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For laser ablation propulsion’s applications in space (e.g., space-debris removal, etc.), the laser power is well above the critical power for self-focusing in the atmosphere. Therefore, the self-focusing effect on the beam quality is very significant. In addition, a high-power laser beam is usually accompanied with spherical aberration due to nonlinear effects in its generation process. In this paper, the influence of spherical aberration on the beam quality of high-power laser beams propagating upwards in the atmosphere is studied by using numerical simulation. It is shown that for the large beam size case, the target intensity may be improved by applying the positive spherical aberration. However, for the small beam size case, the target intensity may be improved by using the negative spherical aberration. Furthermore, a laser beam with a large size is more suitable for laser ablation propulsion’s applications in space than that with a small size. Owing to the linear diffraction effect and the nonlinear self-focusing effect, there exists optimal beam power to maximize the target intensity. The formula of the optimal beam power is fitted for the large beam size case in this paper. On the other hand, the focal shift appears due to diffraction, self-focusing and spherical aberration, which results in a degradation of the beam quality on the target. For the large beam size case, to move the actual focus to the target and improve the beam quality on the target, the formula of the modified focal length is also derived in this paper. The results obtained in this paper are of important theoretical significance and practical value.
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Keywords:
- spherical aberration /
- nonlinear self-focusing effect /
- high-power laser beam propagation upwards in the atmosphere /
- beam quality
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Google Scholar
[2] Esmiller B, Jacquelard C, Eckel H A, Wnuk E 2014 Appl. Opt. 53 I45
Google Scholar
[3] Phipps C R, Albrecht G, Friedman H, Gavel D, George E V, Murray J, Ho C, Priedhorsky W, Michaelis M M, Reilly J P 1996 Laser Part. Beams 14 1
Google Scholar
[4] Phipps C R 2018 Laser Ablation Propulsion and Its Applications in Space (Switzerland: Springer Cham) pp217−246
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
Zhao G P, Lü B D 2004 Acta Phys. Sin. 53 2974
Google Scholar
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Google Scholar
[17] 李晓庆, 王涛, 季小玲 2014 63 134209
Google Scholar
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Google Scholar
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[21] 张翔, 苏礼坤, 蔡青 2010 光学学报 30 802
Google Scholar
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[22] 蒲继雄 1998 光子学报 27 234
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Google Scholar
[23] 苏亚辉, 汪超炜, 韩蒙蒙, 汪金礼, 傅旭川, 代维, 刘畅 2014 光学学报 34 s122005
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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图 1 靶面光强I (r, z = L)分布 (a), (b) 大尺寸光束, w0 = 1.414 m, β = 5.9275; (c), (d) 小尺寸光束, w0 = 0.821 m, β = 1.03
Figure 1. Intensity distributions on the target I (r, z = L): (a), (b) For a large beam size, w0 = 1.414 m, β = 5.9275; (c), (d) for a small beam size, w0 = 0.821 m, β = 1.03.
图 2 靶面峰值光强I (r = 0, z = L)随相对发射功率P/PcrGs的变化 (a) 大尺寸光束, w0 = 1.414 m, β = 5.9275; (b) 小尺寸光束: w0 = 0.821 m, β = 1.03
Figure 2. Peak intensity on the target I (r = 0, z = L) versus the relative beam power P/PcrGs: (a) For a large beam size, w0 = 1.414 m, β = 5.9275; (b) for a small beam size, w0 = 0.821 m, β = 1.03.
图 3 (5)式的验证. 相对最佳发射功率Popt/PcrGs随初始束宽w0和球差系数kC4的变化. 黑点: 数值模拟计算结果, 曲面: (5)式计算结果
Figure 3. Confirmation of the formula of Eq. (5). Relative optimal beam power Popt/PcrGs versus the initial beam radius. w0 and the spherical aberration coefficient kC4. Black dots: results by using numerical simulation method; surfaces: results by using Eq. (5).
图 5 透镜修正焦距Fmod随球差系数kC4和相对发射功率P/PcrGs的变化, w0 = 1.414 m, β = 5.9275
Figure 5. Modified focal length Fmod versus the spherical aberration coefficient kC4 and the relative beam power P/PcrGs, w0 = 1.414 m, β = 5.9275.
图 6 靶面光强分布, w0 = 1.414 m, β = 5.9275, P = 2000PcrGs (a) 修正焦距前; (b) 修正焦距后
Figure 6. Intensity distributions on the target. w0 = 1.414 m, β = 5.9275, P = 2000PcrGs: (a) For the unmodified focal length case; (b) for the modified focal length case.
系数 值 系数 值 u $5.6 \times {10^{ { - }5} }\exp (- 6.121 w_0)$ b –2.46 v $2.351 \times {10^{ { - }5} }\exp (-2.326w_0)$ c $1.022 \times {10^{ { - }4} }$ s $26-35.3w_0-0.00167P /P_{ {\text{crGs} } }$ d $1.9 \times {10^{ { - }4} }$ a –0.2 e –0.12 
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[1] Kessler D J, Cour-Palais B G 1978 J. Geophys. Res. 83 2637
Google Scholar
[2] Esmiller B, Jacquelard C, Eckel H A, Wnuk E 2014 Appl. Opt. 53 I45
Google Scholar
[3] Phipps C R, Albrecht G, Friedman H, Gavel D, George E V, Murray J, Ho C, Priedhorsky W, Michaelis M M, Reilly J P 1996 Laser Part. Beams 14 1
Google Scholar
[4] Phipps C R 2018 Laser Ablation Propulsion and Its Applications in Space (Switzerland: Springer Cham) pp217−246
[5] Rubenchik A M, Fedoruk M P, Turitsyn S K 2014 Light Sci. Appl. 3 e159
Google Scholar
[6] Vaseva I A, Fedoruk M P, Rubenchik A M, Turitsyn S K 2016 Sci. Rep. 6 30697
Google Scholar
[7] Zhang Y Q, Ji X L, Zhang H, Li X Q, Wang T, Wang H, Deng Y 2018 Opt. Express 26 14617
Google Scholar
[8] Deng Y, Ji X L, Li X Q, Wang H, Huang Z Y, Zhang H 2021 IEEE Photonics J. 13 6500110
Google Scholar
[9] Wang H, Ji X L, Deng Y, Li X Q, Wang T, Yu H, Li Q 2019 J. Quant. Spectrosc. Radiat. Transfer 235 244
Google Scholar
[10] Fan X L, Ji X L, Wang H, Deng Y, Zhang H 2020 J. Opt. Soc. Am. A: 38 168
[11] Deng Y, Wang H, Ji X L, Li X Q, Yu H, Chen L F 2020 Opt. Express 28 27927
Google Scholar
[12] Klein, Claude A 1990 Opt. Eng. 29 343
Google Scholar
[13] Dabby F W, Whinnery J R 1968 Appl. Phys. Lett. 13 284
Google Scholar
[14] 季小玲, 陶向阳, 吕百达 2004 53 952
Google Scholar
Ji X L, Tao X Y, Lü B D 2004 Acta Phys. Sin. 53 952
Google Scholar
[15] 赵光普, 吕百达 2004 53 2974
Google Scholar
Zhao G P, Lü B D 2004 Acta Phys. Sin. 53 2974
Google Scholar
[16] 雍康乐, 闫家伟, 唐善发, 张蓉竹 2020 69 014201
Google Scholar
Yong K L, Yan J W, Tang S F, Zhang Z R 2020 Acta Phys. Sin. 69 014201
Google Scholar
[17] 李晓庆, 王涛, 季小玲 2014 63 134209
Google Scholar
Li X Q, Wang T, Ji X L 2014 Acta Phys. Sin. 63 134209
Google Scholar
[18] Yoshida A, Asakura T 1996 Opt. Commun. 123 694
Google Scholar
[19] Pu J X 1998 J. Mod. Opt. 45 239
Google Scholar
[20] Lü B D, Ji X L, Luo S R 2001 J. Mod. Opt. 48 1171
Google Scholar
[21] 张翔, 苏礼坤, 蔡青 2010 光学学报 30 802
Google Scholar
Zhang X, Su L K, Cai Q 2010 Acta Optic. Sin. 30 802
Google Scholar
[22] 蒲继雄 1998 光子学报 27 234
Google Scholar
Pu J X 1998 Acta Photonica Sin. 27 234
Google Scholar
[23] 苏亚辉, 汪超炜, 韩蒙蒙, 汪金礼, 傅旭川, 代维, 刘畅 2014 光学学报 34 s122005
Google Scholar
Su Y H, Wang C W, Hang M M, Wang J L, Fu X C, Dai W, Liu C 2014 Acta Optic. Sin. 34 s122005
Google Scholar
[24] Deng H L, Ji X L, Li X Q, Wang X Q 2015 Opt. Lett. 40 3881
Google Scholar
[25] Rubenchik A M, Fedoruk M P, Turitsyn S K 2009 Phys. Rev. Lett. 102 233902
Google Scholar
[26] Phipps C R, Baker K L, Libby S B, Liedahl D A, Olivier S S, Pleasance L D, Rubenchik A M, Trebes J E, George E V, Marcovici B, Reilly J P, Valley M T 2012 Adv. Space Res. 49 1283
Google Scholar
[27] Chekalin S V, Kandidov V P 2013 Phys. Uspekhi 56 123
Google Scholar
[28] Pare C, Belanger P A 1992 Opt. Quantum Electron. 24 S1051
Google Scholar
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