Space-dependent Rate Equations Research Articles

Theoretical and experimental study of a laser diode end-pumped passively <inline-formula><math display="inline" overflow="scroll"><mi>Q</mi></math></inline-formula>-switched <inline-formula><math display="inline" overflow="scroll"><msub><mi>Nd:YVO</mi><mrow><mn>4</mn></mrow></msub></math></inline-formula> laser with <inline-formula><math display="inline" overflow="scroll"><msup><mrow><mi>Cr</mi></mrow><mrow><mn>4</mn><mo>+</mo></mrow></msup><mo>:</mo><mi>YAG</mi></math></inline-formula> saturable absorber

The intracavity photon density and the initial population-inversion density are assumed to be Gaussian spatial distributions in the rate equations of a laser diode end-pumped passively Q-switched Nd:YVO4 laser with Cr4+:YAG saturable absorber. These space-dependent rate equations are solved numerically. In an experiment, such a laser has been realized. The dependences of pulse width, pulse repetition rate, single-pulse energy, and peak power on incident pump power were measured, and the experimental results are consistent with the numerical solutions.

Analysis of a laser-diode end-pumped passively Q-switched Nd:GdVO4 laser with Cr4+:YAG saturable absorber

Abstract The intracavity photon density is assumed to be Gaussian spatial distribution and the longitudinal variation of the intracavity photon density is also considered in the rate equations of a laser-diode end-pumped passively Q-switched Nd:GdVO 4 laser with Cr 4+ :YAG saturable absorber. These space-dependent rate equations are solved numerically. From the numerical solutions, we obtain the dependences of pulse width, pulse repetition rate, single-pulse energy and peak power on pump power. The experiments performed on a laser-diode end-pumped Nd:GdVO 4 laser passively Q-switched by a Cr 4+ :YAG saturable absorber are consistent with the theoretical calculations.

Relationship between thermally induced lensing and output power for a high‐power laser‐diode side‐pumped solid‐state laser

AbstractThe variable focal length of thermal lensing in grains of a thermally loaded Nd:YAG crystal rod have been calculated and compared with the measurements of our system. By use of the space‐dependent rate equations, the analytical expression of the output power on the pump power, which consists of the factors of threshold volume and the focal length of thermal lensing, is presented. We investigate the threshold pump power, and the relationships between the output power and the pumping power under different lengths of thermal lensing. Experimental results concerning the output power of fundamental mode and the pump power, which are related to the thermal lensing and agreeable to the theoretical analysis are given. Finally, the optimized experimental output power of our laser system is obtained. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 42: 361–365, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20305

Rate equations and solutions of a laser-diode end-pumped passively Q-switched intracavity doubling laser by taking into account intracavity laser spatial distribution

The intracavity photon density and the initial population-inversion density are assumed to be Gaussian spatial distributions in the rate equations of a laser-diode end-pumped passively Q-switched intracavity-frequency-doubling Nd:YVO 4/KTP laser with Cr 4+:YAG saturable absorber. These space-dependent rate equations are solved numerically. In the experiment, a laser-diode end-pumped passively Q-switched Nd:YVO 4/KTP laser with Cr 4+:YAG saturable absorber is realized. The dependences of pulse width, pulse repetition rate, single-pulse energy and peak power on incident pump power are measured for the generated-green-light pulses, and the experimental results are consistent with the numerical solutions.

Modeling of diode-end-pumped Q-switched solid-state lasers: influence of energy-transfer upconversion

The influence of energy-transfer upconversion (ETU) on diode-end-pumped actively Q-switched lasers is investigated by the space-dependent rate equation analysis. The numerical analysis reveals that as a consequence of the ETU effect there is an optimum pump size for yielding the largest pulse energy and a different optimum pump for yielding the highest peak power at a given pump power. The practical example of the diode-pumped actively Q-switched Nd:YAG laser has been used to verify the present model.

Theory of intracavity-frequency-doubled solid-state four-level lasers

The spatial distributions of the pumping, the population inversion density, and the intracavity photon densities of the fundamental and the second harmonic are taken into account in the rate equations of the intracavity-frequency-doubled cw lasers. By normalizing the related parameters, it is shown that the general solution of these space-dependent rate equations is dependent upon three dimensionless paramenters: the pump to laser-mode size ratio, the normalized pump level, and a parameter written as ηSHG, which is related to the ability of the nonlinear crystal to convert the fundamental to the second harmonic. By numerically solving these rate equations, a group of general curves are obtained to express the relations between the solution and the three dimensioniess parameters. In addition, the optimal pump to laser-mode size ratio and the optimal ηSHG are determined. A comparison with the result obtained under the plane-wave approximation is also given.

Diffraction losses of high power solid state lasers

A uniform pumping distribution is very important in a side pumped rod geometry. Based on space-dependent rate equations, the threshold pump power and the TEM 00 mode output power of a solid state laser with a uniform pump are obtained. The diffraction losses arising from thermally induced spherical aberration have been estimated by the Strehl intensity ratio. The diffraction losses may prevent the solid state laser from ultrahigh power levels before the thermal fracture limitation. The diffraction losses for different sizes of laser beams and the laser rods are discussed. A significant increase in average power and a great decrease in thermal distortion and birefringence at cryogenic temperature have been analyzed in cooperation with thermal induced diffraction losses.

Diffraction losses of Nd:YAG and Yb:YAG laser crystals

Based on space-dependent rate equations, the lowest threshold input power for a diode end-pumped solid-state laser is obtained for the pump spot size w p→0. However, as the pump beam waist is decreased, the thermally induced effects in the laser rod would be very high. Diffraction losses caused by radial and tangential variations of refractive index have been analyzed and compared for the Nd : YAG and the Yb : YAG at room temperature ( 300 K ) and liquid-nitrogen temperature ( 77 K ).

Dynamics and control of a multimode laser: Reduction of space-dependent rate equations to a low-dimensional system.

We suggest a quantitatively correct procedure for reducing the spatial degrees of freedom of the space-dependent rate equations of a multimode laser that describe the dynamics of the population inversion of the active medium and the mode intensities of the standing waves in the laser cavity. The key idea of that reduction is to take advantage of the small value of the parameter that defines the ratio between the population inversion decay rate and the cavity decay rate. We generalize the reduction procedure for the case of an intracavity frequency doubled laser. Frequency conversion performed by an optically nonlinear crystal placed inside the laser cavity may cause a pronounced instability in the laser performance, leading to chaotic oscillations of the output intensity. Based on the reduced equations, we analyze the dynamical properties of the system as well as the problem of stabilizing the steady state. The numerical analysis is performed considering the specific system of a Nd:YAG (neodymium-doped yttrium aluminum garnet) laser with an intracavity KTP (potassium titanyl phosphate) crystal.

Influence of the thermal effect on the TEM_00 mode output power of a laser-diode side-pumped solid-state laser

A fraction of pump power has been converted to TEM00 mode laser power for a side-pumped solid-state laser by use of a space-dependent rate equation. We investigated the pump-to-mode (TEM00) ratio when scaling laser-diode side-pumped solid-state lasers to high-power levels by including the thermal effect in the space-dependent rate equation. Based on the assumption that Gaussian pump power is the same at any cross section of a laser rod, we resolved the output power with a space-dependent rate equation; temperature distribution in the laser rod was obtained; the optical path difference distribution was derived, and we estimated the diffraction losses that result from thermally induced spherical aberration by use of the Strehl intensity ratio. We determined that thermally induced diffraction losses are strongly dependent on pump power and on the pump-to-mode ratio.

Modeling of passively Q-switched lasers

The intracavity photon density and the initial population-inversion density in the diode-pumped passively Q-switched laser rate equations are assumed to be Gaussian spatial distributions. These space-dependent rate equations are solved numerically, and a group of general curves are generated. These curves clearly show the dependence of the pulse characteristics on the pump- to laser-mode size ratio and the parameters of the gain medium, the saturable absorber, and the resonator. They can also be used to estimate the pulse parameters of an arbitrary diode-pumped passively Q-switched laser and to determine the optimal pump- to laser-mode size ratio. In addition, these curves are not limited to diode-pumped lasers. Sample calculations for a diode-pumped Nd3+:YVO4 laser and a flash-lamp pumped Nd3+:YAG laser are presented to demonstrate the use of the curves and the related formulas.

Influence of energy-transfer upconversion on the performance of high-power diode-end-pumped CW lasers

The influence of energy-transfer upconversion (ETU) on the performance of diode-end-pumped lasers is studied by including ETU effects into the space-dependent rate equations. The dependence of ETU rates on the mode-to-pump size ratio and on the output mirror transmission is derived. Experiments for Nd:YAG and Nd:YVO/sub 4/ crystals are performed to validate the present model. It is found that the ETU process increases the sensitivity of the output power to the output mirror transmission but its influence on the output power is not significant for low output transmission.

Influence of pump beam size on laser diode end-pumped solid state lasers

Based on space-dependent rate equation, the lowest threshold input power for diode end-pumped solid state lasers is obtained for pump spot size w p → 0. However, when the pump beam waist is decreased, the far-field half-angle increases due to the same beam quality, which will influence the match between the pump volume and mode volume. Most importantly, when the pump beam waist is decreased, the temperature and temperature gradient in the laser rod would be very high due to the resulting heat, which would cause material distortion, variation of refractive index, instability of laser resonator etc. We analyze the temperature distributions with different pump beam sizes and conclude that the condition w p ≈ w 0 (the radius of the laser beam at the laser rod) is often taken as a rough guide to the optimum case.

Modeling of diode-pumped actively Q-switched lasers

The intracavity photon density and initial population inversion density in the diode-pumped actively Q-switched laser rate equations are assumed to be Gaussian distributions. These space-dependent rate equations are solved numerically and a group of general curves are generated. By using these curves and the related formulas, the pulse parameters of an arbitrary actively Q-switched laser can be easily estimated and an optimally coupled Q-switched laser can be designed. A sample calculation for a Q-switched Nd/sup 3+/:YVO/sub 4/ laser is presented to demonstrate the use of the curves and the related formulas.

Performance of an optical fiber butt-coupled Cr 3+:LiSrAlF 6 laser

Pumping of a Cr 3+:LiSAF laser through a butt-coupled optical fiber is investigated for a compact all-solid-state laser assembly. Theoretical space-dependent rate equation analysis is used to predict the output characteristics of the Cr 3+:LiSAF laser for different cavity parameters, optical fiber characteristics, and Cr 3+ doping rates. The effect of the positional and angular mismatch of the pump beam with respect to the laser mode is also included in the model. The analysis explicitly shows that the slope efficiency can be improved by improving the mode coupling volume in the Cr 3+:LiSAF crystal. Experimental output characteristics are reported when the Cr 3+:LiSAF laser is pumped through optical fibers with different combinations of core diameter and numerical aperture. The experimental results are in good agreement with the theoretical modeling.

Performance of a neodymium yttrium aluminum borate green laser pumped with a fiber-coupled laser diode

Using a space-dependent rate-equation model and considering the effect of pump beam quality, the optimum pump condition for a fiber-coupled diode end-pumped neodymium yttrium aluminum borate laser has been determined. Under optimum pump conditions, greater than 10% optical-to-optical conversion efficiency was obtained when the laser was pumped by a fiber-coupled laser diode with good beam quality. The influence of pump beam quality on the conversion efficiency is also discussed.

Optimization in scaling fiber-coupled laser-diode end-pumped lasers to higher power: influence of thermal effect

The optimum mode-to-pump ratio in scaling fiber-coupled laser-diode end-pumped lasers to higher power has been investigated by including the thermal effect into the space-dependent rate equation analysis. The optical path difference (OPD) distribution has been derived as a function of the pump-beam quality, focus position of pumping light, and pump radius at the focal plane under the assumption that the end faces of the crystal are thermally insulated. The diffraction losses arising from thermally induced spherical aberration have been estimated by the Strehl intensity ratio. The present results for the optimum mode-to-pump ratio are markedly different from previous analyses in which thermal effects are neglected. Here, the optimum mode-to-pump ratio is a decreasing function of input pump power, and is less than unity in the case of a slightly high pump power. The practical example of a Nd:YAG laser pumped by a 13-W fiber-coupled laser diode is considered to confirm our physical analysis.

Polarization-mode dynamics in strained 1.3 μm [formula omitted] lasers under picosecond current modulation

The dynamic behaviour of the TE and TM polarized output from ridge-waveguide InGaAsP InP lasers which are electrically pumped with 300 ps pulses is studied experimentally and theoretically. For the first time, different polarization characteristics depending on the amplitude of the current pulse and the level of the dc bias are reported. While strong mode competition resulting in TE or TM mode emission in separate current intervals is found in the cw regime, simultaneous lasing of both modes, transients between TE and TM in the ps range as well as common GHz relaxation oscillations of TE and TM emission are observed under pulsed excitation. TE and TM pulses shorter than 40 ps are measured. The laser dynamics is modelled through space-dependent rate equations. Numerical results suggest, that the fast polarization switching is due to a lateral shift of the TE and TM modes against each other.

Misalignment sensitivity of laser-diode pumped solid-state lasers

An analysis of the misalignment sensitivity of diode-pumped solid-state lasers is presented, based on a space-dependent rate equation approach. The drop in the laser output power, mainly related to the spatial overlap of the laser mode with the pump beam distribution inside the active material, is calculated as a function of displacement and rotation of the mode axis with respect to the pump beam axis. For any given resonator geometry, laser sensitivity to mirror tilting or pump beam perturbations can then be easily evaluated. The experimental results obtained with a diode-pumped Nd: YAG laser are in good agreement with the theoretical predictions.

Design criteria for mode size optimization in diode-pumped solid-state lasers

Based on space-dependent rate equation analysis, design and optimization criteria for the mode size of diode-pumped solid-state lasers are proposed, assuming an TEM/sub 00/ single transverse mode in the resonator and circular or elliptic Gaussian pump beam. The optimum ratio between mode and pump spot size increases with input power and ellipticity of the pump beam. Simple plots may be used as guidelines to determine, in addition to the optimum spot size, the corresponding laser threshold, slope efficiency, and expected output power. Experimental examples are given for an end-pumped Nd:YAG laser, showing good agreement with the design predictions. >