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The high-order Laguerre-Gaussian (LG) mode output from an end-pumped Nd:YVO4 laser cavity with strong spherical aberration (SA) induced by short-focal-length lens is studied in this work. A long-focal-length lens L1 is used in the cavity to expand and collimate the beam, so that the beam incident on another short-focal-length lens L2 in the cavity undergoes a strong SA. Since the ring-shaped LG modes with different values of angular index m have different beam radii, the actual focal points of each order of beam are then spatially displaced. A flat output coupler (OC) is located near the focal point of L2, which is composed of a cat-eye retroreflector together with the lens. Such a retroreflector can provide only ideal retroreflection to the incident beam with a focal point exactly on the OC. Given the focal point displacements of the LG beams with different orders, such a mechanism can be used for implementing the transverse mode selection. The mode which has an actual focal point on the OC has a smaller loss than the other defocused modes. With an a-cut Nd:YVO4 as laser crystal, scalar (linear-polarized) single-mode LG output with radical index p = 0 and angular index m>0 is obtained. The laser mode-order is selectable from LG0, ±10 to LG0, ±33 under 878.6-nm incident diode pump power of 1.03 W, by simply adjusting the distance between the OC and L2 in a range of 0.5 mm, when using lens L1 with f = 150 mm and lens L2 of f = 33.9 mm. It is found that sufficient SA which makes the optical paths of the neighboring modes well distinguishable is essential for single-mode operation of a wanted order of LG mode. However, too strong an SA can stop the high-order mode beam from oscillating, since the width and radius of the ring-shaped LG mode are an increasing function of indices p and m, which bring a stronger loss to the corresponding mode. Based on this analysis, we turn to a focal-length combination of f1 = 100 mm and f2 = 51.8 mm, to reduce the SA to a level suitable for further higher mode operation. A highest-order LG0, ±75 is obtained by such an SA mode-selecting technique under fixed pump power of 1.03 W.
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Keywords:
- Laguerre-Gaussian mode /
- solid-state laser /
- mode selection /
- spherical aberration
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Google Scholar
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Google Scholar
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Google Scholar
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图 1 高阶拉盖尔-高斯模式激光器光路示意图
Figure 1. Schematic of the high-order Laguerre-Gaussian mode laser.
图 2 不同角向指数m的LG0, ±m光束理论相对尺寸
Figure 2. Calculated relative beam sizes of the LG0, ±m mode laser.
图 3 输出镜M2处于不同位置时激光输出的典型近场和远场光斑(入射泵浦功率1.03 W)
Figure 3. Typical near- and Far-field beam patterns of the laser output when the output coupler M2 was located at different positions (incident pump power 1.03 W).
图 4 激光器处于不同运转模式时的激光输出功率(泵浦功率1.03 W)
Figure 4. Laser output power when the laser operating in different modes (pump power 1.03 W).
图 5 不同环形光斑半径时球差引起的焦点偏移计算值
Figure 5. Calculated focal point displacement induced by SA considering the radius of the ring LG beams.
图 6 不同角向指数m对应的透镜L2处LG0, m模式的光斑半径以及环宽度（对基模TEM00光斑半径w归一）
Figure 6. Calculated beam radii and the ring widths of the LG0, m mode with different angular indices m at the lens L2 (normalized to the beam radius w of fundamental mode TEM00).
图 7 LG0, ±75高阶横模输出的近场(a)和远场(b)激光光斑(泵浦功率1.03 W)
Figure 7. (a) Near-field and (b) far-field beam patterns of the LG0, ±75 high-order transverse mode output (pump power 1.03 W).
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[1] Miles J P 2017 Opt. Express 25 11265
Google Scholar
[2] Forbes A 2019 Laser Photonics Rev. 13 1900140
Google Scholar
[3] Omatsu T, Miyamoto K, Lee A J 2017 J. Opt. 19 123002
Google Scholar
[4] 王延娜, 赵迪, 方爱平, 蒋臣威, 高韶燕, 李福利 2015 64 224214
Google Scholar
Wang Y N, Zhao D, Fang A P, Jiang C W, Gao S Y, Li F L 2015 Acta Phys. Sin. 64 224214
Google Scholar
[5] 张光宇, 刘琳婧, 张成龙 2017 光子学报 46 0101001
Zhang G Y, Liu L J, Zhang C L 2017 Acta Phot. Sin. 46 0101001
[6] Bisson J F, Senatsky Y, Ueda K I 2005 Laser Phys. Lett. 2 327
Google Scholar
[7] Zhao Y, Liu Q, Zhou W, Shen D 2016 Opt. Express 24 15596
Google Scholar
[8] 徐云, 余俊杰, 韩侠辉, 李桂运, 夏克贵, 周常河, 李建郎 2016 中国激光 43 14
Xu Y, Yu J J, Han X H, Li G Y, Xia K G, Zhou C H, Li J L 2016 Chin. J. Las. 43 14
[9] Ma Y, Lee A J, Pask H M, Miyamoto K, Omatsu T 2020 Opt. Express 28 24095
Google Scholar
[10] Ito A, Kozawa Y, Sato S 2010 J. Opt. Soc. Am. A 27 2072
[11] Lee A J, Omatsu T, Pask H M 2013 Opt. Express 21 12401
Google Scholar
[12] Chen Y F, Lan Y P, Wang S C 2001 Appl. Phys. B 72 167
Google Scholar
[13] Luo S Y, Cai Z P, Sheng C X, Li L, Chen Q 2020 Opt. Laser Technol. 127 106185
Google Scholar
[14] Kogelnik H, Li T 1966 Appl. Opt. 5 1550
[15] Belanger P, Pare C 1991 Opt. Lett. 16 1057
Google Scholar
[16] Yonezawa K, Kozawa Y, Sato S 2006 Opt. Lett. 31 2151
Google Scholar
[17] 郁道银, 谈恒英 2016 工程光学 (北京: 机械工业出版社)
Yu D Y, Tan H Y 2016 Engineering Optics (Vol. 4) (Beijing: China Machine Press) (in Chinese)
[18] 姚强强, 王启晗, 冯池, 陈思, 金光勇, 董渊 2018 67 174204
Google Scholar
Yao Q Q, Wang Q H, Feng C, Chen S, Jin G Y, Dong Y 2018 Acta Phys. Sin. 67 174204
Google Scholar
[19] Senatsky Y, Bisson J F, Shelobolin A, Shirakawa A, Ueda K 2009 Laser Phys. 19 911
Google Scholar
[20] Thirugnanasambandam M P, Senatsky Y 2010 Laser Phys. Lett. 7 637
Google Scholar
[21] Senatsky Y, Bission J F, Li J, Shirakawa A, Thirugnanasambandam M, Ueda K 2012 Opt. Rev. 19 201
Google Scholar
[22] Wang M, Ma Y, Sheng Q, He X, Liu J, Shi W, Yao J, Omatsu T 2021 Opt. Express 29 27783
Google Scholar
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