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Laser self-mixing interferometry (SMI) has been widely researched and applied to the field of traditional physical quantities (such as displacement, distance, velocity and vibration) detection due to the well-known merits of compact structure, low-cost and high sensitivity, additionally, it has also shown great potential in nano-particle sizing during the last two decades, primarily depending on the incoherent stochastic superposition of laser beam’s interaction with each particle in the illuminating volume, and the particle diameter can be determined from the power spectra of self-mixed signals through Lorentz fitting. SMI particle sensing generally uses constant current driving laser diodes (LD), so the power spectrum peak occurs around zero-frequency and merely exhibits the right-hand half. Some other particle sensors using solid-state lasers (SSL), however, prefer to employ a pair of acousto-optic modulators (AOM) as frequency shifters, which pronouncedly increases the complexity and the cost of the whole system. In this paper, linear modulation current is applied to a LD to achieve laser frequency tuning and conveniently shift the concerned Lorentz peak to any desired spectrum position. Moreover, higher-order harmonics of the shifted Lorentz peak, arising from intrinsically tilted SMI fringes, exhibit wider spectrum broadening than the main peak and can be employed to improve the sensitivity in nano-particle recognition. The technique proposed has been validated by simulation and experimental results, and it is beneficial to developing low-cost, compact and highly sensitive SMI particle sensors or instruments.
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Keywords:
- laser feedback /
- linear frequency tuning /
- particle sizing /
- higher-order harmonics /
- sensitivity
[1] 毛威, 张书练, 张连清, 朱钧, 李岩, 2006 55 4704
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图 1 仿真信号生成原理图
Figure 1. Schematic diagram of the simulated signal generation
图 2 不同光反馈强度下单一粒子激光回馈仿真信号及其功率谱图
Figure 2. Power spectra of laser feedback signals of a single particle at different feedback strength levels
图 3 激光回馈仿真信号示例
Figure 3. Exemplary simulation signal of laser feedback
图 4 不同光反馈强度下激光回馈仿真信号功率谱图
Figure 4. Power spectra of laser feedback signals at different feedback strength levels
图 5 实验结构示意图
Figure 5. Schematic diagram of the experimental setup.
图 6 激光回馈实验信号功率谱示例
Figure 6. Exemplary power spectrum of laser feedback signal in experiments
图 7 添加滤光片之后激光回馈实验信号功率谱示例
Figure 7. Exemplary power spectrum of laser feedback signal in experiments after optical filter inserted
图 8 不同粒径激光回馈信号功率谱的洛伦兹宽度
Figure 8. Lorentz width of power spectra of laser feedback signals under different particle sizes
表 1 仿真参数
Table 1. Simulation parameters
参数 数值 参数 数值 反馈强度 C $ C< 1 $ 粒子数目 $ \left\langle N\right\rangle $ 100 线宽展宽因子 α 5 环境温度 T 298 K 样品距离 $ L_0 $ 8 cm 溶剂黏度 η $ 8.935\times 10^{-4} $ Pa·s 激光波长 λ 850 nm 粒子粒径 x 500 nm 溶剂折射率 n 1.33 电流调谐系数 γ $ 8\times 10^{9} $ Hz/mA 波尔兹曼常数 $k_{\rm{B} }$ $ 1.3806488\times 10^{-23} $ 采样率 100 kHz 调制电流峰峰值 5 mA 调制电流频率 100 Hz 
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表 2 不同谐波阶次下洛伦兹峰的宽度
Table 2. Width of Lorentz peak under different harmonic orders
谐波阶次 1 2 3 4 5 6 $ Dq^2 $ 250.74 553.48 735.08 1028.34 1225.51 1464.29
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表 3 本方案与其他两种方案的定性比较
Table 3. Comparison between this scheme and other two typical methods
方案 结构 成本 灵敏度提升 本方案 简单 较低 有 方案一 简单 最低 无 方案二 较复杂 很高 无
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[1] 毛威, 张书练, 张连清, 朱钧, 李岩, 2006 55 4704
Google Scholar
Mao W, Zhang S L, Zhang L Q, Zhu J, Li Y 2006 Acta Phys. Sin. 55 4704
Google Scholar
[2] 谈宜东, 张书练 2007 56 6408
Google Scholar
Tan Y D, Zhang S L 2007 Acta Phys. Sin. 56 6408
Google Scholar
[3] 郝辉, 夏巍, 王鸣, 郭冬梅, 倪小琦 2014 63 234202
Google Scholar
Hao H, Xia W, Wang M, Guo D M, Ni X Q 2014 Acta Phys. Sin. 63 234202
Google Scholar
[4] 张玉燕, 周航, 闫美素 2015 64 054203
Google Scholar
Zhang Y Y, Zhou H, Yan M S 2015 Acta Phys. Sin. 64 054203
Google Scholar
[5] Sadiq Orakzai M, Amin S, Ahmad Khan Z, Akram F 2022 Opt. Mater. 129 112553
Google Scholar
[6] Cavedo F, Esmaili P, Norgia M 2022 Sensors 22 8456
Google Scholar
[7] Xiang R, Wang C, Lu L 2019 J. Opt. 48 384
Google Scholar
[8] Zhang Z, Wang F, Yuan T, Li C 2020 Opt. Rev. 27 313
Google Scholar
[9] Zhao Y, Xiang R, Chen J, Huang Z, Wang X, Ma Y, Yu B, Lu L 2021 Precis. Eng. 68 256
Google Scholar
[10] Zakian C, Dickinson M, King T 2005 J. Opt. A: Pure Appl. Opt. 7 S445
Google Scholar
[11] Otsuka K, Abe K, Sano N, Sudo S, Ko J Y 2005 Appl. Opt. 44 1709
Google Scholar
[12] Sudo S, Miyasaka Y, Kamikariya K, Nemoto K, Otsuka K 2006 Jpn. J. Appl. Phys. 45 L926
Google Scholar
[13] Sudo S, Miyasaka Y, Otsuka K, Takahashi Y, Oishi T, Ko J Y 2006 Opt. Express 14 1044
Google Scholar
[14] Sudo S, Miyasaka Y, Nemoto K, Kamikariya K, Otsuka K 2007 Opt. Express 15 8135
Google Scholar
[15] Wang H R, Shen J Q 2008 Chin. Opt. Lett. 6 871
Google Scholar
[16] Wang H R, Shen J Q, Wang B, Yu B, Xu Y 2010 Appl. Phys. B 101 173
Google Scholar
[17] Wang H R, Shen J Q 2012 Appl. Phys. B 106 127
Google Scholar
[18] Wang H R, Shen J Q 2014 Appl. Phys. B 115 285
Google Scholar
[19] Contreras V, Lönnqvist J, Toivonen J 2016 Opt. Express 24 260908
Google Scholar
[20] Ramírez-Miquet E E, Perchoux J, da Costa Moreira R, Zhao Y, Luna-Arriaga A, Tronche C, Sotolongo-Costa O 2017 Revista Cubana de Fisica 34 48
[21] da Costa Moreira R, Perchoux J, Zhao Y, Tronche C, Jayat F, Bosch T 2017 2017 IEEE Sensors (Glasgow: IEEE) pp1–3
[22] Herbert J, Bertling K, Taimre T, Rakić A D, Wilson S 2018 Opt. Express 26 25778
Google Scholar
[23] Zhao Y, Zhang M, Zhang C, Yang W, Chen T, Perchoux J, Ramírez-Miquet E E, da Costa Moreira R 2019 Appl. Sci. 9 5563
Google Scholar
[24] Zhao Y, Camps T, Bardinal V, Perchoux J 2019 Appl. Sci. 9 3903
Google Scholar
[25] Plantier G, Bes C, Bosch T 2005 IEEE J. Quantum Electron. 41 1157
Google Scholar
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