Rate Equation Model Research Articles

Combined resonant tunneling and rate equation modeling of terahertz quantum cascade lasers

Terahertz (THz) quantum cascade lasers (QCLs) are technologically important laser sources for the THz range but are complex to model. An efficient extended rate equation model is developed here by incorporating the resonant tunneling mechanism from the density matrix formalism, which permits to simulate THz QCLs with thick carrier injection barriers within the semi-classical formalism. A self-consistent solution is obtained by iteratively solving the Schrödinger–Poisson equation with this transport model. Carrier–light coupling is also included to simulate the current behavior arising from stimulated emission. As a quasi-ab initio model, intermediate parameters, such as pure dephasing time and optical linewidth, are dynamically calculated in the convergence process, and the only fitting parameters are the interface roughness correlation length and height. Good agreement has been achieved by comparing the simulation results of various designs with experiments, and other models such as density matrix Monte Carlo and non-equilibrium Green's function method that, unlike here, require important computational resources. The accuracy, compatibility, and computational efficiency of our model enable many application scenarios, such as design optimization and quantitative insights into THz QCLs. Finally, the source code of the model is also provided in the supplementary material of this article for readers to repeat the results presented here, investigate, and optimize new designs.

Deuterium uptake, desorption and sputtering from W(110) surface covered with oxygen

Rate equation modelling is performed to simulate D2 and D2+D2+ exposure of the W(110) surface with varying coverage of oxygen atoms (O) from the clean surface up to 0.75 monolayer of O. Density Functional Theory (DFT) calculated energetics are used as inputs for the surface processes and desorption energies are optimized to best reproduce the Thermal Desorption Spectrometry (TDS) experiments obtained for D2 exposure. For the clean surface, the optimized desorption energies (1.10 eV–1.40 eV) are below the DFT ones (1.30 eV–1.50 eV). For the O covered surface, the main desorption peak is reproduced with desorption energies of 1.10 eV and 1.00 eV for 0.50 and 0.75 monolayer of O respectively. This is slightly higher than the DFT predicted desorption energies. In order to simulate satisfactorily the total retention obtained experimentally for D2+D2+ exposure, a sputtering process needs to be added to the model, describing the sputtering of adsorbed species (D atoms) by the incident D ions. The impact of the sputtering process on the shape of the TDS spectra, on the total retention and on the recycling of D from the wall is discussed. In order to better characterize the sputtering process, especially its products and yields, atomistic calculations such as molecular dynamics are suggested as a next step for this study.

Orientation Growth of N-Doped and Iron-Based Metal-Organic Framework and Its Application for Removal of Cr(VI) in Wastewater.

A series of NH2-functionalized nano-sized magnetic metal-organic frameworks (MOFs) were prepared in this study for Cr(VI) removal from wastewater. It was observed that not only the morphological, i.e., orientation growth of N-doped and iron-based metal-organic frameworks, but also the adsorption of magnetic MOFs is largely related to the used amount of ammonium hydroxide in preparation. For example, with increasing amounts of ammonium hydroxide used in preparation, the morphology of magnetic MOFs changed from spherical to cube and triangular cone. Moreover, the maximum adsorption capacity of spherical-magnetic MOFs, cubic-magnetic MOFs and triangular cone-magnetic MOFs could be up to 204.08 mg/g, 232.56 mg/g and 270.27 mg/g, respectively. Under optimal conditions, the adsorption process of magnetic MOFs for Cr(VI) was consistent with the pseudo-second-order rate equation (R2 = 1) and Langmuir isotherm model (R2 > 0.99). Therefore, magnetic MOFs developed in this work offered a viable option for the removal of Cr(VI) from wastewater.

Study of Active Medium Length Effect on Characteristics of Passive QSwitching and Stokes with Anti-Stokes Pulse

Objective: To study the effect of active medium length on the characteristics of passive Q-switching pulses, Stokes pulses, and anti-Stokes pulses generated by laser-Raman medium interaction in optical systems, theoretically. Methods: The optical system consists of Nd+3:YVO4, PbWO4, and Cr+4:YAG as active mediums, Raman medium, and saturable absorber materials, respectively. The rate equations model has been used in the study, and the Rung-Kutta-Fehelberg numerical method was used to solve the rate equations. Finding: The result shows that, decreasing of the active medium length leads to emit high power pulses at advanced time. It also leads to increase in initial value and the maximum value of population inversion density, and leads to increase in the energy of passive Q-switching pulses, Stokes pulses, and anti-Stokes pulses. So the decreasing of the active medium length leads to decrease in the pulses duration and the final population inversion density. To increase the power of the three generated pulses, the length of the active medium used in the system must be decreased. Novelty: The characteristics of two pulses generated by Laser-Raman interaction (passive Q-switching pulse and Stokes pulse) have been of interest in some studies. This study investigates the effect of the active medium length on the characteristics of three pulses generated (anti-Stokes pulse with Stokes pulse as well as the passive Q-switching pulses) by the optical system rather than two pulses. Keywords: Laser; Nd+3 :YVO4; passive Q-­switching pulse; Stokes and anti-­Stokes pulses 1

Unveiling the electronic structure of GaSb/AlGaSb quantum dots emitting in the third telecom window

Epitaxially-grown semiconductor quantum dots (QDs) provide an attractive platform for the development of deterministic sources of high-quality quantum states of light. Such non-classical light sources are essential for quantum information processing and quantum communication. QDs emitting in the telecom wavelengths are especially important for ensuring compatibility with optical fiber systems required to implement quantum communication networks. To this end, GaSb QDs fabricated by filling local-droplet etched nanoholes are emerging as a viable approach, yet the electronic properties of such nanostructures have not been studied in detail. In this article, an insight into the electronic structure and carrier dynamics in GaSb/AlGaSb QDs is provided through a systematic experimental analysis of their temperature-dependent photoluminescence behavior. A steady-state rate equation model is used to reveal the relevant energy barriers for thermally activated carrier capture and escape processes. Furthermore, results of detailed theoretical simulations of quantum-confined energy states using the multi-band k·p model and the effective mass method are presented. The purpose of the simulations is to reveal the direct and indirect energy states, carrier wavefunctions, and allowed optical transitions for GaSb QDs with different physical dimensions.

Ultrafast photocarrier dynamics in InAs/GaAs self-assembled quantum dots investigated via optical pump-terahertz probe spectroscopy

Optical pump-terahertz probe (OPTP) spectroscopy was performed to measure the lifetime of photogenerated carriers in the barrier and the wetting layer (WL) regions of an indium arsenide on gallium arsenide (InAs/GaAs) single-layer self-assembled quantum dot (QD) sample. A modified rate equation model of carrier dynamics was proposed where possible state-filling in both QD and WL is considered. Drude model fitting was also performed to extract the time-dependent plasma frequency and phenomenological scattering time from the terahertz transmission spectra. The results of the OPTP experiment show two prominent recombination processes that occur at different timescales after photoexcitation. These two processes were attributed to carrier recombination in the GaAs barrier and the quantum well-like states of the WL based on the fitted lifetimes. Calculations using the coupled differential rate equations were also able to replicate the experimental trend at low fluence. The lack of agreement between experimental data and numerical calculations at high optical fluence was mainly attributed to the possible saturation of the GaAs density of states. Lastly, the results of the parameter fitting for the plasma frequency and scattering time indicate a transition from the barrier to the WL recombination as the dominant carrier recombination mechanism within the time scale of the OPTP scan. This further lends credence to the proposed model for carrier dynamics in SAQD systems under state-filling conditions.

Relaxation enhancement by microwave irradiation may limit dynamic nuclear polarization.

Dynamic nuclear polarization enables the hyperpolarization of nuclear spins beyond the thermal-equilibrium Boltzmann distribution. However, it is often unclear why the experimentally measured hyperpolarization is below the theoretically achievable maximum polarization. We report a (near-) resonant relaxation enhancement by microwave (MW) irradiation, leading to a significant increase in the nuclear polarization decay compared to measurements without MW irradiation. For example, the increased nuclear relaxation limits the achievable polarization levels to around 35% instead of hypothetical 60%, measured in the DNP material TEMPO in 1H glassy matrices at 3.3 K and 7 T. Applying rate-equation models to published build-up and decay data indicates that such relaxation enhancement is a common issue in many samples when using different radicals at low sample temperatures and high Boltzmann polarizations of the electrons. Accordingly, quantification and a better understanding of the relaxation processes under MW irradiation might help to design samples and processes towards achieving higher nuclear hyperpolarization levels.

Beam-profile compensation for quantum yield characterisation of Yb-Tm codoped upconverting nanoparticles emitting at 474 nm, 650 nm and 804 nm.

Upconverting nanoparticles (UCNPs) have found widespread applications in biophotonics and energy harvesting due to their unique non-linear optical properties arising from energy transfer upconversion (ETU) mechanisms. However, accurately characterising the power density-dependent efficiency of UCNPs using the internal quantum yield (iQY) is challenging due to the lack of methods that account for excitation beam-profile distortions. This limitation hinders the engineering of optimal UCNPs for diverse applications. To address this, this work present a novel beam profile compensation strategy based on a general analytical rate-equations model, enabling the evaluation of iQY for ETU processes of arbitrary order, such as ETU2, ETU3, and beyond. The method was applied to characterise the ETU2 and ETU3 processes corresponding to the main emission peaks (474 nm, 650 nm, and 804 nm) of a Yb-Tm codoped core-shell β-UCNP. Through this approach, the transition power density points (which delimit the distinct non-linear regimes of the upconversion luminescence (UCL)), and the saturation iQY values (which are reached at high excitation power densities above the transition points) were determined. The ETU2 process exhibits a single transition power density point, denoted as ρ2, while the ETU3 processes involve two transition points, ρ2 and ρ3. By compensating for the beam profile, we evaluate the iQY of individual lines across a wide dynamic range of excitation power densities (up to 105 W cm-2), encompassing both non-linear and linear regimes of UCL. This study introduces a valuable approach for accurately characterising the iQY of UCNPs, facilitating a deeper understanding of the upconversion and its performance. By addressing excitation beam-profile distortions, this method provides a comprehensive and reliable assessment of the power density-dependent iQY. The results highlight the applicability and effectiveness of this beam profile compensation strategy, which can be employed for a wide range of UCNPs. This advancement opens new avenues for the tailored design and application of UCNPs in various fields, especially for biophotonics.

Initial Transmission Influence on Saturable Absorber Absorption Activity of Passive Q-Switching Erbium -Doped Fiber Laser System

The initial transmission effect on the activity of Cr+4: YAG saturable absorber with Er +3 doped fiber laser was investigated. Software computer program was built in this study for solving the rate equations model by Rung - Kutta –Fehlberg numerical method. The study reported that the absorption activity of ground state of saturable absorber decreases with the decreasing of the initial transmission, while the activity absorption of excited state begins to increase. Moreover, the total absorption activity of saturable absorber also decreases with the decreasing of the initial transmission.

A new rate equation model of continuous wave Tm:YAP laser

A new rate equation model of continuous wave Tm:YAP laser

Uniform spike trains in optically injected quantum cascade oscillators.

It has been experimentally and theoretically analyzed that noise-induced excitability in quantum well and quantum dot semiconductor laser systems usually produces sharp spike patterns of non-uniform amplitude. In this paper, we experimentally record that a quantum cascade oscillator injected externally with a monochromatic laser beam exhibits a series of highly uniform spike trains, which occur in the proximity of the saddle-node bifurcation. Theoretical analysis based on a properly designed single-mode rate equation model endowed with quantum noise reveals that this high uniformity has its primary origin in the ultrashort carrier lifetime of the quantum cascade laser gain medium that is typically close to 1 ps.

Investigation of noise correlations in the phase-locked class-A VECSEL array

We theoretically and experimentally study the noise correlations in an array of lasers based on a VECSEL (Vertical External Cavity Surface Emitting Laser) architecture. The array of two or three lasers is created inside a planar degenerate cavity with a mask placed in a self-imaging position. Injection from each laser to its neighbors is created by diffraction, which creates a controllable complex coupling coefficient. The noise correlations between the different modes are observed to be dramatically different when the lasers are phase-locked or unlocked. These results are well explained by a rate equation model that takes into account the class-A dynamics of the lasers. This model permits the isolatation of the influence of the complex coupling coefficients and of the Henry α-factor on the noise behavior of the laser array.

Rate Equations Model to Simulate the Dual Generation of Nd+3: YAG Passive Q-Switched Laser Pulses

Rate Equations Model to Simulate the Dual Generation of Nd+3: YAG Passive Q-Switched Laser Pulses

604 nm&639 nm Dual-wavelength double pulse Pr:YLF laser

A theoretical model of dual-mode rate equation has been developed to accurately describe the oscillation mechanism of a visible dual-wavelength double pulse Pr:YLF laser. The insertion angle of F-P etalon and the two-step loss of Q-switching are found to be critical factors in controlling dual-wavelength intensity ratio and master–slave pulse energy ratio. Experimental results demonstrate that tuning these parameters enables the production of a dual-wavelength double-pulse laser, with a maximum output power of 98mW, a pulse width of 100 ns, and a PRF of 10 kHz. To the best of our knowledge, this is the first investigation of a visible dual-wavelength double pulse Pr:YLF laser.

Rate Equations Model to Simulate the Performance of Passive Q-Switched Laser with Raman Medium Optical System

Rate Equations Model to Simulate the Performance of Passive Q-Switched Laser with Raman Medium Optical System

Grating magneto-optical traps with complicated level structures

We study the forces and optical pumping within grating magneto-optical traps (MOTs) operating on transitions with non-trivial level structure. In contrast to the standard six-beam MOT configuration, rate equation modeling predicts that the asymmetric laser geometry of a grating MOT will produce spin-polarized atomic samples. Furthermore, the Landé g-factors and total angular momenta of the trapping transition strongly influence both the confinement and equilibrium position of the trap. Using the intuition gained from the rate equation model, we realize a grating MOT of fermionic 87Sr and observe that it forms closer to the center of the trap’s quadrupole magnetic field than its bosonic counterpart. We also explore the application of grating MOTs to molecule laser cooling, where the rate equations suggest that dual-frequency operation is necessary, but not sufficient, for stable confinement for type-II level structures. To test our molecule laser cooling models, we create grating MOTs using the D 1 line of 7Li and see that only two of the four possible six-beam polarization configurations operate in the grating geometry. Our results will aid the development of portable atom and molecule traps for time keeping, inertial navigation, and precision measurement.

Rate equations description of the asymmetric double barrier electronic cooler

Recent experimental results showed that an electron gas in an asymmetrical double barrier heterostructure can be effectively cooled down under resonant tunneling condition, thus leading to the realization of an electronic cooler. The cooling process is a multi-parameters phenomenon and it is desirable to handle this problem through a reasonably simple approach, in order to understand the role of each parameter. To this end, we present a rate equation modeling of the electron cooling. We model the resonant tunnel injection of the electrons in the well and their thermionic emission assisted by Longitudinal Optical (LO) phonons absorption and emission. The influence of several parameters on the electronic temperature is discussed. This simple model compares rather well to the predictions of non-equilibrium Green function approach and to the experiments.

Simultaneous realization of FIR-based multimode optical thermometry and photonic molecular logic gates in Er3+ and Yb3+ co-doped SrTiO3 phosphor

Er3+ and Yb3+ co-doped SrTiO3 phosphors were synthesized and characterized by using the x-ray powder diffraction method, field emission scanning electron microscopy, and photoluminescence spectroscopy. The samples were subjected to thorough luminescence analysis. Under 980 nm infrared (IR) excitation, the (2H11/2,4S3/2) → 4I15/2 and 4F9/2 → 4I15/2 transitions of Er3+ gave green and red emissions, respectively. The up-conversion mechanism of the synthesized phosphor was studied using the power-dependent emission spectra of the SrTiO3:Yb3+, Er3+ phosphor. A rate equation model for the up-conversion mechanism of SrTiO3:Yb3+, Er3+ has been proposed. The temperature-dependent responses of various thermal and non-thermally coupled emission lines of Er3+ ions were used to elaborate the thermal sensing capabilities of the synthesized phosphor. The fluorescence intensity ratio technique was used for the temperature sensing measurements. Sensing measurements were performed in the temperature range of 303 to 618 K. Relative sensitivities of 1.28% K−1, 0.15% K−1, 0.98% K−1, and 0.15% K−1 were observed using various thermally and non-thermally coupled energy levels. Furthermore, using heat and incident IR excitation as physical inputs, we have shown that the synthesized phosphor can also be used to design various elementary logic gates such as AND, INHIBIT, and DEMULTIPLEX photonic molecular logic gates. A high switching ratio of ∼143% for the AND gate and ∼44.8% for the INHIBIT gate was observed using the scheme presented in this manuscript. The synthesized phosphor has the potential to be used as a bifunctional material for optical thermometry and molecular logic devices.

Generation of optical frequency combs by Q-switching integrated multi-section semiconductor lasers.

In this work we perform a theoretical and simulation analysis of the behavior of an integrated four section distributed Bragg reflector semiconductor laser under optical injection and Q-switching operation. An electro-absorption modulator is introduced into the laser cavity to control the total losses and perform Q-switching. The simulations are done using a rate equation model. Q-switching operation produces very short and high power pulses. This, together with the use of optical injection, allows obtaining flat and broad optical frequency combs with up to 2100 optical lines within 10 dB (642 lines within 3 dB) at a repetition frequency of 100 MHz. The high chirp of the pulses is responsible for the broad spectra of these combs in comparison with gain switched combs, and the device structure allows fabrication in commercial foundries using standard building blocks.

Competition between Zeeman and hyperfine pumping in thermal atomic vapor

We present ab initio reduced rate equation models to study the interplay of Zeeman and hyperfine pumping, which determines the Doppler-broadened absorption spectra of an arbitrarily polarized probe laser, in thermal atomic vapor. Our simple models (with maximum seven levels) accurately predict the dependence of probe absorption on its polarization for the 87Rb D2 line (residual error <2%) without any fitting parameters, while being ∼100× less computational resource intensive as compared to numerically complex full multi-level models that treat all (up to 23) the magnetic (m F ) sub-levels present in the system individually. We demonstrate that either Zeeman or hyperfine pumping dominates depending on whether the atomic transitions being probed are primarily closed or open.