搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

离轴抽运厄米-高斯模固体激光器

连天虹 王石语 寇科 刘芸

引用本文:
Citation:

离轴抽运厄米-高斯模固体激光器

连天虹, 王石语, 寇科, 刘芸

Off-axis pumped Hermite-Gaussian mode solid-state laser

Lian Tian-Hong, Wang Shi-Yu, Kou Ke, Liu Yun
PDF
HTML
导出引用
  • 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.
    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.
      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)
      Corresponding author: Lian Tian-Hong, thlian@xaut.edu.cn
    [1]

    Sayan Ö F, Gerçekcioğlu H, Baykal Y 2020 Opt. Commun. 458 124735Google Scholar

    [2]

    Beijersbergen M W, Allen L, van der Veen H E L O, Woerdman J P 1993 Opt. Commun. 96 123Google Scholar

    [3]

    Chu S C, Chen Y T, Tsai K F, Otsuka K 2012 Opt. Express 20 7128Google Scholar

    [4]

    王亚东, 甘雪涛, 俱沛, 庞燕, 袁林光, 赵建林 2015 物理学报 64 034204Google Scholar

    Wang Y D, Gan X T, Ju P, Pang Y, Yuan L G, Zhao J L 2015 Acta Phys. Sin. 64 034204Google Scholar

    [5]

    Yang Y J, Zhao Q, Liu L L, Liu Y D, Guzman C R, Qiu C W 2019 Phys. Rev. Appl. 12 064007Google Scholar

    [6]

    付时尧, 高春清 2019 光学学报 39 0126014Google Scholar

    Fu S Y, Gao C Q 2019 Acta Opt. Sin. 39 0126014Google Scholar

    [7]

    Austin J, William J, Alan L, Linda M, Brandon C 2018 Opt. Express 26 2668Google 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 21Google Scholar

    [9]

    Forbes A 2017 Phil. Trans. R. Soc. A 375 20150436Google Scholar

    [10]

    Ngcobo S, Litvin I, Burger L, Forbes A 2013 Nat. Commun. 4 2289Google Scholar

    [11]

    Zhang M M, He H S, Dong J 2017 IEEE Photonics J. 9 1501214Google Scholar

    [12]

    Fang Z Q, Xia K G, Yao Y, Li J L 2015 IEEE J. Sel. Top. Quantum Electron. 21 1600406Google Scholar

    [13]

    Tuan P H, Liang H C, Huang K F, Chen Y F 2018 IEEE J. Sel. Top. Quantum Electron. 24 1600809Google Scholar

    [14]

    Shen Y J, Meng Y, Fu X, Gong M L 2018 Opt. Lett. 43 291Google Scholar

    [15]

    Kubodera K, Otsuka K 1979 J. Appl. Phys. 50 653Google Scholar

    [16]

    Chen Y F, Huang T M, Kao C F, Wang C L, Wang S C 1997 IEEE J. Quantum Electron. 33 1025Google 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 18164Google Scholar

    [19]

    朱一帆, 耿滔 2020 物理学报 69 014205Google Scholar

    Zhu Y F, Geng T 2020 Acta Phys. Sin. 69 014205Google Scholar

    [20]

    Liu Q Y, Zhao Y G, Ding M M, Yao W C, Fan X L, Shen D Y 2017 Opt. Express 25 23312Google Scholar

    [21]

    付时尧, 高春清 2018 物理学报 67 034201Google Scholar

    Fu S Y, Gao C Q 2018 Acta Phys. Sin. 67 034201Google Scholar

  • 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.

    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.

    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.

    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.

    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.

    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.

    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.

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

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

    图 9  离轴抽运实验装置图

    Fig. 9.  Schematic of the experimental setup.

    图 10  不同离轴量下的输出光斑

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

    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.

    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.

  • [1]

    Sayan Ö F, Gerçekcioğlu H, Baykal Y 2020 Opt. Commun. 458 124735Google Scholar

    [2]

    Beijersbergen M W, Allen L, van der Veen H E L O, Woerdman J P 1993 Opt. Commun. 96 123Google Scholar

    [3]

    Chu S C, Chen Y T, Tsai K F, Otsuka K 2012 Opt. Express 20 7128Google Scholar

    [4]

    王亚东, 甘雪涛, 俱沛, 庞燕, 袁林光, 赵建林 2015 物理学报 64 034204Google Scholar

    Wang Y D, Gan X T, Ju P, Pang Y, Yuan L G, Zhao J L 2015 Acta Phys. Sin. 64 034204Google Scholar

    [5]

    Yang Y J, Zhao Q, Liu L L, Liu Y D, Guzman C R, Qiu C W 2019 Phys. Rev. Appl. 12 064007Google Scholar

    [6]

    付时尧, 高春清 2019 光学学报 39 0126014Google Scholar

    Fu S Y, Gao C Q 2019 Acta Opt. Sin. 39 0126014Google Scholar

    [7]

    Austin J, William J, Alan L, Linda M, Brandon C 2018 Opt. Express 26 2668Google 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 21Google Scholar

    [9]

    Forbes A 2017 Phil. Trans. R. Soc. A 375 20150436Google Scholar

    [10]

    Ngcobo S, Litvin I, Burger L, Forbes A 2013 Nat. Commun. 4 2289Google Scholar

    [11]

    Zhang M M, He H S, Dong J 2017 IEEE Photonics J. 9 1501214Google Scholar

    [12]

    Fang Z Q, Xia K G, Yao Y, Li J L 2015 IEEE J. Sel. Top. Quantum Electron. 21 1600406Google Scholar

    [13]

    Tuan P H, Liang H C, Huang K F, Chen Y F 2018 IEEE J. Sel. Top. Quantum Electron. 24 1600809Google Scholar

    [14]

    Shen Y J, Meng Y, Fu X, Gong M L 2018 Opt. Lett. 43 291Google Scholar

    [15]

    Kubodera K, Otsuka K 1979 J. Appl. Phys. 50 653Google Scholar

    [16]

    Chen Y F, Huang T M, Kao C F, Wang C L, Wang S C 1997 IEEE J. Quantum Electron. 33 1025Google 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 18164Google Scholar

    [19]

    朱一帆, 耿滔 2020 物理学报 69 014205Google Scholar

    Zhu Y F, Geng T 2020 Acta Phys. Sin. 69 014205Google Scholar

    [20]

    Liu Q Y, Zhao Y G, Ding M M, Yao W C, Fan X L, Shen D Y 2017 Opt. Express 25 23312Google Scholar

    [21]

    付时尧, 高春清 2018 物理学报 67 034201Google Scholar

    Fu S Y, Gao C Q 2018 Acta Phys. Sin. 67 034201Google Scholar

  • [1] 刘俊杰, 盛泉, 王盟, 张钧翔, 耿兴宁, 石争, 王爱华, 史伟, 姚建铨. 基于腔内球差选模产生高阶拉盖尔-高斯模式激光. 物理学报, 2022, 71(1): 014204. doi: 10.7498/aps.71.20211514
    [2] 杨温渊, 董烨, 孙会芳, 董志伟. 磁绝缘线振荡器中模式竞争的物理分析和数值模拟. 物理学报, 2020, 69(19): 198401. doi: 10.7498/aps.69.20200383
    [3] 李锟影, 李璞, 郭晓敏, 郭龑强, 张建国, 刘义铭, 徐兵杰, 王云才. 利用光反馈多模激光器结合滤波器产生平坦混沌. 物理学报, 2019, 68(11): 110501. doi: 10.7498/aps.68.20190171
    [4] 杨文海, 刁文婷, 蔡春晓, 宋学瑞, 冯付攀, 郑耀辉, 段崇棣. 1064 nm固体激光器和光纤激光器在制备压缩真空态光场实验中的对比研究. 物理学报, 2019, 68(12): 124201. doi: 10.7498/aps.68.20182304
    [5] 黄丽萍, 洪斌斌, 刘畅, 唐昌建. 220GHz三次谐波光子带隙谐振腔回旋管振荡器的研究. 物理学报, 2014, 63(11): 118401. doi: 10.7498/aps.63.118401
    [6] 何广源, 郭靖, 焦中兴, 王彪. 固体激光器热透镜效应的调控. 物理学报, 2012, 61(9): 094217. doi: 10.7498/aps.61.094217
    [7] 杜朝海, 李铮迪, 薛志浩, 刘濮鲲, 薛谦忠, 张世昌, 徐寿喜, 耿志辉, 顾伟, 粟亦农, 刘高峰. W波段损耗介质加载回旋返波振荡器中模式竞争的研究. 物理学报, 2012, 61(7): 070703. doi: 10.7498/aps.61.070703
    [8] 刘漾, 巩华荣, 魏彦玉, 宫玉彬, 王文祥, 廖复疆. 有效抑制光子晶体加载矩形谐振腔中模式竞争的方法. 物理学报, 2009, 58(11): 7845-7851. doi: 10.7498/aps.58.7845
    [9] 杨 浩, 郭 霞, 关宝璐, 王同喜, 沈光地. 注入电流对垂直腔面发射激光器横模特性的影响. 物理学报, 2008, 57(5): 2959-2965. doi: 10.7498/aps.57.2959
    [10] 梁慧敏, 杜惊雷, 王宏波, 王治华, 罗时荣, 杨经国, 郑万国, 魏晓峰, 朱启华, 黄晓军, 王晓东, 郭 仪. 不同波长激光激发下C6H12受激拉曼散射模式竞争. 物理学报, 2007, 56(12): 6994-6998. doi: 10.7498/aps.56.6994
    [11] 李 磊, 赵长明, 张 鹏, 杨苏辉. 激光二极管抽运频差可调谐双频固体激光器的研究. 物理学报, 2007, 56(5): 2663-2669. doi: 10.7498/aps.56.2663
    [12] 张秋琳, 苏红新, 孙 江, 郭庆林, 付广生. LD抽运被动调Q固体激光器的脉冲稳定性. 物理学报, 2007, 56(10): 5818-5820. doi: 10.7498/aps.56.5818
    [13] 武丁二, 周 睿, 张晓华, 丁 欣, 姚建铨, 颜彩繁, 张光寅. LD端抽运平直腔Nd:YVO4固态激光器的输出功率特性研究. 物理学报, 2006, 55(3): 1196-1200. doi: 10.7498/aps.55.1196
    [14] 朱洪涛, 楼祺洪, 漆云凤, 马海霞, 董景星, 魏运荣. 钛宝石激光器端面抽运Nd:YAG陶瓷激光器热沉积理论和实验研究. 物理学报, 2005, 54(12): 5648-5653. doi: 10.7498/aps.54.5648
    [15] 柳 强, 巩马理, 潘圆圆, 李 晨. 边缘抽运复合Yb:YAG/YAG薄片激光器设计与功率扩展. 物理学报, 2004, 53(7): 2159-2164. doi: 10.7498/aps.53.2159
    [16] 关 俊, 李金萍, 程光华, 陈国夫, 侯 洵. 端面抽运固体激光器热透镜效应的实验研究. 物理学报, 2004, 53(6): 1804-1809. doi: 10.7498/aps.53.1804
    [17] 王石语, 过 振, 傅君眉, 蔡德芳, 文建国, 薛海中, 唐映德. 激光二极管抽运固体激光器场分布的热不稳定性研究. 物理学报, 2003, 52(2): 355-361. doi: 10.7498/aps.52.355
    [18] 尚连聚. 端面抽运固体激光器的腔模匹配分析. 物理学报, 2003, 52(6): 1408-1411. doi: 10.7498/aps.52.1408
    [19] 张潮波, 宋峰, 孟凡臻, 丁欣, 张光寅, 商美茹. 利用输出功率测量激光二极管端面抽运的固体激光器热透镜焦距. 物理学报, 2002, 51(7): 1517-1520. doi: 10.7498/aps.51.1517
    [20] 冯衍, 宋峰, 赵丽娟, 张潮波, 郭红沧, 张光寅. LD抽运Nd:YVO4晶体中的上转换及其影响. 物理学报, 2001, 50(2): 335-340. doi: 10.7498/aps.50.335
计量
  • 文章访问数:  6529
  • PDF下载量:  103
  • 被引次数: 0
出版历程
  • 收稿日期:  2020-01-13
  • 修回日期:  2020-03-07
  • 刊出日期:  2020-06-05

/

返回文章
返回