the self-consistent conventional rate equations. The theory can predict the presence or lack of coupled modes in lasing in agreement with the recent experimental results.

Gain of intersubband Raman lasing in modulation-doped asymmetric coupled double quantum wells

A microscopic theory is developed for the laser gain due to stimulated intersubband electronic Raman effect pumped by CO 2 laser in modulation-doped asymmetric coupled double quantum wells. We focus on the charge density excitation mechanism for electronic Raman scattering, taking into account the coupling between intersubband plasmons and LO phonons. Numerical simulations for the temporal variation of stimulated Stokes photon density, subband populations and output Raman laser power are carried out by using the self-consistent conventional rate equations with stimulated Raman gain coefficient.

Temperature investigation of infrared-to-visible frequency upconversion in erbium-doped tellurite glasses excited at 1540 nm

Temperature investigation of infrared-to-visible frequency upconversion in erbium-doped tellurite glasses excited by CW laser radiation at 1540nm and under cryogenic temperatures is reported. Intense upconversion emission signals around 530, 550 and 660nm corresponding to the 2H11/2, 4S3/2, and 4F9/2 transitions to the 4I15/2 ground state were generated and studied as a function of the laser intensity and temperature. The upconversion excitation mechanism of the Er3+ ions emitting energy levels was accomplished via stepwise multiphoton absorption. The green upconversion luminescence exhibited a fivefold intensity enhancement when the temperature of the sample was varied in the range between 5 and 300K. A maximum green upconversion intensity was attained around 120K and a steady decreasing behavior for higher temperatures up to 300K was observed. A model based upon conventional rate equations was used to model the observed temperature evolution of the upconversion luminescence.

Effects of the spatial nonuniformity of optical transverse modes on the modulation response of vertical-cavity surface-emitting lasers

We present detailed numerical simulations to clarify the important role that the nonuniformity of the transverse optical mode plays for the high-speed response of oxide-confined vertical-cavity surface-emitting lasers (VCSELs). The comprehensive laser diode simulator, Minilase, as well as a one-dimensional rate equation model are used as simulation tools. It is demonstrated that, due to the nonuniform optical intensity, carriers at different locations in the quantum well have different stimulated recombination rates, and therefore exhibit different dynamic responses to small signal modulation. This nonuniformity causes an overdamping of the relaxation oscillation, as well as a low-frequency roll-off of the modulation response. Due to this nonlinear effect, the intrinsic maximum bandwidth of VCSELs with oxide confined apertures is shown to be much smaller than predicted by the conventional rate equation model which assumes uniform optical intensity. We further demonstrate that this damping effect can be greatly reduced by restricting the current injection to be well within the transverse optical field. This is achievable by using tapered oxides to make the electrical aperture smaller than the optical aperture, which thereby improves the modulation bandwidth significantly.

Thermal effect on upconversion fluorescence emission in Er-doped chalcogenide glasses under anti-Stokes, Stokes and resonant excitation

Abstract We investigate thermal effects upon infrared to visible frequency upconversion fluorescence emission in Er3+-doped chalcogenide glasses, pumped under anti-Stokes, Stokes and resonant excitation. The upconversion emission signals is found to decrease with increasing temperature in the range of 23–200 °C. The observed thermal effect is modeled by conventional rate equations considering a temperature-dependent effective absorption cross-section for the 4 I 15/2 → 4 I 9/2 and 4 I 11/2 → 4 F 3/2 , 4F5/2 erbium transitions. The temperature dependence is mainly attributed the nonradiative decays. This model accurately reproduces the experimental results.

Simulating the modulation response of VCSELs: the effects of diffusion capacitance and spatial hole-burning

The comprehensive semiconductor laser simulator, Minilase, has been extended to simulate the dynamic response of vertical cavity surface emitting lasers (VCSELs). Unlike conventional rate equation approaches, Minilase is capable of correctly modelling nonlinear gain effects in the modulation response without the introduction of an empirical gain suppression factor. Various oxide-confined single-mode VCSEL structures are simulated with Minilase to examine the effects of real-space carrier transport on the modulation response in both vertical and lateral directions. It is demonstrated that a roll-off in the dynamic response is closely associated with the diffusion capacitance caused by vertical carrier leakage. By either grading the separate confinement regions or reducing the thickness of the SCH cavity, the vertical carrier leakage is shown to be greatly suppressed, and the modulation response is significantly improved. Simulations also reveal that the nonuniform HE11-like transverse optical intensity in the quantum well results in an overdamping of the relaxation oscillation, and this effect is greatly reduced by making the electrical aperture smaller than the optical aperture. Finally, a comparison with experimental results is presented and discussed.

Rate equations of vertical-cavity semiconductor optical amplifiers

We rigorously establish the rate equations for vertical-cavity semiconductor optical amplifiers, starting from a general energy rate equation. Our results show that the conventional rate equation used so far in the literature is incorrect because of an inappropriate calculation of the mirror losses. Our calculations include the effect of amplified spontaneous emission and can be used to describe the properties of resonant-cavity-enhanced photodetectors.

Drying of solutions and suspensions in the modified spouted bed with draft tube

A modified spouted bed dryer with inert particles was used for drying of solutions and suspensions. The effects of the operating conditions on dryer throughput and product quality were investigated. Experiments were performed in a cylindrical column 215 mm in diameter and 1150 mm in height with a draft tube 70 mm in diameter and 900 mm length. The bed was made of polyethylene particles 3.3 mm in diameter and of density of 921 kg/m3. The pesticide Cineb, inorganic compound calcium carbonate, organic compound calcium stearate, and pure water were used as feeding materials. A drying model using the continuity and momentum equations for turbulent accelerating two-phase flow and conventional rate equations is proposed and discussed. The work is relevant for estimating dryer performance.

Problems in recent analysis of injected carrier dynamics in semiconductor quantum dots

This brief letter discusses conceptual problems that appeared in recent analysis of injected carrier dynamics in semiconductor quantum dots. It is pointed out that the frequently adopted approximation of neglecting the upward relaxation transitions severely restricts the validity of rate equations analysis. The proposed alternative approach with master equations for the transitions between microstates has, in principle, validity equivalent with conventional rate equations, but the presented form of equations neglects the upward transitions and has inaccurate expressions for the downward flow contributions.

Modelling of hardening due to grain growth for a superplastic alloy

Combined analytical and numerical optimisation procedures have been developed to determine the material constants in superplastic constitutive equations. The conventional grain growth rate equation has been modified to enable accurate modelling of the isothermal and plastic-strain-induced grain growths for different microstructures of a titanium alloy. A set of unified viscoplastic constitutive equations for Ti–6Al–4V at 927°C, which incorporates isotropic hardening and grain growth, has been fully determined from experimental data for different initial grain sizes and strain rates. Close agreement between the predicted and experimental stress–strain relationships has been achieved. In addition, the contributions of hardening constituents, such as strain-rate hardening, isotropic hardening and the hardening due to grain growth have been modelled.

Analysis of a diode-pumped Nd:YVO 4 laser passively Q switched with GaAs

A diode-pumped Nd:YVO 4 laser passively Q switched with GaAs is studied theoretically and experimentally. We have demonstrated the influence of single-photon absorption, two-photon absorption and free-carrier absorption in GaAs on the Q-switched pulse characteristics. The pulse profile, pulse energy and pulse width of the Q switching with GaAs are simulated by using the conventional rate equations of the four-level laser system. The experimental results show reasonable agreement with the theoretical results on the whole.

Approximate accelerated stochastic simulation of chemically reacting systems

The stochastic simulation algorithm (SSA) is an essentially exact procedure for numerically simulating the time evolution of a well-stirred chemically reacting system. Despite recent major improvements in the efficiency of the SSA, its drawback remains the great amount of computer time that is often required to simulate a desired amount of system time. Presented here is the “τ-leap” method, an approximate procedure that in some circumstances can produce significant gains in simulation speed with acceptable losses in accuracy. Some primitive strategies for control parameter selection and error mitigation for the τ-leap method are described, and simulation results for two simple model systems are exhibited. With further refinement, the τ-leap method should provide a viable way of segueing from the exact SSA to the approximate chemical Langevin equation, and thence to the conventional deterministic reaction rate equation, as the system size becomes larger.

Influence of the injection current dependence of gain suppression on the nonlinear dynamics of semiconductor lasers

A detailed numerical analysis of the nonlinear dynamics of a directly modulated 1.55 μm InGaAsP distributed-feedback laser diode (LD) is carried out. Results show that when simulating the nonlinear dynamics of LDs, it is important to account for the gain suppression being dependent on the injection current. Only when this dependency of gain suppression is included in the conventional single-mode rate equations, can excellent agreement between simulated and measured results be achieved.

IR-visible upconversion and thermal effects in Pr3+/Yb3+-codoped Ga2O3:La2S3 chalcogenideglasses

IR-visible upconversion fluorescence spectroscopy and thermaleffects in Pr3+/Yb3+-codoped Ga2O3:La2S3chalcogenide glasses excited at 1.064 µm is reported. Intense visibleupconversion emission in the wavelength region of 480-680 nm peaked around500, 550, 620 and 660 nm is observed. Upconversion excitation of thePr3+ excited-state visible emitting levels is achieved by acombination of phonon-assisted absorption, energy-transfer and phonon-assistedexcited-state absorption processes. A threefold upconversion emissionenhancement induced by thermal effects when the codoped sample was heated inthe temperature range of 20-200 °C is demonstrated. Thethermal-induced enhancement is attributed to a multiphonon-assistedanti-Stokes process which takes place in the excitation of the ytterbium andexcited-state absorption of the praseodymium. The thermal effect is modelledby conventional rate equations considering temperature-dependent effectiveabsorption cross-sections for the 2F7/2-2F5/2 ytterbiumtransition and 1G4-3P0 praseodymium excited-state absorption, andit is shown to agree very well with experimental results. Frequencyupconversion in singly Pr3+-doped samples pumped at 836 nm and1.064 µm in a two-beam configuration is also examined.