A method of measuring depth of focus in ultrafast pulsed laser systems based on <i>Z</i>-scanning technology

LIN Kesheng; GAO Yu; ZHONG Xiaoqing; JIANG Xiaofang

doi:10.7498/aps.74.20241658

Abstract

With the development of technology, ultrafast pulse lasers are increasingly used in many fields, such as material processing, imaging, and medical treatments. The precision of these applications often depends on the ability to focus the laser beam into a tight spot with a minimal divergence in a certain range along the optical axis. Therefore, accurate measurement of depth of focus (DOF) is crucial for optimizing the performance of ultrafast laser systems and ensuring the reliability of the results obtained in various experiments and applications. Traditional methods of measuring the DOF mainly rely on directly capturing the beam size, which is impractical in high-intensity environments of ultrafast pulse laser systems due to potential damage to sensors and limitations in measurement accuracy. Furthermore, using autocorrelation or moving sensors to measure DOF in ultrafast pulse lasers introduces complex optical paths, leading to measurement errors and making them unreliable in precise focusing applications.To solve the problem of the limitations of current DOF measurement techniques for ultrafast pulse laser, in this work we propose a novel method based on Z-scan technique. According to nonlinear optical theory, it is found that the transmittance curves obtained from open-aperture (OA) Z-scan measurements of samples exhibiting two-photon absorption (TPA) all follow a Lorentzian distribution. By fitting this curve by Lorentzian distribution, the DOF of ultrafast pulse lasers and the full widths at half maximum (FWHM) of the OA Z-scan curves can be determined rapidly. The transmittance curves of solid and liquid samples with TPA across different types of lenses and microscope objectives within ultrafast optical systems are measured. The results show that the FWHM of the OA Z-scan curves and the theoretical DOF values are well consistent. This method effectively relates the size of the DOF to the beam waist radius derived from the distribution of the Lorentzian function in the OA Z-scan experimental curves, eliminating the influence of other parameters on the measurement results. In conclusion, a novel method of measuring DOF in ultrafast pulse laser systems by using the OA Z-scan technique is proposed. It provides a rapid, accurate and reliable way for determining the DOF in ultrafast laser focusing systems, thereby precisely controlling the ultrafast laser beam for a wide range of applications.

Keywords:

Authors and contacts

1.
Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter, Key Laboratory of Atomic and Subatomic Structure and Quantum Control (Ministry of Education), School of Physics, South China Normal University, Guangzhou 510006, China
2.
Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, South China Normal University, Guangzhou 510006, China

Corresponding author: JIANG Xiaofang, jiangxf@scnu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 62075065), the Science and Technology Program Project of Guangzhou, China (Grant Nos. 2019050001, 20202030148), the Natural Science Foundation of Guangdong Province, China (Grant No. 2021A1515011388), and the Guangdong Provincial Laboratory of Optical Information Materials and Technology, China (Grant No. 2017B030301007).

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References

[1]	Chen B Y, Chakraborty T, Daetwyler S, Manton J D, Dean K, Fiolka R 2020 Biomed. Opt. Express 11 3830 Google Scholar
[2]	Bo E, Luo Y M, Chen S, Liu X Y, Wang N S, Ge X, Wang X H, Chen S F, Chen S, Li J H, Liu L B 2017 Optica 4 701 Google Scholar
[3]	刘有海, 秦天翔, 王英策, 亢兴旺, 刘君, 吴佳琛, 曹良才 2023 72 084205 Google Scholar Liu Y H, Qin T X, Wang Y C, Kang X W, Liu J, Wu J C, Cao L C 2023 Acta Phys. Sin. 72 084205 Google Scholar
[4]	王华英, 张志会, 廖薇, 宋修法, 郭中甲, 刘飞飞 2012 61 044208 Google Scholar Wang H Y, Zhang Z H, Liao W, Song X F, Guo Z J, Liu F F 2012 Acta Phys. Sin. 61 044208 Google Scholar
[5]	韦芊屹, 倪洁蕾, 李灵, 张聿全, 袁小聪, 闵长俊 2023 72 178701 Google Scholar Wei Q Y, Ni J L, Li L, Zhang Y Q, Yuan X C, Min C J 2023 Acta Phys. Sin. 72 178701 Google Scholar
[6]	Adachi S, Ishii H, Kanai T, Ishii N, Kosuge A, Watanabe S 2007 Opt. Lett. 32 2487 Google Scholar
[7]	Cheng J, Liu C S, Shang S, Liu D, Perrie W, Dearden G, Watkins K 2013 Opt. Laser Technol. 46 88 Google Scholar
[8]	Guo B S, Sun J Y, Lu Y F, Jiang L 2019 Int. J. Extreme Manuf. 1 032004 Google Scholar
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[18]	Fan Z B, Qiu H Y, Zhang H L, Pang X N, Zhou L D, Liu L, Ren H, Wang Q H, Dong J W 2019 Light Sci. Appl. 8 67 Google Scholar
[19]	Flores A, Wang M R, Yang J J 2004 Appl. Opt. 43 5618 Google Scholar
[20]	Wang Z W, Li Q, Yan F 2021 J. Phys. D: Appl. Phys. 54 085103 Google Scholar
[21]	Vázquez-Villa A, Delgado-Atencio J A, Vázquez-Montiel S, Castro-Ramos J, Cunill-Rodríguez M 2015 Opt. Lett. 40 2842 Google Scholar
[22]	Aydin T, Akgul Y S 2010 Opt. Express 18 14212 Google Scholar
[23]	Banerji S, Meem M, Majumder A, Sensale-Rodriguez B, Menon R 2020 Optica 7 214 Google Scholar
[24]	Moreno-Larios J A, Rosete-Aguilar M, Rodríguez-Herrera O G, Garduño-Mejía J 2020 Appl. Opt. 59 7247 Google Scholar
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[27]	Yin M, Li H P, Tang S H, Ji W 2000 Appl. Phys. B 70 587 Google Scholar

Cited By

图 1 测量DOF的开孔Z扫描实验装置

Figure 1. Open-aperture Z-scan setup for measuring DOF.

DownLoad: Full-Size Img PowerPoint

图 2 在(a)低光强和(b)高光强条件下, 开孔Z扫描计算公式前m项近似仿真的透射率分布曲线以及洛伦兹函数拟合; 取m = 3时, 理论模拟的不同(c)样品厚度、(d)非线性吸收系数下的透射率分布曲线. 插图为相应的归一化透射率分布

Figure 2. Under conditions of (a) low laser intensity and (b) high laser intensity, the simulated transmittance distribution curves for the first m terms of the open-aperture Z-scan calculation formula, and the Lorentzian function fits; simulated transmittance distributions for varying (c) sample thicknesses and (d) nonlinear absorption coefficients when m = 3. The insets show the corresponding normalized transmittance distributions.

DownLoad: Full-Size Img PowerPoint

图 3 (a)对光斑直径D进行测量的示意图; (b)光束沿光轴的光强分布模拟及DOF计算值; (c) 1 mm ZnSe的开孔Z扫描曲线及FWHM拟合值

Figure 3. (a) Schematic of measuring the diameter D of the light spot; (b) simulation of intensity distribution along the optical axis and calculated DOF; (c) open-aperture Z-scan curve for 1 mm ZnSe and measured FWHM.

DownLoad: Full-Size Img PowerPoint

图 4 (a)相同入射光强下, 不同厚度ZnSe的开孔Z扫描结果; (b)归一化至[0, 1]的结果

Figure 4. (a) Open-aperture Z-scan results for ZnSe with varying thicknesses at a constant incident light intensity; (b) results normalized to the range [0, 1].

DownLoad: Full-Size Img PowerPoint

图 5 (a)相同厚度ZnSe, 不同入射光强下的开孔Z扫描结果; (b)归一化到[0, 1]的结果

Figure 5. (a) Open-aperture Z-scan results for ZnSe with varying incident peak intensities at a constant thickness; (b) the results normalized to the range [0, 1].

DownLoad: Full-Size Img PowerPoint

图 6 (a)光束沿光轴的光强分布模拟及DOF计算结果; (b) 1 mm 比色皿中的荧光素染料的开孔Z扫描曲线及FWHM拟合值

Figure 6. (a) Simulation of intensity distribution along the optical axis and calculated DOF; (b) open-aperture Z-scan curve for fluorescein in a 1 mm cuvette and measured FWHM.

DownLoad: Full-Size Img PowerPoint

图 7 开孔Z扫描结果以及对应的洛伦兹拟合曲线　(a) 20倍消色差显微物镜(焦距10 mm); (b)平凸透镜(焦距50 mm); (c)消色差透镜(焦距50 mm); (d)平凸透镜(焦距100 mm)

Figure 7. Open-aperture Z-scan results and their Lorentzian fit results: (a) 20× apochromatic microscope objective lens (f = 10 mm); (b) planoconvex lens (f = 50 mm); (c) achromatic lens (f = 50 mm); (d) plano-convex lens (f = 100 mm).

DownLoad: Full-Size Img PowerPoint

表 1 焦深计算值DOF_Cal与实验值DOF_Exp的比较(DOF_Cal通过(4)式计算, DOF_Exp是在图7所示的实验中得出的测量值)

Table 1. Depth of focus comparison (the DOF_Cal calculated using Eq. (4) and the DOF_Exp measured from the experimental transmittance data in Fig. 7).

聚焦元件	DOF_Cal/mm	Z扫描实验测量的DOF_Exp/mm
聚焦元件	DOF_Cal/mm	洛伦兹拟合FWHM(m = 1, (3)式)	高阶项矫正FWHM(m = 11, (2)式)
20倍消色差显微物镜 (f = 10 mm)	0.36	0.40±0.01	0.34±0.01
平凸透镜(f = 50 mm)	1.51	1.65±0.04	1.47±0.04
消色差透镜(f = 50 mm)	1.51	1.53±0.04	1.46±0.02
平凸透镜(f = 100 mm)	4.58	4.89±0.15	4.58±0.14

DownLoad: CSV

map

[1]	Chen B Y, Chakraborty T, Daetwyler S, Manton J D, Dean K, Fiolka R 2020 Biomed. Opt. Express 11 3830 Google Scholar
[2]	Bo E, Luo Y M, Chen S, Liu X Y, Wang N S, Ge X, Wang X H, Chen S F, Chen S, Li J H, Liu L B 2017 Optica 4 701 Google Scholar
[3]	刘有海, 秦天翔, 王英策, 亢兴旺, 刘君, 吴佳琛, 曹良才 2023 72 084205 Google Scholar Liu Y H, Qin T X, Wang Y C, Kang X W, Liu J, Wu J C, Cao L C 2023 Acta Phys. Sin. 72 084205 Google Scholar
[4]	王华英, 张志会, 廖薇, 宋修法, 郭中甲, 刘飞飞 2012 61 044208 Google Scholar Wang H Y, Zhang Z H, Liao W, Song X F, Guo Z J, Liu F F 2012 Acta Phys. Sin. 61 044208 Google Scholar
[5]	韦芊屹, 倪洁蕾, 李灵, 张聿全, 袁小聪, 闵长俊 2023 72 178701 Google Scholar Wei Q Y, Ni J L, Li L, Zhang Y Q, Yuan X C, Min C J 2023 Acta Phys. Sin. 72 178701 Google Scholar
[6]	Adachi S, Ishii H, Kanai T, Ishii N, Kosuge A, Watanabe S 2007 Opt. Lett. 32 2487 Google Scholar
[7]	Cheng J, Liu C S, Shang S, Liu D, Perrie W, Dearden G, Watkins K 2013 Opt. Laser Technol. 46 88 Google Scholar
[8]	Guo B S, Sun J Y, Lu Y F, Jiang L 2019 Int. J. Extreme Manuf. 1 032004 Google Scholar
[9]	Gattass R R, Mazur E 2008 Nat. Photonics 2 219 Google Scholar
[10]	Kravtsov V, Ulbricht R, Atkin J M, Raschke M B 2016 Nat. Nanotechnol. 11 459 Google Scholar
[11]	Kumar R S S, Rao S V, Giribabu L, Rao D N 2007 Chem. Phys. Lett. 447 274 Google Scholar
[12]	Bindra K S, Kar A K 2001 Appl. Phys. Lett. 79 3761 Google Scholar
[13]	Krausz F, Ivanov M 2009 Rev. Mod. Phys. 81 163 Google Scholar
[14]	Tang H C, Men T, Liu X L, Hu Y D, Su J Q, Zuo Y L, Li P, Liang J Y, Downer M C, Li Z Y 2022 Light Sci. Appl. 11 244 Google Scholar
[15]	Castro-Marín P, Castro-Olvera G, Garduño-Mejia J, Rosete-Aguilar M, Bruce N C, Reid D T, Rodríguez-Herrera O G 2017 Opt. Express 25 14473 Google Scholar
[16]	Ramírez-Guerra C, Rosete-Aguilar M, Garduño-Mejía J 2020 Appl. Opt. 59 1519 Google Scholar
[17]	Castro-Marín P, Castro-Olvera G, Ruíz C, Garduño-Mejía J, Rosete-Aguilar M, Bruce N C 2017 AIP Adv. 7 105014 Google Scholar
[18]	Fan Z B, Qiu H Y, Zhang H L, Pang X N, Zhou L D, Liu L, Ren H, Wang Q H, Dong J W 2019 Light Sci. Appl. 8 67 Google Scholar
[19]	Flores A, Wang M R, Yang J J 2004 Appl. Opt. 43 5618 Google Scholar
[20]	Wang Z W, Li Q, Yan F 2021 J. Phys. D: Appl. Phys. 54 085103 Google Scholar
[21]	Vázquez-Villa A, Delgado-Atencio J A, Vázquez-Montiel S, Castro-Ramos J, Cunill-Rodríguez M 2015 Opt. Lett. 40 2842 Google Scholar
[22]	Aydin T, Akgul Y S 2010 Opt. Express 18 14212 Google Scholar
[23]	Banerji S, Meem M, Majumder A, Sensale-Rodriguez B, Menon R 2020 Optica 7 214 Google Scholar
[24]	Moreno-Larios J A, Rosete-Aguilar M, Rodríguez-Herrera O G, Garduño-Mejía J 2020 Appl. Opt. 59 7247 Google Scholar
[25]	Sheik-bahae M, Said A A, Wei T H, Wu Y Y, Hagan D J, Soileau M J, Stryland E W V 1990 Proc. SPIE Int. Soc. Opt. Eng. 1148 41 Google Scholar
[26]	Sheik-Bahae M, Said A A, Wei T H, Hagan D J, Van Stryland E W 1990 IEEE J. Quantum Electron. 26 760 Google Scholar
[27]	Yin M, Li H P, Tang S H, Ji W 2000 Appl. Phys. B 70 587 Google Scholar

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A method of measuring depth of focus in ultrafast pulsed laser systems based on Z-scanning technology

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Corresponding author: JIANG Xiaofang, jiangxf@scnu.edu.cn

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A method of measuring depth of focus in ultrafast pulsed laser systems based on Z-scanning technology

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Corresponding author: JIANG Xiaofang, jiangxf@scnu.edu.cn

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