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In order to obtain focal spot with high power and spot size comparable to wavelength scale, a novel approach to achieving the coherent combination of beam array by tightly focusing is proposed. The physical model of coherent beam combination of beam array via tightly focusing is built up by the use of the vector diffraction integral. Therefore the influences of beam configuration, polarization state, beam width, beam interval and numerical aperture of the tight focusing system on the characteristics of the combined beam are discussed in detail. The results indicate that the coherent combination effect of beam array with linear and circular polarization via tight focusing is the first best, and that with the radial polarization is the second best but that with the azimuthal polarization is the worst. The beam array of linear and circular polarization with rectangle configuration can be tightly focused onto center point, and the beam array with hexagon is also focused onto center point but with lower efficiency. In addition, by enlarging the beam width and the beam interval to a certain extent, the combination efficiency can be increased. By optimizing the beam configuration, beam width and interval, and selecting rational numerical aperture of the tightly focusing geometry, the focal spot with high energy concentration can be obtained with high beam quality and combination efficiency.
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Keywords:
- tight focusing /
- beam array /
- coherent combination /
- numerical aperture
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Google Scholar
Yang R F, Yang P, Shen F 2009 Acta Phys. Sin. 58 8297
Google Scholar
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Fang X Y 2010 Ph. D. Dissertation (Harbin: Harbin Institute Of Technology) (in Chinese)
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Lu Y Q, Hu S L, Lu Y, Xu J, Wang J 2015 Acta Phys. Sin. 64 097301
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Wang S C, Li X P 2016 Chin. Opt. 9 185
Google Scholar
[8] 张洲 2016 博士学位论文 (合肥: 安徽大学)
Zhang Z 2016 Ph. D. Dissertation (Hefei: Anhui University) (in Chinese)
[9] 赵维, 唐芳, 邱丽荣, 刘大礼 2013 物理学报 62 054201
Google Scholar
Zhao W Q, Tang F, Qiu L R, Liu D L 2013 Acta Phys. Sin. 62 054201
Google Scholar
[10] Byrnes S J, Lenef A, Aieta F, Capasso F 2016 Opt. Express 24 5110
Google Scholar
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Google Scholar
[15] 谭毅, 李新阳 2014 物理学报 63 094202
Google Scholar
Tan T, Li X Y 2014 Acta Phys. Sin. 63 094202
Google Scholar
[16] Gilad M L, Uriel L 2008 Opt. Express 16 4567
Google Scholar
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图 1 阵列光束经紧聚焦方式合成的光路图
Figure 1. Light path of beam combination of beam array via tight focusing.
图 2 光束排布方式 (a)矩形; (b)六边形
Figure 2. Beam configurations: (a) Rectangle; (b) hexagon.
图 3 矩形排布方式下, 不同偏振态阵列光束的聚焦光斑
Figure 3. Tight-focused spots of beam array with different polarization states under rectangle configuration.
图 4 六边形排布方式下, 不同偏振态阵列光束的聚焦光斑
Figure 4. Tight-focused spots of beam array with different polarization states under hexagon configuration.
图 5 不同光束排布和偏振态时, 焦斑的PIB曲线
Figure 5. PIB curves of the focal spots of beam array with different beam configurations and polarization states.
图 6 矩形排布方式下, 不同偏振态阵列光束的焦斑光强
Figure 6. Focused intensity distribution of beam array with different polarization states under rectangle configuration.
图 7 矩形排布方式下, 不同束宽及γ时的聚焦光斑
Figure 7. Focused spots of beam array with different beam widths and γ under rectangle configuration.
图 8 矩形排布方式下, (a)不同间距比时聚焦光斑的PIB曲线, 以及(b)不同束宽时聚焦光斑的PIB曲线
Figure 8. PIB curves of the focal spots of beam array with different (a) beam widths and (b) γ under rectangle configuration.
图 9 矩形排布方式下, 不同数值孔径和介质折射率下聚焦光斑的PIB曲线
Figure 9. PIB curves of the focal spots of beam array with numerical apertures and refractive indices under rectangle configuration.
偏振态 线偏振 左旋圆偏振 径向偏振 角向偏振 矩阵 $\left[ \begin{aligned} 1 \\ 0 \\ 0 \\ \end{aligned} \right]$ $\left[ \begin{aligned} { {1{\rm{i} } } }/{ {\sqrt 2 } } \\ {1}/{ {\sqrt 2 } } \\ 0\;\;\end{aligned} \;\right]$ $\left[ \begin{aligned} \cos \varphi \\ \sin\; \varphi \\ 0\;\;\;\end{aligned} \right]$ $\left[ \begin{aligned} - \sin \varphi \\ \cos \varphi \\ 0\;\;\;\;\end{aligned} \right]$ 
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表 2 矩形排布方式下, 圆偏振阵列光束的合成效率
Table 2. Combining efficiency of beam array with circular polarization under rectangle configuration.
束宽/ μm 80 100 120 γ = 2.2 63.5% 75.2% 88.4% γ = 2.6 70.0% 79.4% 89.5%
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表 3 不同数值孔径和介质下, 阵列光束焦斑尺寸
Table 3. Focal-spot width of beam array with numerical apertures and refractive indices under rectangle configuration.
介质 空气 水 油 NA 0.75 0.80 0.85 0.90 0.95 0.95 0.95 阵列光束焦斑
半径/μm0.50 0.49 0.47 0.46 0.45 0.40 0.35
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[1] 杨若夫, 杨平, 沈锋 2009 物理学报 58 8297
Google Scholar
Yang R F, Yang P, Shen F 2009 Acta Phys. Sin. 58 8297
Google Scholar
[2] 范馨燕 2010 博士学位论文 (哈尔滨: 哈尔滨工业大学)
Fang X Y 2010 Ph. D. Dissertation (Harbin: Harbin Institute Of Technology) (in Chinese)
[3] Christensen S, Koski O 2007 Advanced Solid-State Photonics. Optical Society of America, Vancouver, Canada, January 28–31, 2007 WC1
[4] 刘作业, 李露, 胡碧涛 2012 激光技术 5 657
Google Scholar
Liu Z Y, Li L, Hu B T 2012 Laser Tech. 5 657
Google Scholar
[5] Zhang F, Yu H, Fang J, Zhang M, Chen S, Wang J, He A, Chen J 2016 Opt. Express 24 6656
Google Scholar
[6] 陆云清, 呼斯楞, 陆懿, 许吉, 王瑾 2015 物理学报 64 097301
Google Scholar
Lu Y Q, Hu S L, Lu Y, Xu J, Wang J 2015 Acta Phys. Sin. 64 097301
Google Scholar
[7] 王思聪, 李向平 2016 中国光学 9 185
Google Scholar
Wang S C, Li X P 2016 Chin. Opt. 9 185
Google Scholar
[8] 张洲 2016 博士学位论文 (合肥: 安徽大学)
Zhang Z 2016 Ph. D. Dissertation (Hefei: Anhui University) (in Chinese)
[9] 赵维, 唐芳, 邱丽荣, 刘大礼 2013 物理学报 62 054201
Google Scholar
Zhao W Q, Tang F, Qiu L R, Liu D L 2013 Acta Phys. Sin. 62 054201
Google Scholar
[10] Byrnes S J, Lenef A, Aieta F, Capasso F 2016 Opt. Express 24 5110
Google Scholar
[11] Shen W, Hu C, Li S, Hu X T 2017 Appl. Surf. Sci. 421 535
Google Scholar
[12] Wolf E 1959 P. Roy. Soc. A Mat. 253 349
[13] Richards B, Wolf E 1959 P. Roy. Soc. A Mat. 253 358
[14] Moh K J, Yuan X C, Bu J, Burge R E, Gao B Z 2007 Appl. Opt. 46 7544
Google Scholar
[15] 谭毅, 李新阳 2014 物理学报 63 094202
Google Scholar
Tan T, Li X Y 2014 Acta Phys. Sin. 63 094202
Google Scholar
[16] Gilad M L, Uriel L 2008 Opt. Express 16 4567
Google Scholar
[17] Uberna R, Bratcher A, Tiemann B G 2010 IEEE J. Quantum. Electron. 46 1191
Google Scholar
[18] Liu Z J, Ma P F, Su R T, Tao R M, Ma Y X, Wang X L, Zhou P 2017 J. Opt. Soc. Am. B 34 A7
Google Scholar
[19] Tian B, Pu J X 2011 Opt. Lett. 36 2014
Google Scholar
[20] Cheng Z, Zhou Y Y, Xia M, Li W, Yang K C, Zhou Y F 2015 Opt. Laser Technol. 73 77
Google Scholar
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