Measurement of στ product of solid state laser materials by an alternative method: Application to Nd3+ doped YVO4 crystal for 4 F 3/2→4 I 11/2 transition

In this paper an alternative approach for measurement of στ product for ⁴ F _3/2→⁴ I _11/2 transition of Nd³⁺ doped YVO₄ crystal is reported. In this method a microchip laser is formed by keeping a small piece of the sample in plane-plane resonator and a diode laser (808 nm) is used for pumping. The pump power induced thermal lensing effect is used to make the cavity stable. The cavity mode area is estimated by measuring the thermal lens focal length at the threshold and the average pump area is measured by Gaussian fit to the intensity profiles of the pump beam. The value of στ product of Nd:YVO₄ crystal obtained by this method is within 10% of the reported values. The advantage of this method is that it is a simple method for direct measurement of στ product of laser crystals.     

Measurement of beam quality factor (M) by slit-scanning method

Beam quality factor (M²) and far-field scattering angle of LD end-pump Nd : YVO₄ laser were measured by slit-scanning method. The experimental results showed that the laser operated on a multi-mode state. The corresponding analytical treatments for slit-scanning method and M² factor measurement also were presented in this paper.     

A simple method to determine the thermal focal length of solid-state lasers with rate equation

A simple method to measure the thermal focal length of solid-state laser with rate equation was presented. By measuring the output beam power of lasers, the beam waist of oscillating wave can be deduced from rate equation under the stable oscillation condition. Based on the ABCD matrix theory, the thermal focus of the gain medium was easily obtained. The thermal focus of a LD end-pumped Nd:GdVO₄ laser was measured and the experimental results agreed with the theoretical predication.     

An alternative approach to determine the spot-size of a multi-mode laser beam and its application to diode laser beams

An alternative approach is suggested to determine the spot-size of a multi-mode laser beam. It has been shown by simulations that the suggested approach can give the beam quality factor and characteristic radius with less than 5% error. Unlike the power content method, the proposed method is applicable to the beams even with diameter one tenth of the CCD size. The new approach has been applied to a multi-mode diode laser output and it is shown that the ABCD matrix analysis can be used for beam propagation, with the measured parameters of the laser.     

Compact, efficient diode-end-pumped Nd:GdVO4 slab continuous-wave 912-nm laser

A fiber-coupled laser-diode (LD) end-pumped Nd:GdVO₄ slab continuous-wave (CW) 912-nm laser and an LD bar end-pumped Nd:GdVO₄ slab CW 912-nm laser are both demonstrated in this paper. Using the fiber-coupled LD of end-pumped type, a highest CW 912-nm laser output power of 10.17 W is obtained with a high optical-to-optical conversion efficiency of 24.6% and a slope efficiency of 34.5%. The measured M² factors of beam quality in x and y directions are 5.3 and 5.1, respectively. Besides, an LD bar of end-pumped type is used to realize CW 912-nm laser output, which has the advantages of compactness and low cost. When the pump power is 38.8 W, the output power is 8.87 W and the measured M² factors of beam quality in x and y directions are 16 and 1.31, respectively. In order to improve the beam quality of the 912-nm laser at x direction, a new quasi-concentric laser resonator will be designed, and an LD bar end-pumped Nd:GdVO₄ slab high-power CW 912-nm TEM₀₀ laser will be realized in the future.     

Effect of absorbed pump power on the quality of output beam from monolithic microchip lasers

The dependence of the beam propagation factor (M ² parameter) with the absorbed pump power in the case of monolithic microchip laser under face-cooled configuration is extensively studied. Our investigations show that the M ₂ parameter is related to the absorbed pump power through two parameters (α and β) whose values depend on the laser material properties and laser configuration. We have shown that one parameter arises due to the oscillation of higher order modes in the microchip cavity and the other parameter accounts for the spherical aberration associated with the thermal lens induced by the pump beam. Such dependency of M ² parameter with the absorbed pump power is experimentally verified for a face-cooled monolithic microchip laser based on Nd³⁺ -doped GdVO₄ crystal and the values of α and β parameters were estimated from the experimentally measured data points.     

Estimation of thermal lensing effect in the high-power end-pumped direct-cut crystal lasers

At this working, analytical (with Gaussian pump beam profile) and numerical FEM (with super-Gaussian pump beam profile) methods were compared for estimation of thermal lensing effect in the diode-end-pumped solid-state laser rods. These results were applied to the design and realization of a direct-cut (i.e., cut in right-angle ) crystal Nd:YVO₄ laser. The results showed that for such crystal (direct-cut), two methods obtained almost the same results, but slightly different from experimental results. However, estimation of thermal lensing effect led to realization of a diode-end-pumped Nd:YVO₄ cw high-power laser with good optical quality.     

二极管端面抽运的固体激光放大器自身热透镜焦距测量

通过分析激光经过热透镜后光束半径的变化，提出了利用放大器测量热透镜焦距的方法.根据激光束传输与变换理论，得到了热透镜焦距的表达式，并分析了其前提条件和近似偏差.最后，基于上述理论分析，测量了激光二极管端面抽运Tm,Ho∶GdVO₄放大器的热透镜焦距. 关键词： 热透镜焦距 固体激光 激光束传输与变换     

High-power end-pumped CW Nd:GdVO4 laser formed with a flat–flat cavity

Formed with a flat–flat resonator, a diode-laser-array end-pumped CW Nd:GdVO₄ laser at 1.06 μm, capable of generating 8.6 W of TEM₀₀ output power with optical conversion efficiency of 43% and slope efficiency of 48%, has been developed. The laser beam was nearly diffraction limited, with the beam quality factor measured to be M²=1.22. Under the conditions of multi-mode operation, the laser was able to produce 11.2 W of low-order transverse mode radiation (M²<2) at the incident pump power of 22 W, giving an optical conversion efficiency of 51%, and a slope efficiency of 55%.     

激光光束传输因子M2的一些问题

本文讨论与M²因子有关的一些问题,指出在近轴近似条件下由光束的二阶强度矩定义的M²因子满足M²≥1,其中只有对基模高斯光束等式才成立.由光束的功率通量值定义的M²因子(M_pc²)有可能小于1,M_pc²的大小取决于所定义的光斑半径内包含的光功率的百分数.通过计算光场的二阶矩,我们获得了轴向相干叠加的高斯光束的M²因子的解析解.     

截断部分相干厄米-高斯光束的广义M2G因子

基于广义截断二阶矩法,推导出了截断部分相干厄米-高斯(H-G)光束的广义M²_G因子的解析表达式. 截断完全相干H-G光束、截断高斯谢尔模型(GSM)光束以及截断高斯光束可以做为本文结果的特例给出. 研究表明:截断部分相干H-G光束的广义M²_G因子与截断参数δ,模阶数m以及相干参数α有关. 当δ非常小时,M^{2关键词： 截断部分相干厄米高斯光束 M2_G因子')" href="#">广义M2_G因子 广义截断二阶矩法}     

基于M2因子测量的大气湍流参数的确定方法

基于广义惠更斯-菲涅尔原理以及大气湍流理论,推导出部分相干光束在大气湍流中传输的光束传输M ^{2因子的解析表达式.定量分析了表征大气湍流参数的折射率结构常数 C2_n}和涡旋内尺度 l _{0对 M ^{2因子的影响,并由此提出了一种通过实验测量大气湍流中光束的 M 2因子,进而确定出大气湍流参数的新方法.研究结果表明,由于大气湍流对相干性好的光束影响更为明显,在测量中可采用具有高相干性的基模高斯光束作为测量光源,而测量装 关键词： 2因子')" href="#">光束传输 M 2因子 大气湍流参数 湍流折射率结构常数 湍流涡旋内尺度}}     

厄米-高斯光束的M2因子矩阵

提出了厄米-高斯光场的M²因子矩阵.引入束半宽平方的交叉项、M²因子的交叉项,理论推导出了在同一坐标系下光场旋转一定角度后的M²因子矩阵,数值模拟了与M²因子矩阵有关的各参数随光场旋转角度变化的规律,给出了光场的M²因子矢量点随光场旋转角度变化的轨迹曲线.计算结果与理论推导结果相符,证实了利用M²因子矩阵可以将旋转前后的二维厄米-高斯光场用旋转矩阵统一起来.该方法可推广到对一般的二维高阶高斯光束的光束质量的理论分析上,具有普适性,对光束质量的实际测量有重要的理论指导意义. 关键词： M²因子矩阵')" href="#">M²因子矩阵 厄米-高斯光束 非对称激光束 矩阵光学     

LD端面泵浦Cr4:YAG被动调Q激光器输出特性研究

对激光二极管端面泵浦Cr⁴⁺:YAG被动调QNd:YAG激光器输出特性进行了实验研究.实验研究发现,激光器输出功率及脉冲重复频率随谐振腔长度增大而增大.为解释这一实验现象,测量了泵浦光斑在激光晶体内尺寸,同时计算了激光晶体及Cr⁴⁺:YAG晶体内的基模激光光斑半径随谐振腔长度变化.分析结果表明:激光晶体内泵浦光斑尺寸远小于激光晶体内基模光斑半径,腔模间交叠效率较低;当腔长增加时,激光晶体内的基模激光光斑减小,腔模间交叠效率增加,从而导致输出功率及脉冲重复频率随腔长增加而增加;另外,Cr⁴⁺:YAG晶体内光斑半径也随谐振腔长度减小,引起Cr⁴⁺:YAG晶体漂白时间缩短,导致脉冲重复频率随腔长增加而增加.     

Irradiance-moments characterization of off-axis Gaussian beam combinations by means of the Wigner distribution function

The irradiance-moments characterization of off-axis Gaussian beam combinations is presented in use of the Wigner distribution function (WDF). Analytical expressions for the propagation through an optical paraxial ABCD system, beam propagation factor (M² factor), beam width, far field divergence angle and kurtosis parameter of the resultant beam are derived and illustrated with specific numerical examples. It is reexamined that a flat-topped irradiance profile of the resultant beam can be achieved at a certain plane by appropriately choosing beamlet parameters. As compared with previous work, our results show the advantage of using the WDF and irradiance-moments methods.     

激光二极管双端直接抽运混合腔板条激光器

为减少热透镜效应的影响, 获得高光束质量的激光, 本文利用激光二极管阵列双端直接抽运Nd:YVO₄, 采用负支共焦折叠混合腔结构, 获得最高功率为416 W 1064 nm的激光输出, 光–光转换效率为54.3%, 斜效率为61.6%. 在输出功率为370 W时, 光束质量因子M²在非稳腔和稳腔方向上分别为3.9和4.7.     

High-power continuous-wave Nd:GdVO4 slab laser pumped directly into the F3/2 emitting level

95.6 W continuous-wave laser power output in 880 nm LD partially end-pumped Nd:GdVO₄ slab laser with a hybrid resonator is presented. The slope efficiency and optical-to-optical efficiency were 46.5% and nearly 42.6%, respectively. At the output power of 82 W, beam quality M² factors were 1.1 in the unstable direction and 1.36 in the stable direction, respectively.     

激光二极管抽运下铥/镱共掺碲镓酸盐玻璃光谱特性研究

研究了808 nm和977 nm激光二极管抽运下铥/镱共掺TeO₂-Ga₂O₃-R₂O(R=Li，Na，K)玻璃光谱特性.利用Judd-Ofelt 理论计算了Tm³⁺离子在碲镓酸盐玻璃中自发辐射跃迁概率、荧光分支比和辐射寿命等光谱参数.在977 nm激光二极管抽运下，观测到Tm³⁺/Yb³⁺共掺碲镓酸盐玻璃很强的476 nm上转换蓝光(¹G₄→³H₆)和较弱的650 nm上转换红光(¹G₄→³H₄和³F_2，3→³H₆).分析表明476 nm蓝光发射为三光子吸收过程，650 nm红光发射为双光子和三光子混合吸收过程；而在808 nm激光二极管抽运下，玻璃上转换蓝色荧光为双光子吸收过程.实验发现，随着碱金属离子半径的增大，977 nm激光二极管抽运下蓝光上转换发光强度增强，而用808 nm激光二极管抽运蓝光上转换发光无明显的变化. 关键词： 碲镓酸盐玻璃 铥镱共掺 Judd-Ofelt 理论 上转换     

Beam quality of truncated laser beams with amplitude modulations and phase fluctuations in turbulence

The closed-form expressions for the Rayleigh range z_R and the M²-factor of truncated laser beams with amplitude modulations (AMs) and phase fluctuations (PFs) in turbulence are derived, and the beam quality is studied by taking the z_R and the M²-factor as the characteristic parameters of beam quality. The M²-factor of truncated laser beams with AMs and PFs is always larger than that of truncated Gaussian beams both in free space and in turbulence. However, in turbulence the beam quality of truncated laser beams with AMs and PFs may be better than that of truncated Gaussian beams if the z_R is taken as the characteristic parameter of beam quality. For laser beams with AMs and PFs in turbulence, the beam quality expressed in terms of z_R is consistent with that in terms of the M²-factor versus the phase fluctuation parameter α, but not versus the intensity modulation parameter σ_A. The beam quality of truncated laser beams with AMs and PFs is less sensitive to turbulence than that of truncated Gaussian beams. The beam quality of laser beams with smaller α and larger σ_A is less affected by turbulence than those with larger α and smaller σ_A.     

High-power diode-end-pumped CW Nd:GdVO4 laser

We report on a high-power diode-end-pumped CW Nd:GdVO₄ laser. Under the pump power of 39.5 W, a maximum output power of 19.8 W and a slope efficiency of 58.5% were obtained. The beam quality M² at maximum output power was measured to be around 2.62. The thermal focal length in Nd:GdVO₄ crystal under the pump power from 22 to 40.6 W was measured. The pump-induced damage threshold was estimated to be 28.6 kW/cm².