Space-dependent Rate Equations Research Articles

Numerical modeling of the actively Q-switched dual-wavelength Raman laser with a small wavelength separation

Assuming the intracavity photon number densities and initial population-inversion density are Gaussian distributions, the rate equations of the actively Q-switched dual-wavelength Raman laser based on one Raman mode are deduced. Under the condition that the wavelength separation of the two Raman lasers is very small, these space-dependent rate equations are normalized and solved numerically. A set of universal theoretical curves describing the operations of the dual-wavelength Raman laser is obtained. The influence of the composite normalization variables on the performances of the dual-wavelength Raman laser is analyzed. The normalization theory is verified with experimental data. The experimental results are consistent with the numerical ones, which proves that the proposed rate equations are correct and feasible.

Influence of thermal population of lower laser levels on the performance of end-side-pumped Ce:Nd:YAG solar laser

We report the results of a theoretical study of the combined end-side pumped solar lasers to solve the problem associated with a recent experimental finding where the unexpected underperformance of the Ce doped Nd:YAG lasers in comparison to pure Nd:YAG lasers was observed. For this, we have developed a theoretical model based on space-dependent rate equations, which considers the effect of the thermal population of the laser levels on the laser output. It is shown that the main reason for the lower laser performance of recently experimentally realized Ce:Nd:YAG solar laser in the end-pumped regime and the fracture of the Ce:Nd:YAG rod at the process is the excessively high thermal load on the end of the laser rod. As a result of our study, we propose easily-feasible solutions based on optimal pumping and cooling configurations. The results of this study also demonstrate that under the necessary conditions, using Ce:Nd:YAG as an alternative to Nd:YAG in the combined end-side pumping configuration could increase the laser output by more than 1.5 times.

Numerical modeling of the intracavity coherent anti-Stokes Raman laser

The space-dependent rate equations of intracavity coherent anti-Stokes Raman lasers are deduced by adding the term describing the coherent anti-Stokes scattering effect to the rate equations of the intracavity Raman laser. The intracavity photon densities of the fundamental and first Stokes lights and the initial population-inversion density are assumed to be Gaussian spatial distributions. The rate equations are normalized and solved numerically, and a group of general curves is generated. The influence of normalized parameters on the pulse parameters of the output anti-Stokes laser is investigated. The normalized rate-equation theory and numerical results will be of help in the design of high-performance intracavity coherent anti-Stokes Raman lasers.

Analysis of actively Q-switched infrared Raman lasers with crystalline media of multi-Raman-modes

Actively Q-switched intracavity Raman lasers can generate multi-wavelength infrared laser based on rich modes of crystalline Raman media. Assuming the intracavity photon densities and initial population inversion densities to be of Gaussian spatial distributions, the space-dependent rate equations of actively Q-switched intracavity Raman lasers with two Raman modes are deduced. The rate equations are solved numerically to investigate the influences of normalized variables on pulse energy, peak power, pulse duration, and conversion efficiency of Raman laser outputs, respectively. There are obvious discrepancies between the results of two Raman modes. The dependence of Raman laser conversion efficiency at 1103 nm on normalized initial population inversion density is numerically calculated, the experimental results are consistent with the numerical ones, and the optimum conditions are proposed theoretically in the end.

The influence of energy transfer upconversion on Q-switched single resonator optical parametric oscillator

The influence of energy transfer upconversion on Q-switched single resonator intracavity optical parametric oscillator is investigated by a space-dependent rate equation model. The numerical analysis shows that the energy transfer upconversion effect causes the pump size to have an optimum for yielding the largest output power at a given pump power. To verify the presented model, the practical example of Q-switched Nd : YVO4—KTA single resonator intracavity optical parametric oscillator has been used. The optimum pump size, calculated by presented model is 320 μm which is reported 300 μm.

Optimum design considerations for CW intra-cavity second harmonic generation in end-pumped solid-state lasers

An understanding of performance of a laser system in terms of design parameters is of the great importance to the engineer who is designing a laser system. This manuscript describes a theoretical report on the optimum design key parameters of an intracavity frequency doubled end-pumped solid-state laser based on the combination of space-dependent rate equations and nonlinear coupled-wave analysis of second-harmonic generation. The theoretical framework along with the results presenting the effect of various parameters such as pump beam characteristics, gain medium and nonlinear crystal properties to optimize the SHG efficiency has been investigated. By considering the optimized root mean square of pump beam radius as the effective value of pump spot size in the gain medium and perfect phase matching between fundamental and second harmonic waves,optimum nonlinear crystal's length, optimum mode size and second harmonic output power are derived as a function of pump-beam characteristics, and properties of the nonlinear and gain medium crystals. The results show that the optimum nonlinear crystal's length depends not only on the nonlinear coefficient and spot radius of laser beam but also on the pump beam properties and gain medium characteristic. In addition, the effect of pump and gain medium properties on the optimal fundamental beam by taking into account thermal aberration are investigated. The obtained results give useful guidelines for choosing the suitable active and nonlinear crystals for a given pump source and allow the straightforward evaluation of laser parameters for efficient intracavity doubling in end-pumped solid-state lasers.

Theoretical and experimental study on passively Q-switched intracavity frequency-doubled solid-state yellow Raman lasers

Normalized space-dependent rate equations of passively Q-switched intracavity frequency-doubled Raman lasers are deduced for the first time. The normalized rate equations are solved numerically to investigate the influences of the normalized variables on the yellow laser performance. The LD end-pumped passively Q-switched Nd:YAG/SrWO(4)/KTP/Cr:YAG yellow Raman laser is realized, and the maximum yellow laser output power is 350 mW with the incident pump power of 5.9 W with Cr:YAG of 85% initial transmission. The theoretical analysis and optimization are taken out for the experiment, and the theoretical results are in accordance with the experimental ones.

Experimental and theoretical study of a laser-diode-pumped passively Q-switched intracavity-frequency-doubled Nd:GdVO_4/KTP red laser with V:YAG saturable absorber

A laser-diode-pumped passively Q-switched intracavity-frequency-doubled Nd:GdVO4/KTP red laser with V:YAG saturable absorber is realized in a V-type resonator. The dependences of the pulse repetition rate, pulse width, single-pulse energy, and peak power on the incident pump power are measured and contrasted. By assuming the intracavity photon density and the initial population-inversion density to be Gaussian spatial distributions, the space-dependent rate equations of this laser are given. The numerical solutions of the rate equations are consistent with the experimental results. In order to optimize the described system, the variations of the pulse width, peak power, single-pulse energy, and laser efficiency with the initial transmission of the saturable absorber and the ratio of the laser beam radius to the pump beam radius are also calculated, respectively.

Analysis of actively Q-switched intracavity frequency-doubled solid-state yellow Raman lasers

The actively Q-switched solid-state yellow Raman laser with intracavity frequency doubling has attracted extensive research due to its high efficiency, simplicity and compactness. In this paper, the normalized space-dependent rate equations of this kind of lasers are deduced and analyzed to illustrate the effects of the composite variables on the yellow-laser performance, and several general curves are generated. The optimized values of the composite parameters are analyzed for the efficient yellow-laser output. In the end, application examples are given to shown that these theoretical results can predict the performance of actively Q-switched intracavity frequency-doubled solid-state yellow Raman lasers effectively.

Analysis of a laser-diode end-pumped passively Q-switched Nd:GdVO4 laser with V3+:YAG saturable absorber

By considering both the transversal and longitudinal Gaussian spatial distribution of the intracavity photon density, a couple of rate equations describing a laser-diode end-pumped passively Q-switched Nd:GdVO4 laser with V3+:YAG saturable absorber have been proposed. Solving these space-dependent rate equations numerically, we obtain the dependences of pulse width, pulse repetition rate, single-pulse energy and peak power on pump power. In the experiment, a laser-diode end-pumped Nd:GdVO4 laser passively Q-switched by a V3+:YAG saturable absorber has been realized, and the experimental results are consistent with the theoretical calculations.

Diode-pumped passively Q-switched and modelocked Nd:GdVO_4 laser at 134 μm with V:YAG saturable absorber

Using V:YAG as the saturable absorber, a diode-pumped passively Q-switched and mode-locked Nd:GdVO(4) laser at 1.34 microm is realized. Nearly 100% modulation depth of mode-locking has been achieved. The width of the mode-locked pulse is estimated to be less than 460 ps with 125 MHz repetition rate within an about 1 micros-long Q-switched pulse envelope. A maximum output power of 220 mW and Q-switched pulse energy of 10.5 microJ is obtained. Using the hyperbolic secant function methods, a fluctuation rate equation model considering the Gaussian distribution of the intracavity photon density and the population inversion in the gain medium as well as the ground-state population intensity of the saturable absorber has been proposed to describe the mode-locking process of diode-pumped Nd:GdVO(4)/V(3+):YAG laser. With the space-dependent rate equations solved numerically, the theoretical calculations reproduce the laser characteristics well.

Investigations on Transverse-Mode Competition and Beam Quality Modeling in End-Pumped Lasers

The transverse-mode competition and beam quality modeling in scaling fiber-coupled laser diode (LD) end-pumped lasers to higher power and better beam quality have been investigated with the space-dependent multimode rate equations by including the thermal effect. The total photon number and threshold of the pumping rate for each mode in the cavity were obtained by solving these equations with an iterative method, and so the threshold of the pumping power, output power, optical and slope efficiency of the single mode and laser could all be calculated. Several lasers, including one ideal laser, one multimode laser, one quasi-fundamental mode laser with folded structure, were brought forward to demonstrate the modeling process and investigate the transverse-mode competition process. The calculated results were compared with the experimental ones and the rationality of the model built in this paper was validated. The model presented here may serve as the designing guideline for a practical laser, especially one with beam quality requirement.

Modeling of Actively $Q$-Switched Intracavity Raman Lasers

The normalized space-dependent rate equations are deduced assuming the intracavity photon densities and initial population-inversion density to be of Gaussian spatial distributions in the diode-pumped actively Q-switched intracavity Raman lasers. Numerical calculations are carried out to investigate the influences of these normalized variables on the pulse parameters of the first Stokes. The rate equations under the planewave approximation are also normalized and solved numerically, and the results show the obvious discrepancies from those of the space-dependent theory. The spontaneous Raman scattering factor in rate equations are deduced in detail for the first time, and the oscillating threshold of the first Stokes inside the resonator is deduced analytically. A sample calculation for an actively Q-switched self-Raman laser is presented to demonstrate the use of the curves and related formulas.

Numerical modelling of passively Q-switched intracavity Raman lasers

Assuming intracavity photon densities to be of Gaussian spatial distributions, the space-dependent rate equations of passively Q-switched intracavity Raman lasers are deduced for the first time for the pumping beams of Gaussian and top-head spatial distributions, respectively. The new rate equations are normalized and solved numerically to investigate the influences of the normalized initial population inversion density, normalized Raman gain coefficient, saturable absorber parameter, beam size ratio of pump to fundamental laser and loss ratio of the first Stokes to fundamental laser on the pulse parameters of the first Stokes. The results of the Gaussian and top-head pumpings show similar trends despite some discrepancies. The new theories and numerical results will help design passively Q-switched intracavity Raman lasers of high performance.

Optimization of pulse-width of passively Q-switched lasers by taking into account intracavity laser spatial distribution

The intracavity photon density and the initial population-inversion density in the diode-pumped passively Q-switched lasers are assumed to be Gaussian spatial distributions. The space-dependent rate equations are solved numerically. The key parameters of a passively Q-switched laser with the shortest pulse-width under Gaussian approximation are determined, and a group of general curves are generated for the first time. The curves clearly show the dependence of the optimal key parameters on the parameters of the gain medium, the saturable absorber, and the resonator. In addition, the importance including the space variation is also shown. The optimal calculations for a diode-pumped passively Nd:YVO 4 laser are presented to demonstrate the use of the curves and the related formulas.

Theoretical and Experimental Study on the Self-Raman Laser With<tex>$hbox Nd:YVO_4$</tex>Crystal

The intracavity photon densities and the initial population inversion density were assumed to be Gaussian distributions in the rate equations of the laser diode end-pumped actively Q-switched intracavity Raman laser. These space-dependent rate equations were solved numerically. In the experiment, an efficient self-Raman laser was realized based on the multifunctional Nd:YVO4 laser crystal with the acoustooptic Q-switch. The output, temporal, and spectral characteristics of the self-Raman laser were investigated experimentally in detail. The performance of the self-Raman laser was studied numerically, and the theoretical results showed the main trends of the intracavity Raman laser, which are in agreement with the experimental ones

Optimization of Passively Q-switched Lasers by Taking into Account Intracavity Laser Spatial Distribution

The intracavity photon density and the initial population-inversion density in the diode-pumped passively Q-switched lasers are assumed to be Gaussian spatial distributions. The space-dependent rate equations are solved numerically. The key parameters of an optimally coupled passively Q-switched laser under Gaussian approximation are determined, and a group of general curves are generated for the first time. These key parameters include the optimal normalized coupling parameter and the optimal normalized saturable absorber parameter that maximize the output energy, and the corresponding normalized energy, normalized peak power, and normalized pulse width. The curves clearly show the dependence of the optimal key parameters on the parameters of the gain medium, the saturable absorber, and the resonator. In addition, the importance including the space variation is also shown. The optimal calculations for a diode-pumped passively Nd: YVO4 laser are presented to demonstrate the use of the curves and the related formulas.

Optimization of peak power of passively Q-switched lasers by taking into account intracavity laser spatial distribution

The intracavity photon density and the initial population-inversion density in the diode-pumped passively Q-switched lasers are assumed to be Gaussian spatial distributions. The space-dependent rate equations are solved numerically. The key parameters of an optimally coupled passively Q-switched laser under Gaussian approximation are determined, and a group of general curves are generated for the first time. These key parameters include the optimal normalized coupling parameter and the optimal normalized saturable absorber parameter that maximize the peak power, and the corresponding normalized energy, normalized peak power, and normalized pulse width. The curves clearly show the dependence of the optimal key parameters on the parameters of the gain medium, the saturable absorber, and the resonator. In addition, the importance including the space variation is also shown. The optimal calculations for a diode-pumped passively Nd : YVO 4 laser are presented to demonstrate the use of the curves and the related formulas.

Diode-pumped passively Q-switched intracavity-frequency-doubling Nd:GdVO4/KTP green laser with Cr4+:YAG saturable absorber

The intracavity photon density is assumed to be Gaussian spatial distributions and the nonlinear loss that is due to second-harmonic generation (SHG) to the photon-density equation is given under Gaussian spatial distributions in the rate equations for a diode-pumped passively Q-switched intracavity-frequency-doubling Nd:GdVO 4 /KTP laser with Cr 4+ :YAG saturable absorber. These space-dependent rate equations are solved numerically. The dependences of pulse width, pulse repetition rate, single-pulse energy and peak power on incident pump power are obtained for the generated-green-laser pulses. In the experiment, a diode-pumped passively Q-switched intracavity-frequency-doubling Nd:GdVO 4 /KTP laser with Cr 4+ :YAG saturable absorber is realized and the experimental results are consistent with the numerical solutions.

Laser-diode end-pumped passively Q-switched intracavity-frequency-doubling Nd:GdVO/sub 4//KTP Green laser with GaAs saturable absorber

The intracavity photon density is assumed to be Gaussian spatial distributions, and the nonlinear loss that is due to second-harmonic generation (SHG) to the photon-density equation is given under Gaussian spatial distributions in the rate equations for a laser-diode end-pumped passively Q-switched intracavity-frequency-doubling Nd:GdVO/sub 4//KTP laser with a GaAs saturable absorber. These space-dependent rate equations are solved numerically. The dependences of pulsewidth, pulse repetition rate, single-pulse energy, and peak power on incident pump power are obtained for the generated-green-laser pulses. In the experiment, a laser-diode end-pumped passively Q-switched intracavity-frequency-doubling Nd:GdVO/sub 4//KTP laser with a GaAs saturable absorber is realized, and the experimental results are consistent with the numerical solutions.