离轴抽运厄米-高斯模固体激光器

连天虹; 王石语; 寇科; 刘芸

doi:10.7498/aps.69.20200086

摘要

给出了离轴抽运固体激光器多模速率方程组在阈值附近的小信号求解方法, 用这种方法研究了模式随离轴量的变化以及厄米-高斯模的竞争行为. 抽运光斑较小时, 离轴量增加高阶模式依次出现; 抽运光斑较大时, 模式变化呈现复杂性. 用小信号近似得到的模式光子数比例与较高抽运功率下数值求解速率方程组的结果接近, 表明可以用该方法估算实际较高功率激光器的模式分布, 这可以方便这类激光器的研究. 对离轴抽运下的多厄米-高斯模激光器, 阈值附近的模竞争体现为, 随着抽运功率的增加, 第一个净增益由负变正的模式, 光子数随即开始增加, 增加趋势接近线性. 而第二个净增益由负变正的模式, 光子数并不立即开始增加, 而要等到抽运功率进一步增加后才开始增加, 其开始增加后第一个模式的增长趋势变缓. 从动态过程看, 各个模式经过交叉尖峰和交叉弛豫振荡竞争后, 逐渐达到稳态. 实验获得了HG₀₀-HG₅₀模光束, 实验所得到的模式分布与理论计算结果符合很好.

关键词:

Abstract

To study the modes’ pattern and the modes’ competition behavior of an off-axis pumped solid-state laser, a small signal approximation method is derived, which simplifies the multiple-mode differential equations into liner algebraic equations. When the pump beam radius is small, the higher-order Hermite-Gaussian modes emerge successively with the off-axis displacement increasing, while the pattern evolution shows some complexity when the pump radius is larger. The percentage of the modes with a small pump power near the threshold, calculated with the small signal method, is close to that calculated at a higher pump power by directly solving the rate equations numerically. This indicates that we can estimate the modes’ pattern of an actual high power laser by using the small signal method. For a multiple Hermite-Gaussian modes off-axis pumped solid state laser, as the pump power increases, the photon number of the mode increases linearly as its net gain becomes positive, while that of the second mode with a smaller net gain does not increase immediately as it becomes positive successively. Larger pump power is required until the photon number begins to increase. The increasing slope of first mode decreases as the second mode begins to grow. The dynamics of the modes’ competition presents cross spiking and cross relaxation process before they become stable. Moreover, the outputs of the modes HG₀₀-HG₅₀ are experimentally demonstrated, and the spot evolution with the off-axis displacement agrees very well with the calculated result.

Keywords:

作者及机构信息

1.
西安理工大学机械与精密仪器工程学院, 西安　710048

2.
西安电子科技大学物理与光电工程学院, 西安　710071

通信作者: 连天虹, thlian@xaut.edu.cn

基金项目: 国家级-国家自然科学基金(61805196)

Authors and contacts

1.
School of Mechanical and Precision Instrument Engineering, Xi’an University of Technology, Xi’an 710048, China

2.
School of Physics and Optoelectronic Engineering, Xidian University, Xi’an 710071, China

Corresponding author: Lian Tian-Hong, thlian@xaut.edu.cn

文章全文 : translate this paragraph

参考文献

[1]	Sayan Ö F, Gerçekcioğlu H, Baykal Y 2020 Opt. Commun. 458 124735 Google Scholar
[2]	Beijersbergen M W, Allen L, van der Veen H E L O, Woerdman J P 1993 Opt. Commun. 96 123 Google Scholar
[3]	Chu S C, Chen Y T, Tsai K F, Otsuka K 2012 Opt. Express 20 7128 Google Scholar
[4]	王亚东, 甘雪涛, 俱沛, 庞燕, 袁林光, 赵建林 2015 物理学报 64 034204 Google Scholar Wang Y D, Gan X T, Ju P, Pang Y, Yuan L G, Zhao J L 2015 Acta Phys. Sin. 64 034204 Google Scholar
[5]	Yang Y J, Zhao Q, Liu L L, Liu Y D, Guzman C R, Qiu C W 2019 Phys. Rev. Appl. 12 064007 Google Scholar
[6]	付时尧, 高春清 2019 光学学报 39 0126014 Google Scholar Fu S Y, Gao C Q 2019 Acta Opt. Sin. 39 0126014 Google Scholar
[7]	Austin J, William J, Alan L, Linda M, Brandon C 2018 Opt. Express 26 2668 Google Scholar
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[21]	付时尧, 高春清 2018 物理学报 67 034201 Google Scholar Fu S Y, Gao C Q 2018 Acta Phys. Sin. 67 034201 Google Scholar

施引文献

图 1 端面离轴抽运固体激光器图示

Fig. 1. Schematic of an off-axis end-pumped solid-state laser.

下载: 全尺寸图片幻灯片

图 2 抽运功率0.25 W、抽运光半径0.075 mm时, 16个离轴量下的光斑

Fig. 2. Laser beam profiles with different mode distributions in the sixteen transverse displacements when the pump power is 0.25 W and the pump beam radius is 0.075 mm.

下载: 全尺寸图片幻灯片

图 3 在阈值附近, HG₀₀和HG₁₀模光子数(a), 光子数比例(b); HG₁₀和HG₂₀模光子数(c), 光子数比例(d)随抽运功率的变化

Fig. 3. Photon numbers of the mode HG₀₀ and HG₁₀ (a), and their percentages (b); photon numbers of the modes HG₁₀ and HG₂₀ (c), and their percentages (d) near the threshold.

下载: 全尺寸图片幻灯片

图 4 净增益随抽运功率的变化　(a) 0.08 mm; (b) 0.155 mm

Fig. 4. Dependence of the net gains on the pump power: (a) 0.08 mm; (b) 0.155 mm.

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图 5 抽运功率0.5 W、抽运光半径0.15 mm时, 8个离轴量下的光斑

Fig. 5. Laser beam profiles with different mode distributions in the eight transverse displacements when the pump power is 0.5 W and the pump beam radius is 0.15 mm.

下载: 全尺寸图片幻灯片

图 6 在阈值附近, HG₀₀, HG₁₀和HG₂₀模光子数 (a), 光子数比例(b); HG₁₀, HG₂₀, HG₃₀和HG₄₀模光子数((c), (e)), 光子数比例((d), (f))随抽运功率的变化

Fig. 6. Photon numbers of the modes HG₀₀ , HG₁₀ and HG₂₀ (a) and their percentages (b); photon numbers of the modes HG₁₀, HG₂₀ and HG₃₀ ((c), (e)) and their percentages ((d), (f)) near the threshold.

下载: 全尺寸图片幻灯片

图 7 净增益随抽运功率的变化　(a) 离轴量0.1 mm; (b) 离轴量0.2 mm

Fig. 7. Dependence of the net gains on the pump power: (a) 0.1 mm; (b) 0.2 mm.

下载: 全尺寸图片幻灯片

图 8 光子数的动态变化过程　(a) ω_p = 0.075 mm, Δx = 0.08 mm, P_a = 0.25 W; (b) ω_p = 0.075 mm, Δx = 0.08 mm, P_a = 5 W; (c) ω_p = 0.15 mm, Δx = 0.1 mm, P_a = 0.5 W; (d) ω_p = 0.15 mm, Δx = 0.1 mm, P_a = 5 W; (e) ω_p = 0.15 mm, Δx = 0.2 mm, P_a = 0.5 W; (f)ω_p = 0.15 mm, Δx = 0.2 mm, P_a = 5 W

Fig. 8. Dynamics of the photon numbers: (a) ω_p = 0.075 mm, Δx = 0.08 mm, P_a = 0.5 W; (b) ω_p = 0.075 mm, Δx = 0.08 mm, P_a = 5 W; (c) ω_p = 0.15 mm, Δx = 0.1 mm, P_a = 0.5 W; (d) ω_p = 0.15 mm, Δx = 0.1 mm, P_a = 5 W; (e) ω_p = 0.15 mm, Δx = 0.2 mm, P_a = 0.5 W; (f) ω_p = 0.15 mm, Δx = 0.2 mm, P_a = 5 W.

下载: 全尺寸图片幻灯片

图 9 离轴抽运实验装置图

Fig. 9. Schematic of the experimental setup.

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图 10 不同离轴量下的输出光斑

Fig. 10. Output spots with different off-axis displacements.

下载: 全尺寸图片幻灯片

图 11 光斑随激光功率保持不变

Fig. 11. The spot keeps unchanged with the variation of the laser power.

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图 12 (a)激光功率随离轴量的变化; (b)模式能达到的最大功率

Fig. 12. (a) Dependence of the output power on the displacement; (b) the maximum powers of the modes.

下载: 全尺寸图片幻灯片

[1]	Sayan Ö F, Gerçekcioğlu H, Baykal Y 2020 Opt. Commun. 458 124735 Google Scholar
[2]	Beijersbergen M W, Allen L, van der Veen H E L O, Woerdman J P 1993 Opt. Commun. 96 123 Google Scholar
[3]	Chu S C, Chen Y T, Tsai K F, Otsuka K 2012 Opt. Express 20 7128 Google Scholar
[4]	王亚东, 甘雪涛, 俱沛, 庞燕, 袁林光, 赵建林 2015 物理学报 64 034204 Google Scholar Wang Y D, Gan X T, Ju P, Pang Y, Yuan L G, Zhao J L 2015 Acta Phys. Sin. 64 034204 Google Scholar
[5]	Yang Y J, Zhao Q, Liu L L, Liu Y D, Guzman C R, Qiu C W 2019 Phys. Rev. Appl. 12 064007 Google Scholar
[6]	付时尧, 高春清 2019 光学学报 39 0126014 Google Scholar Fu S Y, Gao C Q 2019 Acta Opt. Sin. 39 0126014 Google Scholar
[7]	Austin J, William J, Alan L, Linda M, Brandon C 2018 Opt. Express 26 2668 Google Scholar
[8]	Willner A E, Zhao Z, Ren Y X, Li L, Xie G D, Song H Q, Liu C, Zhang R Z, Bao C J, Pang K 2018 Opt. Commun. 408 21 Google Scholar
[9]	Forbes A 2017 Phil. Trans. R. Soc. A 375 20150436 Google Scholar
[10]	Ngcobo S, Litvin I, Burger L, Forbes A 2013 Nat. Commun. 4 2289 Google Scholar
[11]	Zhang M M, He H S, Dong J 2017 IEEE Photonics J. 9 1501214 Google Scholar
[12]	Fang Z Q, Xia K G, Yao Y, Li J L 2015 IEEE J. Sel. Top. Quantum Electron. 21 1600406 Google Scholar
[13]	Tuan P H, Liang H C, Huang K F, Chen Y F 2018 IEEE J. Sel. Top. Quantum Electron. 24 1600809 Google Scholar
[14]	Shen Y J, Meng Y, Fu X, Gong M L 2018 Opt. Lett. 43 291 Google Scholar
[15]	Kubodera K, Otsuka K 1979 J. Appl. Phys. 50 653 Google Scholar
[16]	Chen Y F, Huang T M, Kao C F, Wang C L, Wang S C 1997 IEEE J. Quantum Electron. 33 1025 Google Scholar
[17]	Shen Y J, Wang X J, Xie Z W, Min C J, Fu X, Liu Q, Gong M L, Yuan X C 2019 Light: Science & Applications 8 90
[18]	Wang S, Zhang S L, Li P, Hao M H, Yang H M, Xie J, Feng G Y, Zhou S H 2018 Opt. Express 26 18164 Google Scholar
[19]	朱一帆, 耿滔 2020 物理学报 69 014205 Google Scholar Zhu Y F, Geng T 2020 Acta Phys. Sin. 69 014205 Google Scholar
[20]	Liu Q Y, Zhao Y G, Ding M M, Yao W C, Fan X L, Shen D Y 2017 Opt. Express 25 23312 Google Scholar
[21]	付时尧, 高春清 2018 物理学报 67 034201 Google Scholar Fu S Y, Gao C Q 2018 Acta Phys. Sin. 67 034201 Google Scholar

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