Developed Rate Equation Research Articles

Silica polymerization and nanocolloid nucleation and growth kinetics in aqueous solutions

Amorphous silica precipitation from aqueous solutions at low temperatures (<100 °C) involves the initial nucleation and growth of silica polymers followed by aggregation, cementation and recrystallization to form opaline silica. In this study, silica polymerization was studied at temperature 23–80 °C, pH 2.48–9.65, and ionic strength 0.01–0.53 mol kg−1. Measured changes in the concentration of monomeric silica (SiO2(mono)) were fit assuming the polymerization reaction is fourth-order with respect to the difference between the concentration of silicic acid (Si(OH)4(aq)) and its concentration at equilibrium (Si(OH)4(aq)eq) with respect to amorphous silica:r=-k4AsmSi(OH)4(aq)-mSi(OH)4(aq)eq4where r is the overall rate of the reaction, As is the specific surface area of the formed polymers, calculated assuming particle-size-dependent solubility and a spherical polymer geometry, and k4 is the rate constant. The rate constant at zero ionic strength is given by:k0=Aexp-Ea/RTaOH-nwhere A is a pre-exponential constant (0.3822 mmol−3 cm−2 s−1), Ea is the activation energy (29.87 kJ mol−1), and n is equal to −0.80. The overall rate constant as a function of ionic strength (I) is given by:k4=k0Imwhere m is equal to 0.65. The rate constant increases by approximately six orders of magnitude from pH of 2 to 10 and one order of magnitude between temperature ∼20 and 80 °C. However, hydrolysis of silicic acid (Si(OH)4(aq)) at pH above ∼8 decreases the relative abundance of Si(OH)4(aq) while increasing the solubility of amorphous silica, thereby decreasing the rate of silica polymerization. The inferred reaction order is consistent with a reaction mechanism rate-limited by the formation of the cyclic tetramer across a wide range of pH. The time-dependence of the specific surface area during polymerization reflects the formation of critical nuclei towards the beginning of the polymerization process and Ostwald ripening of larger polymers towards the end of the polymerization process. The developed rate equation can predict rates of silica polymerization across a wide range of aqueous solution compositions.

Dual-wavelength collaboratively pumping scheme for a 3.9 µm continuous-wave Ho:YLF laser

A dual-wavelength collaboratively pumping scheme is proposed to realize the efficient operation of a 3.9 µm continuous wave Ho:YLF laser. An 888 nm laser is used to excite ions from the 5I8 ground-state manifold to the 5I5 laser’s upper manifold. Another 2.1 µm laser is used to excite ions from the 5I6 laser’s lower manifold to the short-lived 5I4 manifold to eliminate the self-terminated effect of 3.9 µm laser oscillation. Numerical simulation of 3.9 µm laser output performances is carried out, based on the developed rate equations. Simulation results indicate that the dual-wavelength collaboratively pumping scheme is feasible to realize the highly efficient output of the 3.9 µm continuous wave Ho:YLF laser. The relationship between the pump power for 888 nm and 2.1 µm laser sources is analyzed to obtain the optimal output. Furthermore, the impacts of crystal doping concentration, crystal length, output mirror transmittance, and important energy-transfer processes on the laser output performances are also analyzed. The dual-wavelength collaboratively pumping scheme provides beneficial guidance for the generation of a 3.9 µm high-power continuous-wave laser in an Ho:YLF laser.

Doubly Q-switched mode-locked Tm:YAP laser at [formula omitted] with ternary MoWS2 alloy and EOM

2D MoWS2 is fabricated by the chemical-vapor transport and liquid-phase exfoliation method. Its nonlinear optical response is measured. By using MoWS2 SA and EOM, an LD-pumped doubly Q-switched mode-locked (QML) Tm:YAP laser at 2μm waveband is presented. The average output power, the pulse width, and the pulse peak power of the Q-switched envelope are measured. In comparison to the singly QML laser with MoWS2 SA or EOM, the doubly QML laser can generate shorter pulse duration and higher peak power. Based on the fluctuation mechanism, a developed rate equation model under plane wave approximation is proposed to describe the doubly QML dynamic process. The pulse characteristics of QML laser are numerically simulated and the theoretical simulations are in agreement with the experiment results. Both the experiments and numerical simulations show that MoWS2 is a promising nanomaterial, and the dual-loss-modulated QML laser displays well performance in pulse width compression and peak power enhancement.

Determination of the activation parameters for the ring-opening polymerization of ε-caprolactone initiated by Sn(II) and Zn(II) chlorides using the fast technique of DSC

The kinetics of the ring-opening polymerization (ROP) of ε-caprolactone (ε-CL) initiated by 1.0 mol% of tin(II) chloride (SnCl2) and zinc(II) chloride (ZnCl2) was completely investigated by the differential scanning calorimetry (DSC) technique. The fast method to determine the activation parameters such as activation enthalpy (∆H≠) and activation entropy (∆S≠) was successfully developed basing on the transition state theory and isoconversional method. From Friedman isoconversional method, the values of activation energy (Ea) for the ROP of ε-CL initiated by SnCl2 (36.2 ± 1.5 to 40.8 ± 1.5 kJ/mol) were lower than ZnCl2 (51.9 ± 2.8 to 62.3 ± 2.8 kJ/mol). From Starink isoconversional method, the Ea values for the ROP of ε-CL initiated by SnCl2 (32.3 ± 1.1 to 35.8 ± 1.1 kJ/mol) were also lower than ZnCl2 (59.2 ± 0.8 to 62.1 ± 0.8 kJ/mol). By using the compensation parameters, the reconstructed monomer conversion function (f(α)) was fitted with the Avrami-Erofeev nucleation model (A2, f(α) = 2(1-α)[-ln(1-α)]1/2). The values of frequency factor (A) for the ROP of ε-CL with SnCl2 and ZnCl2 were 4.3 × 103to 1.6 × 104 min−1 and 2.1 × 105 to 5.3 × 105 min−1, respectively. From the developed rate equation, the values of ∆H≠ and ∆S≠ could be conveniently determined from dynamic heating. The obtained ∆H≠ values for the ROP of ε-CL initiated by SnCl2 and ZnCl2 were similar to the Ea values. The ∆S≠ values for the transition state of the ROP of ε-CL initiated by SnCl2 (-152.0 to -161.7 J/mol.K) were lower than ZnCl2 (-129.6 to -153.1 J/mol.K). The kinetics and the stability of transition state information demonstrated that the reactivity of SnCl2 in the ROP of ε-CL was higher than ZnCl2. The mechanism of the ROP of ε-CL with SnCl2 and ZnCl2 was proposed through a classical coordination-insertion mechanism. From poly(ε-caprolactone) (PCL) synthesis via solvent-free polymerization, SnCl2 acted as the highly effective initiator than ZnCl2. The highest number average molecular weight (Mn) of PCLs obtained from the SnCl2 and ZnCl2 initiator were 1.8 × 105 g/mol and 3.6 × 104 g/mol, respectively. The effectiveness of the slow ZnCl2 initiator in the production of high molecular weight and %yield of PCL could be improved by increasing the synthesis temperature. These SnCl2 and ZnCl2 compounds acted as a powerful initiator for the synthesis of PCL. The obtained results from this work were useful for understanding the transition state formulation in the ROP of other cyclic esters with various initiating systems that still in our attention and would be described in our future work.

Highly ultra-broadband QD-SOA exploiting superimposition of quantum dots

In this paper, for the first time, a highly ultra-broadband QD-SOA based on superimposed Quantum Dots has been proposed to accomplish a broader optical gain spectra range of almost 3.5 µm from blue to Mid-infrared, considering solution-processed nanotechnology as a simple and cost-effective fabrication method. The realization of the ultra-broadband optical gain can be accomplished by the superimposition of the various size-distributed QD groups made of different materials in a way that the broader energy span is covered as a consequence of the variation of the bandgap energy for each QD groups. To this end, different QD groups made of Bismuth Tellurium Sulphide (Bi2Te3-xSx) and Cadmium Tellurium Sulphide (CdTe1-xSx) in the ZnS shell implemented in the active region of QD-SOA have been superimposed, in which the radii of each QD groups can be easily distributed due to incorporating solution-processed method. The performance of the proposed QD-SOA has been modelled based on the developed rate equation framework by assuming inhomogeneous broadening of energy levels as a result of the size distribution of QDs and the superimposition of various QD groups. Furthermore, the bandwidth and, the spectral range, and the flatness of the optical gain in the QD-SOA can be managed by the number of QD groups, the percentage of Tellurium and Sulphur in the Bi2Te3-xSx and CdTe1-xSx alloys, and the size distribution of each QD groups.

Experimental and kinetic modeling studies of methanol synthesis from CO2 hydrogenation using In2O3 catalyst

• Analysis of kinetics of methanol synthesis from CO 2 hydrogenation over Indium Oxide catalyst. • Kinetic model based on single-site Langmuir-Hinshelwood-Hougen-Watson rate equations. • Good agreement between model predictions and experimental data is obtained. • Model predicts steam reforming reduces methanol yield at high temperature. Catalytic hydrogenation of CO 2 to methanol has gained considerable interest for its significant role in CO 2 utilization using heterogeneous catalysts. This study is the first to propose a kinetic model based on Langmuir-Hinshelwood-Hougen-Watson (LHHW) mechanism for CO 2 hydrogenation to methanol over a highly effective indium oxide (In 2 O 3 ) catalyst. The work focuses on different reaction conditions mainly revolving around the variation of operating temperature, total reactor pressure, H 2 /CO 2 molar feed ratio and weight hourly space velocity (WHSV) of the system. The experimental data were modeled using a competitive single-site kinetic model based on LHHW rate equations. A parameter optimization procedure was undertaken to determine the kinetic parameters of the developed rate equations. The model predicts that when the methanol synthesis reaction becomes equilibrium limited, the progress of the RWGS reaction forces the methanol yield to decrease due to the reversal of the methanol synthesis reaction. A mixture of CO 2 and H 2 has been used as the reactor feed in all the cases. Significantly w.r.t. the CO 2 partial pressure, the reaction rate for methanol synthesis initially increased and then slightly decreased indicating a varying order. The single-site model accurately predicted the trends in the experimental data which would enable the development of reliable reactor and process designs.

Modeling the impact of shrinkage effects on photoresist development

Background: Negative-tone development (NTD) photoresists are prone to shrinkage effects during lithographic processing. Along with deformation seen during the postexposure bake (PEB), there are additional effects during the development that cannot be fully explained by a conventional PEB shrinkage model alone. Aim: Understand the impact of PEB shrinkage on the development rate. Develop a model that can help predict resist profiles after chemical development. Approach: A PEB shrinkage model for NTD resists is introduced, which uses the thermal properties of the resist material to help simulate shrinkage. The deformed state of the resist is used as an input to the development rate equation to predict the final feature dimensions observed in experiments. Results: The strain concentration within the resist bulk can have an influence on the stability of the resist during the development. The strain influences the development rate depending on the resist feature shape and contours. Conclusions: The results from this study can help improve optical proximity correction (OPC) modeling performance and help better understand the deformation characteristics of NTD resist materials. The model also shows that the development shrinkage has an influence on the edge placement error.

General rate equation theory for gas–solid reaction kinetics and its application to CaO carbonation

The kinetics of reactions between gases and solids are typically modeled using shrinking-core or shrinking-pore theoretical frameworks, in which the formation of a uniform solid product layer covering the entire solid surface with a sharp interface between the solid reactant and the product is assumed. However, theories involving a uniform solid product layer cannot predict the kinetic transition behavior that occurs in some gas–solid reactions. This work proposes that the growth of solid product islands occurs instead of the progressive formation of a uniform solid product layer in traditional shrinking-core and shrinking-pore models and establishes a general rate equation theory to model the kinetics of gas–solid reactions for solid reactants of various shapes. The growth of the product islands is calculated using the rate equation theory and is integrated into the shrinking-core model and shrinking-pore model, in which the microstructure of the solid reactant is also considered. Elemental steps of chemical reaction, surface diffusion and product layer diffusion are included in the general rate equation theory. The kinetic parameters included in the model are chemical reaction rate constant ks, surface diffusion coefficient Ds, and product layer diffusion coefficient Dp. The resulting model is analyzed at the limits where either the chemical reaction or product layer diffusion is the rate-controlling step. At very small or very high Ds values, the rate equation theory is equal to the kinetics-controlled regime or diffusion-controlled regime in traditional models; therefore, the traditional models represent special cases of this theoretical rate equation model. At intermediate Ds values, the so-called two-stage kinetic behavior occurs. The transition from the fast initial stage to the diffusion-controlled stage depends on the value of Ds, with the conversion at the transition point increasing with increasing Ds. The rate equation theory is demonstrated to successfully predict the CaO carbonation kinetics under a wide range of experimental conditions including temperature, CO2 concentration, sorbent type, and amount of added inert supports as well as for systems that exhibit a temperature rise during the carbonation reaction The rate equation theory is integrated into a particle model to account for the external diffusion of gas around the particle and intraparticle diffusion as well as the effect of particle structural changes on intraparticle diffusion, such as the pore plugging phenomenon. The developed rate equation theory is an analytical model that can be easily used in reactor-scale modeling or computational fluid dynamics simulations.

Switchable Multi-Color Solution-Processed QD-laser

In this paper, for the first time, the switchable two-color quantum dot laser has been realized considering solution process technology, which has both simultaneous and lonely lasing capability exploiting selective energy contacts. Furthermore, both channels can be modulated independently, which is a significant feature in high-speed data transmission. To this end, utilizing superimposed quantum dots with various radii in the active layer provides the different emission wavelengths. In order to achieve the different sizes of QDs, solution process technology has been used as a cost-effectiveness and fabrication ease method. Moreover, at the introduced structure to accomplish the idea, the quantum wells are used as separate selective energy contacts to control the lasing channels at the desired wavelength. It makes the prominent device have simultaneous lasing at different emission wavelengths or be able to lase just at one wavelength. The performance of the proposed device has been modeled based on developed rate equation by assuming inhomogeneous broadening of energy levels as a consequence of the size distribution of quantum dots and considering tunnel injection of carriers into the quantum dots via selective energy contacts. Based on simulation results, the simultaneous lasing in both or at one of two wavelengths 1.31 μm and 1.55 μm has been realized by the superimposition of two different sizes of InGaAs quantum dots in a single cavity and accomplishment of selective energy contacts. Besides, controlling the quantum dot coverage leads to managing the output power and modulation response at the desired wavelengths. By offering this idea, one more step is actually taken to approach the switchable QD-laser by the simple solution process method.

Cryogenic characteristics of GaAs-based near-infrared light emitting diodes

High performance infrared light emitting diodes (LEDs) have drawn wide attention because of their significant applications in biomedicine, agriculture, aquaculture, night vision security systems and scientific researches. Due to the rapid development of infrared up-conversion devices, especially in the terahertz region, the studies on the GaAs-based infrared LEDs operating at low temperature (<20 K) are quite needed. In this paper, two representative GaAs-based LEDs (GaAs/AlGaAs double heterostructure LED (DH-LED) and GaAs (InGaAs)/AlGaAs quantum well infrared LED (QW-LED)) are fabricated and characterized with electroluminescence (EL) spectroscopy and electroluminescence efficiency (ELE) at different temperatures. The ELE of the QW-LED is about 70% higher at low temperatures (<150 K) but lower at high temperatures (>150 K) than that of the DH-LED. A developed rate equation method is used to analyze the ELE superiority of the QW-LED. Finally, the surface EL uniformity of the two LEDs is studied by using the charge coupled devices imaging. This study provides a guidance to choose and design LED structures for different operation temperatures.

Development of novel support for penicillin acylase and its application in 6-aminopenicillanic acid production

There is an ever-increasing demand for the β-lactam bulk intermediate 6-aminopenicillanic acid (6-APA) that has wide applications in the synthesis of newer generations of semisynthetic penicillins. It is commercially synthesized by biocatalytic transformation using penicillin acylase. Since the enzyme is soluble, immobilization on a solid porous support is necessary to make the catalyst recycleable and the process profitable. In this study, we developed a novel support of siliceous foam entrapped in a polymer matrix. Penicillin acylase was covalently immobilized on aminopropyl functionalized mesocellular foam silica (MCF) and was further cross-linked using glutaraldehyde without deactivation and upto 95% efficiency. The resulting biocatalyst had an activity of 1185 IU. mg−1 and demonstrated improved resistance to the substrate and product inhibition. These parameters along with improvement in pH and thermal stability enhanced 6-APA yield by 20% in beads. Intrinsic kinetic parameters were calculated from the developed rate equation to deduce enzyme catalytic mechanism.

Effect of Temperature on the Life Cycle ofEuspilotus azureus(Coleoptera: Histeridae), a Predator of Forensic Importance

Euspilotus azureus (Sahlberg, 1823) (Coleoptera: Histeridae) is one of the most frequently sampled species of Histeridae on carcasses in South America. Determining its physiological responses to different temperatures is essential for providing development rate equations to estimate the period of insect activity and postmortem interval of the body. Thus, to evaluate the influence of temperature on their life cycle and to understand their developmental threshold, experiments were conducted under laboratory conditions at 6 different temperatures (10, 15, 20, 25, 30, and 35 °C). All E. azureus life stages were responsive to thermal variations. Eggs of E. azureus did not hatch at extreme temperatures (10 and 35 °C) and the development time from egg to adult was longer at low temperatures (15 and 20 °C). Their biological responses, such as mean number of eggs produced, the number of eggs per egg mass, and development time at different temperatures, indicate that 20 to 25 °C is optimal for growth. The results suggest that E. azureus shows tolerance and adaptability in its ontogenetic stages over a wide temperature range, which is common in generalist species. Also, this study provides the development rate equation for the species, which is applicable to studies of forensic entomology.

Rate equations for modeling carbon dioxide sequestration in basalt

Dissolution rate equations are developed from published data for glassy and crystalline basalt to predict the silica release flux (JSi) as a function of hydrogen ion activity (2 < pH < 12) and temperature (0° < T < 100 °C). For glassy basalt the silica flux isJSi=(5.00×102)e(−39700R)1TaH+1.01+(5.26×10−5)e(−38400R)1TaH+−0.258and for crystalline basalt the silica flux isJSi=(7.40)e(−40100R)1TaH+0.680+(8.67×10−7)e(−32900R)1TaH+−0.286.These rate equations are implemented in TOUGHREACT to simulate a CO2 saturated solution reacting with glassy and crystalline basalt in batch and semibatch reactors. The crystalline basalt models are compared with a more complex basalt representation comprising a composite mixture of olivine, plagioclase and pyroxene dissolution rates. Results show that numerical models based on the newly developed rate equations make reasonable predictions. Batch reactor models initially contained a solution spiked with CO2. These models showed relatively rapid CO2 consumption followed by cessation of the reaction with the glassy and crystalline basalt after the CO2 was exhausted and a terminal pH near eight. The composite basalt model was less successful because the plagioclase continued to react after the CO2 was exhausted causing the pH to rise to an unreasonably high value near 12. Semibatch reactor models containing a solution continuously supplied with CO2 showed relatively rapid CO2 consumption until all basalt was consumed. Complete semibatch reaction produced a sodium and bicarbonate rich solution with a pH near eight for all three basalt compositions.

Reaction and transport effects in the heterogeneous systems for lean gas purification

Sorption of hydrogen chloride gas by active soda and that of hydrogen sulfide gas by calcium oxide are explored by experiment as promising means of removing these detrimental contaminants from fuel gas: active Na2CO3 was prepared by the calcination of commercial NaHCO3 at 200 °C; reactive CaO was formed by decomposing a fine-grained, high-calcium limestone at 830 °C. Techniques with a differential reactor were employed to explore the rate of reaction of HCl with Na2CO3 at 500 °C and that of H2S with CaO at 800 °C. Time-resolved data on the sorbents’ conversion were collected as a function of mean particle size in the range between 0.285 and 1.12 mm. The surface reaction constants, deduced via the tractable model from the initial reaction rates of the two reactions, slightly increase with the increasing particle size. The proposed correlations enable to interpolate or cautiously extrapolate to other isotropic, irregularly shaped solids. The effective diffusivities educed by means of the model from the experimental curves decrease significantly with the increasing conversion and are affected by the particle size in both sorptions. The developed reaction rate equations can conveniently be applied to the design and simulation of the deep dechloridization and the bulk desulfurization of hot producer gas.

Comparative kinetics of esterification of methanol–acetic acid in the presence of liquid and solid catalysts

ABSTRACTEsterification of acetic acid with methanol to produce methyl acetate in an isothermal stirred batch reactor has been studied. Sulfuric acid was used as a liquid catalyst, and Indion‐180, Indion‐190 and Amberlyst‐16wet ion exchange resins were used as solid catalysts. The feed mole ratio was varied from 1 : 1 to 1 : 4. The reaction temperatures were varied from 305.15 to 333.15 K for sulfuric acid as catalyst and 323.15 to 353.15 K for the solid catalysts. The catalyst concentrations were used in the range of 1% to 5%, for the sulfuric acid catalyst, and 0.01 to 0.05 g/cc, for the solid catalysts. The effect of temperature, catalyst concentration, agitation speed, size of catalyst particle and reactant concentration on the acetic acid conversion was investigated. A second‐order kinetic rate equation was proposed to fit the experimental data. For both forward and backward reactions, the activation energies were estimated from Arrhenius plots. The reaction rate increased with catalyst concentration and temperature for both the liquid and solid catalysts. The acetic acid conversion was found to increase with increases in acetic acid to methanol ratio in the feed. The developed kinetic rate equation was used for the simulation of reactive distillation process, in our laboratory column. © 2014 Curtin University of Technology and John Wiley &amp; Sons, Ltd.

Improvement of stability and pulse energy in a diode-pumped dual-loss-modulated QML Nd:Lu0.2Y0.8VO4 laser with EO modulator and GaAs

The Q-switched and mode-locked (QML) performance in a diode-pumped Nd:Lu0.2Y0.8VO4 laser with electro-optic (EO) modulator and GaAs saturaber absorber is investigated. In comparison with the solely passively QML laser with GaAs, the dual-loss-modulated QML laser with EO and GaAs can generate pulses with higher stability and shorter pulse width of Q-switched envelope, as well as higher pulse energy. At the repetition rate 1kHz of EO, the pulse width of Q-switched pulse envelope has a compression of 89% and the pulse energy has an improvement of 24 times. The QML laser characteristics such as the pulse width, pulse peak power etc. have been measured for different small-signal transmittance (T0) of GaAs, different reflectivity (R) of output coupler and modulation frequencies of the EO modulator (fe). The highest peak power and the shortest pulse width of mode-locked pulses are obtained at fe=1kHz, R=90% and T0=92.6%. By considering the influences of EO modulator, a developed rate equation model for the dual-loss-modulated QML laser with EO modulator and GaAs is proposed. The numerical solutions of the equations are in good agreement with the experimental results.

A dual-loss-modulated Q-switched and mode-locked Nd:GdVO4 laser with AOM and V3 + :YAG saturable absorber at 1.34 µm

Stable and robust pulses can be generated in a diode-pumpedQ-switched and mode-locked(QML) c-cut Nd:GdVO4/V3 + :YAG laser at 1.34 µm by inserting an acousto-optic modulator (AOM) into the laser cavity.In this kind of dual-loss-modulation QML laser, the pulse width of theQ-switched pulse envelope has a compression of 68% and the pulse energy has animprovement of seven times compared with that in the solely passively QML laser withV3 + :YAG. By considering the influence of the turnoff time and the modulation frequency of theAOM as well as the thermal lens effect, a developed rate equation model fordual-loss-modulation QML lasers is given and the numerical solutions of the rate equationsare in good agreement with the experimental results.

Numerical solutions of diode-pumped dual-loss-modulated Q-switched and mode-locked green laser with acousto-optic modulator and Cr4+: YAG saturable absorber

By considering the influence of the acousto-optic (AO) modulator and the nonlinear loss due to harmonic conversion in the intra-cavity frequency-doubling laser, a developed rate equation model for diode-pumped dual-loss-modulated Q-switched and mode-locked (QML) Nd:LuVO4/KTP green laser with acousto-optic (AO) modulator and Cr4+:YAG saturable absorber is presented. With this developed model, the pulse width, single-pulse energy and the other dual-loss-modulated QML green laser characteristics are numerically simulated. The simulation results show that the turnoff time is of great importance for the pulse energy and pulse width of the Q-switched pulse. A diode-pumped dual-loss-modulated QML Nd:LuVO4/KTP laser is constructed to successfully demonstrate the numerical simulation application.

Numerical simulation of dual-loss-modulated Q-switched and mode-locked laser with an acousto-optic and Cr^4+:YAGsaturable absorber

By considering the influence of the turn-off time and the modulation frequency of the acousto-optic (AO) modulator as well as the Gaussian spatial distribution of the photon density, we give a developed rate equation model for a diode-pumped dual-loss-modulated Q-switched and mode-locked (QML) Nd:GdVO(4) laser with AO modulator and Cr(4+):YAG saturable absorber. With this developed model, the dual-loss-modulated QML laser characteristics, such as pulse width and pulse energy, can be numerically simulated, and the theoretical evaluations are in good agreement with the experimental results.

The Performance of Acoustic-Optical $Q$-switched Mode-Locking 1.34 $\mu$m Nd:GdVO$_{4}$ Laser

A diode-end-pumped Q -switched mode-locking Nd:GdVO4 laser operating at 1.34 μm with an acousto-optical (AO) Q-switch in a compact V-type cavity was realized in our experiment for the first time. When the AO Q-switch repetition rate was 10 kHz, the maximum average output power of 750 mW and the pulse energy of 75 μ were obtained at the maximum incident pump power of 9 W. The mode-locking modulation depth of about 100% was obtained at certain pump power over the threshold. The mode-locked pulse inside in the Q-switched pulse had a repetition rate of 341 MHz, and its average pulsewidth was estimated to be about 350 ps. A developed rate equation model for the Q -switched and mode-locked lasers with an AO Q-switch were proposed by using the hyperbolic secant functional methods. The results of numerical calculations of the rate equations were in good agreement with the experimental results.