Influences of pump beam distribution on thermal lensing spherical aberration in an LD end-pumped Nd:YAG laser

A numerical investigation is made on the thermal lensing and spherical aberration effect in an LD end-pumped Nd:YAG laser. Based on the finite element method (FEM), the laser rod temperature distribution is calculated and the focal length of the thermal lens is deduced, the influences of pump beam on the thermal lensing spherical aberration are mainly studied. The results show the thermal lens which focal length varied with the radial coordinate r is not an ideal lens. Given the heat dissipation boundary conditions, the radial dependent focal length will be shortened when the pump power raised or the waist radius of the pump beam reduced, meanwhile the radial differences of the focal length will decrease when the pump power increased. For a Super-Gaussian profile pump beam, the higher the exponent number, the more similar to flat top the pump beam is, and the less the radial differences of the focal length are.     

Beam divergence and refractive power of directly coated solid state lasers

A relation between the far field divergence angle of a laser output beam and the elements of the laser resonator matrix is derived. This relation is applied to the resonator matrix of directly coated laser rods and yields an expression for the far field angle θ_m of the output beam in terms of the pump light induced refractive power D of the rod. By means of this expression D versus the average pumping power is calculated from the experimental values of θ_m for several laser rods and is found to be in good agreement with previously published values.     

Thermal lens determination of LD end-pumped solid-state laser with stable resonator by slit scanning method

A simple method to determine the thermal focal length of LD end-pumped solid-state laser with stable resonator is presented. The M² factor describing the quality of the beam can be obtained by scanning a slit through the multi-mode Gaussian beam field. The waist width of the beam and the corresponding TEM₀₀ under the same parameters of laser are then deduced through the law of multi-mode Gaussian beam propagation. Based on the standard matrix theory of stable resonator, the thermal focal length of the gain medium can be easily achieved. To show the application of this approach, the thermal focal length of an LD pumped Nd:YVO₄ laser is measured and the experimental results are in agreement with the theoretical prediction.     

端面抽运方形复合YAG温度场及热透镜研究

采用数值方法研究了方形截面复合Nd∶YAG激光晶体棒在端面抽运情况下的温度分布及热透镜效应,得到复合激光晶体内温度场的数值解和径向温度梯度引起的轴向传播光相位延迟分布ΔΦT(r),并与同条件下普通晶体的结果进行了比较.结果表明,吸收系数越大,两种晶体中最高温度相差也越大.采用复合晶体可以大幅度降低激光晶体内的温升,同时减小端面形变造成的透镜效应.复合晶体的ΔΦT(r)与普通晶体相似,且不满足对半径r的二次方关系.在rwp时,ΔΦT(r)相对于参考球面透镜的相位畸变Δφ随r的增大而急剧增大.     

Influence of spherical aberrations on the performance of dynamically stable resonators

Spherical aberrations of thermal lens of the active media are severe when the solid state lasers are strongly pumped. The aberrations influence the mode profile, the diffraction loss, the output power and other laser beam properties, especially for a dynamically stable resonator with large TEM₀₀-mode volume. Self-consistent modes in a resonator with aberrations are calculated using Fox-Li diffraction iterative algorithm. There are side lobes with the fundamental mode when the spherical aberration is introduced, hence the beam quality is deteriorated. The calculated results agree well with the experimental data. The beam filling factor plays an important role in the design of a laser system. The optimum value of the beam filling factor should be determined by the experimental results according to the spherical aberration effect.     

InnoSlab混合腔输出光束质量的理论研究

对InnoSlab Laser用混合腔的输出光束质量问题从热透镜效应和腔镜的不对准两个方面的影响进行理论分析,并从远场光强分布、远场发散角、光腰半径、光束质量因子M²值和桶中功率曲线等几个角度进行了讨论,特别是离轴非稳腔方向上腔镜倾斜对光束质量的影响,利用M²值和PIB曲线两个参数共同评价非稳腔的光束质量,对目前并无统一标准的非稳腔光束质量评价问题提供了有意义的参考. 关键词： InnoSlab 混合腔 光束质量 桶中功率     

Influence of spatial mode matching in end-pumped solid state lasers

We present investigations on the influence of mode matching on the efficiency of longitudinally pumped solid state lasers. In a theoretical part we enhance an existing model for four level lasers from idealized cylindrical modes to arbitary pump and laser modes in a random relative position thereby neglecting beam deformation due to thermal effects. The theoretical predictions were confirmed experimentally with an end-pumped Nd:YAG rod operated at 1064 nm. To investigate the effect of misalignment on the efficiency we used a Ti-Sapphire pump laser which was displaced relative to the laser beam. To establish the influence of arbitary pump modes on laser performance a diode laser equipped with coupling optics served as pump source for the same resonator. The resulting decrease in slope efficiency compared to the Ti-Sapphire pumped system could be explained in terms of limited mode overlap due to the characteristic pump field distribution produced by the diode coupling optics.     

二极管侧面抽运Nd:YAG/KTP腔内倍频百瓦级绿光激光器

为了获得百瓦级激光二极管侧面泵浦绿光激光器,设计了双棒串接、双声光调Q的Z型谐振腔结构.依据光束传输矩阵,通过软件模拟并计算了激光晶体内基模半径随屈光度的变化以及倍频晶体附近腔内光场在子午面和弧矢面内的分布情况,筛选出理想的谐振腔参数.在总泵浦功率1 080 W,声光调Q重复频率为10 kHz时,获得532 nm绿光最大平均输出功率为174.1 W,脉冲宽度为160 ns,光-光转换效率为16.1%,光束质量因子M2x＝9.63,M2y＝9.78.实验结果表明,使用双棒串接、双声光调制Z型腔结构,可以获得百瓦级高功率高光束质量532 nm绿光输出.     

Effect of chromatic aberration on Gaussian beams: non-dispersive laser resonators

The propagation of a non-monochromatic (polychromatic) TEM₀₀ Gaussian beam in vacuum, its passage through a thin plate and its transformation by a thin lens are studied in the case of a non-dispersive laser resonator. The basic assumptions of the model are as follows: optical fields are stationary and plane-polarized, the paraxial wave equation is valid, an equivalent non-dispersive hemiconfocal resonator represents the lasing medium and its stable resonator, the laser emits in a single mode. It is also assumed that the plate and the lens have large transverse dimensions. Mathematical expressions, for beam radius, divergence, radius of curvature and beam parameter product, are obtained. A beam quality factor for polychromatic Gaussian beams is defined and its value calculated in each case of interest. It is proposed to simulate a dispersive laser resonator by a non-dispersive resonator complemented with a plate and/or a thin lens.     

二极管侧面抽运Nd∶YAG/KTP腔内倍频百瓦级绿光激光器

为了获得百瓦级激光二极管侧面泵浦绿光激光器,设计了双棒串接、双声光调Q的Z型谐振腔结构。依据光束传输矩阵,通过软件模拟并计算了激光晶体内基模半径随屈光度的变化以及倍频晶体附近腔内光场在子午面和弧矢面内的分布情况,筛选出理想的谐振腔参数。在总泵浦功率1080W,声光调Q重复频率为10kHz时,获得532nm绿光最大平均输出功率为174.1W,脉冲宽度为160ns,光-光转换效率为16.1%,光束质量因子M2x＝9.63,M2y＝9.78。实验结果表明,使用双棒串接、双声光调制Z型腔结构,可以获得百瓦级高功率高光束质量532nm绿光输出。     

激光二极管端面泵浦Yb:YAG圆棒热效应研究

基于激光二极管端面泵浦Yb∶YAG棒工作特点的分析,提出了端面绝热、周边恒温的激光晶体热分析模型,采用了一种新的热传导方程求解方法,得到了超高斯光束端面泵浦Yb∶YAG棒温度场的一般解析表达式。同时分析了不同阶次、不同光斑半径、不同功率超高斯光束以及晶体参数改变时对于Yb∶YAG棒温度场分布的影响。研究结果表明,若准直聚焦到Yb∶YAG棒泵浦面42.5W的光束具有4阶超高斯强度分布时,掺Yb3+质量分数为10.0at.%、长度为2.5mm、半径为2mm的Yb∶YAG棒的泵浦面获得74.20℃的最高温升。新的热传导方程求解方法在研究激光棒温度场分布方面具有计算量小、精度高等特点。研究结果对减小激光晶体的热效应,提高全固态Yb∶YAG激光器性能提供了理论依据。     

脉冲激光二极管侧面抽运Nd∶YAG激光器晶体时变热效应

采用数值计算的方法,对脉冲激光二极管三向侧面抽运固体激光器中,激光晶体的温度场时变分布进行了计算. 分析了三向侧面抽运情况下晶体内光强分布,在此基础上,采用有限元法,以脉冲激光二极管侧面抽运Nd∶YAG激光器为例,对单脉冲过程中晶体温度分布及其影响因素进行分析. 结果表明,晶体升温过程受到抽运条件以及散热条件的影响,但是主要受到抽运条件即抽运光强度和光束半径的影响,降温过程受到晶体热物性参数和晶体半径以及散热条件的影响. 当晶体温度达到周期性分布后,由于晶体径向温度梯度的周期性变化,引起通过晶体的平面光波的中心和边缘光线相对光程差也随时间作周期性变化. 关键词： 激光二极管侧面抽运固体激光器 热效应 有限元法 时变过程     

Propagation parameters of the beam extracted from a diode pumped Nd:YAG ceramic slab laser with a hybrid stable–unstable resonator

We analyze the propagation properties of the beam extracted from a diode pumped ceramic Nd:YAG slab laser adopting a hybrid stable–unstable resonator. Such a resonator produces a beam characterized by an Hermite–Gauss mixture-like distribution in one transverse direction and a hard-edge diffracted distribution on the other transverse direction. The beam propagation parameters M_x² and M_y² are measured for different values of the diodes driving current. We obtain a beam parameter product smaller than 3 mm mrad in both transverse directions and in the whole range of powers, up to an extraction of 220 W in a QCW regime.     

Thermal lensing and spherical aberration in high-power transversally pumped laser rods

A precise knowledge of the thermal effects in laser crystals is very important for high-power laser design, but some relevant parameters are most often neglected in their calculation. In this paper, with the example of transversally pumped, high-power Nd:YAG lasers, we show the importance of the thermal dependence of the gain medium’s physical properties such as the thermal conductivity, the dn/dT and the expansion coefficient on the thermal aberration and thermal lensing values; we also prove that the choice of the resonator can influence the amount of spherical aberration. Finally, analytically calculated values are confronted to experimental values, and show a very good agreement.     

A highly efficient 5 kW peak power Nd:YAG laser with time-shared fiber optic beam delivery

Here, we report on the development of an efficient, high peak power lamp pumped Nd:YAG laser with time-shared fiber optic beam delivery. A maximum average output power of 270 W with 100 J maximum pulse energy and 5 kW peak power has been achieved with an electrical to laser conversion efficiency of 5.4%, which is on higher side for typical lamp pumped solid-state lasers. We have improved efficiency by spectral conversion and water flow optimization in the pump cavity, with a resulting beam quality comparable to commercial systems of similar power level. The resonator has been designed for stable operation from single-shot to 200 Hz repetition rate. A study of pulse-to-pulse laser energy stability for different resonator configurations has also been performed. The resonator was designed to achieve a good beam quality for the whole range of operation with a maximum beam parameter product of 15 mm mrad (M²45). A simple mechanism for time-shared fiber optic port selection has also been devised. Material processing applications such as cutting of stainless steel sheets up to 14 mm thickness and welding of metals such as carbon steel with weld depths up to 2 mm using the developed laser system has also been reported.     

The LD end-pumped Q-switched solid-state laser design software based on the adaptive method

In the LD end-pumped acousto-optic (A-O) Q-switched solid-state laser, according to the requirements of users on the laser peak power, the pulse width, the repetition rate and the beam quality factor M², if the main parameters of the pumping source and the laser resonator can be pre-designed by a software, will effectively guide experiments, and save cost. A kind of laser design software is introduced in this paper, which is based on the adaptive adjustment method and using MATLAB/C mixed programming. According to the user requirements, a compact LD end-pumped A-O Q-switched Nd:YAG laser which peak power is 100-kW-class can be designed and actual outputs can be calculated based on the design results. Drawing the laser pulse waveform, analyzing of the thermal effect in laser gain medium and drawing the temperature distribution map, exporting and saving the data are the additional functions of this software.     

Thermal effects in high-power Nd:YAG disk-type solid state laser

An investigation of thermal effects in a high-power Nd:YAG disk-type solid state laser pumped with different pump beam transverse profiles is carried out by numerical simulation based on the finite element method (FEM). Impact of the heat sink on the thermal effects is included in the simulation. The distribution of first principle stress, thermally induced birefringence, including the distribution and variation of the birefringence loss, are studied. The characteristics of the phase variation are analyzed with consideration of the temperature gradient, deformation, strain and thermal stress. Thermal lensing is explored as a function of pump power and of the radius pumped with different pump beam transverse profiles. The non-parabolic part of optical phase distortion is simulated. Furthermore, the characteristics of the bi-focus of the disk laser are also studied. Experiments on the maximum tensile stress distribution and depolarization loss are carried out. The presented calculations are in qualitative agreement with the experimental observations.     

环形激光二极管抽运棒状激光器中瞬态温度和热应力分析

直接从激光二极管发光强度的角分布出发,采用光线追迹方法获得激光棒内的热沉积分布,在此基础上采用热传导模型和热力模型,比较了不同抽运功率、不同棒半径下达到稳态温度分布的时间,并且对稳态和瞬态热应力进行了详细模拟计算。结果表明,采用环形激光二极管阵列侧面抽运的棒状激光器中的热效应问题十分严重,不同的抽运结构参量下,温度分布不同;达到稳态所需时间随棒半径增大而增加,而不受抽运功率的影响;抽运功率越大,棒内温差增大,热应力也越大;热破坏主要集中于激光棒中心区域和表面区域。     

Numerical investigation of beam quality in unstable optical resonators and the effects of practical imperfections

Field characteristics and beam quality of confocal positive branch unstable resonator under some practical imperfections has been investigated. Based on Fresnel-Kirchhoff integral, the near and far field intensity of the resonator was calculated numerically. Using the second order moment method, the beam quality factor, M² of the resonator was also calculated. Variety of practical distorting affects, mainly misalignment, off-axis, and thermal deflection of the mirrors, as well as gain non-uniformity were considered in these calculations. The results show that the beam quality factor is more sensitive to the off-axis and misalignment distortions while the non-uniform gain has significant effect only for unusual conditions. The effects of geometrical parameters, i.e. Fresnel number as well as magnification factor on the beam quality were also investigated.     

热透镜的球差效应对大基模体积激光谐振腔模式的影响

固体激光器在强抽运的条件下,激光晶体热透镜的球差效应是不容忽视的,尤其是在大基模体积的动态稳定腔中,会影响谐振腔的振荡模式,进而影响腔内损耗和输出功率.通过Fox-Li的衍射迭代算法,分析了谐振腔的自再现模,表明在热透镜球差效应作用下,基模的光强分布出现了旁瓣,并由此带来了光束质量的下降,最后通过实验结果验证了理论分析,指出光束填充因子是激光器设计的一个重要因素,其最佳值需要根据球差效应的强弱,通过实验的方法来确定. 关键词： 热透镜 球差效应 谐振腔模式