Optical field propagation model  of  ring-down cavity light field  based on  angular spectrum propagation theory and evaluation criterion of cavity tuning

He Xing; Tian Zhong-Zhou; Wang Shuai; Yang Ping; Xu Bing

doi:10.7498/aps.72.20221530

Abstract

In cavity ring-down technique, cavity maladjustment has an essential effect on the measurement of intracavity loss. Several adjustment criterions have been adopted to achieve the optimal cavity state. However, experimental study shows that these criterions may correspond to different cavity states, which means that there is discrepancy between different criterions. In view of this problem, a model of intracavity propagation of Gaussian beam is established based on the angular spectrum propagation theory. This model is tested by numerical simulation and experimental research together. In the simulation, the true value of intracavity loss can be known beforehand. The two-dimensional angular scanning is carried out for certain cavity mirror. The two-dimensional distributions of the measure value of intracavity loss and the transmission light intensity are obtained simultaneously. These distributions are both nonlinear and multi-extremum, which will doubtlessly increase the difficulty in realizing the cavity adjustment. By comparing the distributions , we do find the discrepancy between the largest transmission light intensity and the least measured intracavity loss. Meanwhile both of these two states may be not corresponding to the true value in fact. After statistical studies, the relative error of the least measured intracavity loss is (–37.01±11.79) ppm, whereas the relative error of the largest transmission intensity is (–2.70±0.89) ppm. The criterion of the largest transmission intensity shows better stability and repeatability. This model is further tested in a folded cavity ring-down setup. The similar scanning procedure is carried out. A major problem in the experiment is that the true value of intracavity loss cannot be known. So only the repeatability precision of the measured intracavity loss can be analyzed. The statistical results of the largest light intensity and the least measured intracavity loss are ±29.32 ppm and ±70.71 ppm, respectively. The criterion of the largest transmission intensity has better repeatability, which is basically consistent with the simulation result. In this way the rationality of this model can be verified to some degree. In this paper, the criterion of the largest transmission intensity is recommended in the cavity ring-down technique. Furthermore, this model can be a reference for the research of intracavity optical field response, intracavity optical field transmission, unstable resonator alignment, etc.

Keywords:

Authors and contacts

1.
Key Laboratory on Adaptive Optics, Chinese Academy of Sciences, Chengdu 610209, China
2.
Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209, China
3.
University of Chinese Academy of Sciences, Beijing 100049, China

Corresponding author: He Xing, hexingjiayou@126.com ; Yang Ping, pingyang2516@163.com ;

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61805251, 61875203, 11811530290, 11704382).

FullText HTML : translate this paragraph

References

[1]	Sanders V 1977 Appl. Opt. 16 19 Google Scholar
[2]	李斌成, 龚元 2010 激光与光电子学进展 47 021203 Google Scholar Li B C, Gong Y 2010 Laser Opt. Pro. 47 021203 Google Scholar
[3]	Tan Y, Wang J, Zhao X Q, Liu A W, Hu S M 2017 J. Quant. Spectrosc. Radiat. Transf. 187 274 Google Scholar
[4]	康鹏, 孙羽, 王进, 刘安雯, 胡水明 2018 67 104206 Google Scholar Kang P, Sun Y, Wang J, Liu A W, Hu S M 2018 Acta Phys. Sin. 67 104206 Google Scholar
[5]	McHale L E, Hecobian A, Yalin A P 2016 Opt. Express 24 5523 Google Scholar
[6]	Li Z Y, Hu R Z, Xie P H, Chen H, Wu S Y, Wang F Y, Wang Y H, Ling L Y, Liu J G, Liu W Q 2018 Opt. Express 26 A433 Google Scholar
[7]	Yang L Z, Yang J J, Yang Y, Zhang Z W, Wang J F, Zhang Z X, Xue P P, Gong Y K, Copner N 2017 Opt. Express 25 2031 Google Scholar
[8]	Smith I W 1978 Appl. Opt. 17 2476 Google Scholar
[9]	Li B C, Gong Y 2010 US Patent 7 679 750 B2 [2010-03-16]
[10]	Cui H, Li B C, Han Y L, Wang J, Gao C M, Wang Y F 2017 Chin. Opt. Lett. 15 053101 Google Scholar
[11]	Xiao S L, Li B C, Wang J 2020 Metrologia 57 055002 Google Scholar
[12]	Xiang W D, Yang P, Wang S, Xu B, Liu H 2018 Opto-Electronic Advances 1 180024 Google Scholar
[13]	Cui H, Li B C, Han Y L, Wang J, Gao C M, Wang Y F 2016 Opt. Express 24 013343 Google Scholar
[14]	Hamzeh T, Anam C P, Liu J J 2020 Appl. Opt. 59 9464 Google Scholar
[15]	Anderson D Z, Frisch J C, Masser C S 1984 Appl. Opt. 23 1238 Google Scholar
[16]	Paldus B A, Kachanov A A 2005 Cana. J. Phys. 83 975 Google Scholar
[17]	Romanini D 2014 Appl. Phys. B 115 517 Google Scholar
[18]	Shadman S, Rose C, Yalin A P 2016 Appl. Phys. B 122 194 Google Scholar
[19]	Maity A, Maithani S, Pradhan M 2021 Anal. Chem. 93 388 Google Scholar
[20]	易亨瑜 2006 中国激光 33 399 Google Scholar Yi H Y 2006 Chin. J. Lasers 33 399 Google Scholar
[21]	易亨瑜, 吕百达, 张凯 2006 激光技术 30 5 Google Scholar Yi H Y, Lv B D, Zhang K 2006 Laser Tech. 30 5 Google Scholar
[22]	何星 2016 博士学位论文 (北京: 中国科学院大学) He X 2016 Ph. D. Dissertation (Beijing: University of Chinese Academy of Sciences) (in Chinese)
[23]	He X, Tian Z Z, Lai B H, Zhao W, Wang S, Yang P 2021 CN Patent 113984670A [2022-01-28]
[24]	薛颖, 杜星湖, 何星, 王帅, 杨平, 许冰 2020 中国激光 47 0504001 Google Scholar Xue Y, Du X H, He X, Wang S, Yang P, Xu B 2020 Chin. J. Lasers 47 0504001 Google Scholar
[25]	杜星湖, 薛颖, 何星, 王帅, 杨平, 许冰 2020 中国激光 47 0604006 Google Scholar Du X H, Xue Y, He X, Wang S, Yang P, Xu B 2020 Chin. J. Lasers 47 0604006 Google Scholar
[26]	Hodges J T, Looney J P, Zee R D V 1996 J. Chem. Phys. 105 10278 Google Scholar
[27]	Lehmann K K 1996 J. Chem. Phys. 105 10263 Google Scholar
[28]	吕乃光 2006 傅里叶光学(第二版) (北京: 机械工业出版社) 第82—86页 Lv N G 2006 Fourier Optics (Vol. 2) (Beijing: China Machine Press) pp82–86 (in Chinese)
[29]	曲哲超, 李斌成, 韩艳玲 2011 光子学报 40 1366 Google Scholar Qu Z C, Li B C, Han Y L 2011 Acta Phot. Sin. 40 1366 Google Scholar
[30]	He X, Yan H, Dong L Z, Yang P, Xu B 2016 Chin. Phys. B 25 014211 Google Scholar
[31]	He X, Luan Y S, Dong L Z, Yang P, Xu B, Tang G M 2016 Opto-Electronic Engineering 43 46 Google Scholar

Cited By

图 1 双凹衰荡腔模型示意图

Figure 1. Schematic of double-concave ring-down cavity model.

DownLoad: Full-Size Img PowerPoint

图 2 (a)腔损耗观测值分布图; (b)透射光强峰值分布图

Figure 2. (a) Distribution of the cavity loss observation;(b) distribution of the peak value of signal intensity.

DownLoad: Full-Size Img PowerPoint

图 3 实验装置

Figure 3. Experimental setup.

DownLoad: Full-Size Img PowerPoint

图 4 (a)腔损耗观测值分布图; (b)透射光强峰值分布图

Figure 4. (a) Distribution of the cavity loss observation; (b) distribution of the peak value of signal intensity.

DownLoad: Full-Size Img PowerPoint

表 1 衰荡腔模型仿真初始参数列表

Table 1. The initial parameters of simulation model

名称	参数	数值
注入光束	横模模式	TEM₀₀
	中心波长	λ = 1064 nm
	光源线宽*	L_W = 0.5 nm
	束腰半径	w = 0.8 mm
衰荡腔	腔镜反射率	R₁ = R₂ = 99.85%
	腔镜曲率	r₁ = r₂=1 m
	腔长	L = 0.5 m
	腔镜偏移量	$ \delta_{x1} =\delta_{71} =\delta_{x2} =\delta_{y2} = 0 $
传输过程	注入过程	腔内往返传输2000次
传输过程	衰荡过程	腔内往返传输500次
注: *为在光源线宽范围内, 离散选择30个波长进行仿真.

DownLoad: CSV

表 2 重复性扫描仿真结果

Table 2. Simulation results of repetitive scanning.

编号	腔镜M₁的倾斜失调角度/(°)		光强最大峰值下的腔损耗/ppm	最长衰荡时间下的腔损耗/ppm	腔损耗真值/ppm
编号	θ_x1/(°)	θ_y1/(°)	光强最大峰值下的腔损耗/ppm	最长衰荡时间下的腔损耗/ppm	腔损耗真值/ppm
1	0	0.001	1498.06	1471.98	1500
2	–0.0005	0.001	1497.60	1461.02	1500
3	0.001	0.001	1497.51	1447.07	1500
4	0	0	1496.01	1471.87	1500

DownLoad: CSV

表 3 不同腔镜反射率下的腔损耗仿真结果

Table 3. Simulation results under different cavity mirror reflectivity.

腔镜反射率(R₁=R₂)	光强最大峰值下的腔损耗测量结果/ppm	最长衰荡时间下的腔损耗测量结果/ppm
99.80% (2000 ppm)	1996.66±0.80	1959.06±13.03
99.85% (1500 ppm)	1497.30±0.89	1462.99±11.79
99.88% (1200 ppm)	1197.63±1.06	1164.80±9.55

DownLoad: CSV

表 4 腔镜M₁不同倾斜失调量下的实验结果

Table 4. Experimental results of cavity mirror M₁ under different tilt maladjustment.

编号	光强最大峰值下的腔损耗/ppm	最长衰荡时间下的腔损耗/ppm
1	2240.61	2038.26
2	2261.66	2045.96
3	2304.96	1892.29
4	2245.25	1989.59

DownLoad: CSV

map

[1]	Sanders V 1977 Appl. Opt. 16 19 Google Scholar
[2]	李斌成, 龚元 2010 激光与光电子学进展 47 021203 Google Scholar Li B C, Gong Y 2010 Laser Opt. Pro. 47 021203 Google Scholar
[3]	Tan Y, Wang J, Zhao X Q, Liu A W, Hu S M 2017 J. Quant. Spectrosc. Radiat. Transf. 187 274 Google Scholar
[4]	康鹏, 孙羽, 王进, 刘安雯, 胡水明 2018 67 104206 Google Scholar Kang P, Sun Y, Wang J, Liu A W, Hu S M 2018 Acta Phys. Sin. 67 104206 Google Scholar
[5]	McHale L E, Hecobian A, Yalin A P 2016 Opt. Express 24 5523 Google Scholar
[6]	Li Z Y, Hu R Z, Xie P H, Chen H, Wu S Y, Wang F Y, Wang Y H, Ling L Y, Liu J G, Liu W Q 2018 Opt. Express 26 A433 Google Scholar
[7]	Yang L Z, Yang J J, Yang Y, Zhang Z W, Wang J F, Zhang Z X, Xue P P, Gong Y K, Copner N 2017 Opt. Express 25 2031 Google Scholar
[8]	Smith I W 1978 Appl. Opt. 17 2476 Google Scholar
[9]	Li B C, Gong Y 2010 US Patent 7 679 750 B2 [2010-03-16]
[10]	Cui H, Li B C, Han Y L, Wang J, Gao C M, Wang Y F 2017 Chin. Opt. Lett. 15 053101 Google Scholar
[11]	Xiao S L, Li B C, Wang J 2020 Metrologia 57 055002 Google Scholar
[12]	Xiang W D, Yang P, Wang S, Xu B, Liu H 2018 Opto-Electronic Advances 1 180024 Google Scholar
[13]	Cui H, Li B C, Han Y L, Wang J, Gao C M, Wang Y F 2016 Opt. Express 24 013343 Google Scholar
[14]	Hamzeh T, Anam C P, Liu J J 2020 Appl. Opt. 59 9464 Google Scholar
[15]	Anderson D Z, Frisch J C, Masser C S 1984 Appl. Opt. 23 1238 Google Scholar
[16]	Paldus B A, Kachanov A A 2005 Cana. J. Phys. 83 975 Google Scholar
[17]	Romanini D 2014 Appl. Phys. B 115 517 Google Scholar
[18]	Shadman S, Rose C, Yalin A P 2016 Appl. Phys. B 122 194 Google Scholar
[19]	Maity A, Maithani S, Pradhan M 2021 Anal. Chem. 93 388 Google Scholar
[20]	易亨瑜 2006 中国激光 33 399 Google Scholar Yi H Y 2006 Chin. J. Lasers 33 399 Google Scholar
[21]	易亨瑜, 吕百达, 张凯 2006 激光技术 30 5 Google Scholar Yi H Y, Lv B D, Zhang K 2006 Laser Tech. 30 5 Google Scholar
[22]	何星 2016 博士学位论文 (北京: 中国科学院大学) He X 2016 Ph. D. Dissertation (Beijing: University of Chinese Academy of Sciences) (in Chinese)
[23]	He X, Tian Z Z, Lai B H, Zhao W, Wang S, Yang P 2021 CN Patent 113984670A [2022-01-28]
[24]	薛颖, 杜星湖, 何星, 王帅, 杨平, 许冰 2020 中国激光 47 0504001 Google Scholar Xue Y, Du X H, He X, Wang S, Yang P, Xu B 2020 Chin. J. Lasers 47 0504001 Google Scholar
[25]	杜星湖, 薛颖, 何星, 王帅, 杨平, 许冰 2020 中国激光 47 0604006 Google Scholar Du X H, Xue Y, He X, Wang S, Yang P, Xu B 2020 Chin. J. Lasers 47 0604006 Google Scholar
[26]	Hodges J T, Looney J P, Zee R D V 1996 J. Chem. Phys. 105 10278 Google Scholar
[27]	Lehmann K K 1996 J. Chem. Phys. 105 10263 Google Scholar
[28]	吕乃光 2006 傅里叶光学(第二版) (北京: 机械工业出版社) 第82—86页 Lv N G 2006 Fourier Optics (Vol. 2) (Beijing: China Machine Press) pp82–86 (in Chinese)
[29]	曲哲超, 李斌成, 韩艳玲 2011 光子学报 40 1366 Google Scholar Qu Z C, Li B C, Han Y L 2011 Acta Phot. Sin. 40 1366 Google Scholar
[30]	He X, Yan H, Dong L Z, Yang P, Xu B 2016 Chin. Phys. B 25 014211 Google Scholar
[31]	He X, Luan Y S, Dong L Z, Yang P, Xu B, Tang G M 2016 Opto-Electronic Engineering 43 46 Google Scholar

[1]	Xiong Feng, Peng Zhi-Min, Wang Zhen, Ding Yan-Jun, Lü Jun-Fu, Du Yan-Jun. Accurate measurement of trace H₂S concentration based on cavity ring-down absorption spectroscopy under CO₂/CO disturbance. Acta Physica Sinica, 2023, 72(4): 043302. doi: 10.7498/aps.72.20221851
[2]	Huang Zhi-Qiu, Zhang Meng, Peng Zhi-Min, Wang Zhen, Yang Qian-Suo. Influence of finite coherence of injected light on ring-down cavity measurement method and intensity integral method for ring-down time determination. Acta Physica Sinica, 2023, 72(18): 184205. doi: 10.7498/aps.72.20230448
[3]	Wang Xing-Ping, Zhao Gang, Jiao Kang, Chen Bing, Kan Rui-Feng, Liu Jian-Guo, Ma Wei-Guang. Erratum: Uncertainty of optical feedback linear cavity ringdown spectroscopy[Acta Phys. Sin. 2022, 71(12): 124201]. Acta Physica Sinica, 2022, 71(15): 159901. doi: 10.7498/aps.71.159901
[4]	Rao Bing-Jie, Zhang Pan, Li Ming-Kun, Yang Xi-Guang, Yan Lu-Lu, Chen Xin, Zhang Shou-Gang, Zhang Yan-Yan, Jiang Hai-Feng. Multi-branch erbium fiber-based femtosecond optical frequency comb for measurement of cavity ring-down spectroscopy. Acta Physica Sinica, 2022, 71(8): 084203. doi: 10.7498/aps.71.20212162
[5]	Wang Xing-Ping, Zhao Gang, Jiao Kang, Chen Bing, Kan Rui-Feng, Liu Jian-Guo, Ma Wei-Guang. Uncertainty of optical feedback linear cavity ringdown spectroscopy. Acta Physica Sinica, 2022, 71(12): 124201. doi: 10.7498/aps.70.20220186
[6]	Wang Xing-Ping, Zhao Gang, Jiao Kang, Chen Bing, Kan Rui-Feng, Liu Jian-Guo, Ma Wei-Guang. Research on uncertainty of optical feedback linear cavity ringdown spectroscopy. Acta Physica Sinica, 2022, 0(0): 0-0. doi: 10.7498/aps.71.20220186
[7]	He Xing, Tian Zhong-Zhou, Wang Shuai, Yang Ping, Xu Bing. Modeling of intracavity light field for the alignment criterion of cavity ring-down technique based on the angular spectrum propagation theory. Acta Physica Sinica, 2022, 0(0): 0-0. doi: 10.7498/aps.71.20221530
[8]	Wang Jin-Duo, Yu Jin, Mo Ze-Qiang, He Jian-Guo, Dai Shou-Jun, Meng Jing-Jing, Wang Xiao-Dong, Liu Yang. Numerical methods of mode selection in continuous-wave cavity ring-down spectroscopy. Acta Physica Sinica, 2019, 68(24): 244201. doi: 10.7498/aps.68.20190844
[9]	Wang Zhen, Du Yan-Jun, Ding Yan-Jun, Peng Zhi-Min. Wavelength-scanned cavity ring down spectroscopy based on Fourier transform. Acta Physica Sinica, 2019, 68(20): 204204. doi: 10.7498/aps.68.20191062
[10]	Zhang Xi, Liu Hui, Jiang Kun-Liang, Wang Jin-Qi, Xiong Zhuan-Xian, He Ling-Xiang, Lü Bao-Long. Transfer cavity scheme for stabilization of lattice laser in ytterbium lattice clock. Acta Physica Sinica, 2017, 66(16): 164205. doi: 10.7498/aps.66.164205
[11]	Jia Meng, Zhao Gang, Hou Jia-Jia, Tan Wei, Qiu Xiao-Dong, Ma Wei-Guang, Zhang Lei, Dong Lei, Yin Wang-Bao, Xiao Lian-Tuan, Jia Suo-Tang. Research and data processing of double locked cavity ringdown absorption spectroscopy. Acta Physica Sinica, 2016, 65(12): 128701. doi: 10.7498/aps.65.128701
[12]	Liu Zhi-Gang, Liu Wei-Long, Zhao Hai-Jun. Quantum calculations for photodetachment cross sections of H- in an equilateral triangle cavity. Acta Physica Sinica, 2015, 64(16): 163202. doi: 10.7498/aps.64.163202
[13]	Cui Li-Hong, Yan Chang-Xiang, Zhao Wei-Ning, Zhang Xin-Jie, Hu Chun-Hui. Analysis of the positional accuracy of the self-conjugate ray in a misalignment multiple-mirror optical ring cavity. Acta Physica Sinica, 2015, 64(22): 224210. doi: 10.7498/aps.64.224210
[14]	Hu Ren-Zhi, Wang Dan, Xie Pin-Hua, Ling Liu-Yi, Qin Min, Li Chuan-Xin, Liu Jian-Guo. Diode laser cavity ring-down spectroscopy for atmospheric NO3 radical measurement. Acta Physica Sinica, 2014, 63(11): 110707. doi: 10.7498/aps.63.110707
[15]	Cao Lin, Wang Chun-Mei, Chen Yang-Qin, Yang Xiao-Hua. Theoretical investigation of optical heterodyne cavity ring down spectroscopy. Acta Physica Sinica, 2006, 55(12): 6354-6359. doi: 10.7498/aps.55.6354
[16]	FENG JIAN, WANG JI-SUO, GAO YUN-FENG, ZHAN MING-SHENG. INFLUENCE OF NONLINEARITIES OF BOTH THE FIELD AND THE INTENSITY-DEPENDENT ATOM-FIELD COUPLING ON THE EMISSION SPECTRUM OF AN ATOM IN A CAVITY. Acta Physica Sinica, 2001, 50(7): 1279-1283. doi: 10.7498/aps.50.1279
[17]	ZHAO HONG-TAI, LIU XIAO-JUN, CAO JUN-WEN, PENG LIANG-YOU, ZHAN MING-SHENG. MEASUREMENT OF THE TRANSITION OF BARIUM 6s6p1P1←6s6s1S0 USING CAVITY RINGDOWN SPECTROSCOPY. Acta Physica Sinica, 2001, 50(7): 1274-1278. doi: 10.7498/aps.50.1274
[18]	LIU ZHENG-DONG, CAO CHANG-QI, D. L. LIN. AMPLITUDE SQUEEZING OF LIGHT FIELD IN CAVITY. Acta Physica Sinica, 1991, 40(11): 1792-1798. doi: 10.7498/aps.40.1792
[19]	ZHANG WEI-PING, TAN WEI-HAN. GENERATION OF SQUEEZING LIGHT IN A LASER CAVITY. Acta Physica Sinica, 1988, 37(11): 1767-1774. doi: 10.7498/aps.37.1767
[20]	LI TIE-CHENG, FANG LI-ZHI. ON THE RADIATION OF MOLECULES IN A DETUNED CAVITY AND THE PHENOMENA OF DOUBLE-CAVITY MASERS. Acta Physica Sinica, 1964, 20(8): 753-760. doi: 10.7498/aps.20.753

Catalog

Vol. 72, Issue 1 - 2023-01-05

Metrics

Abstract views: 3330
PDF Downloads: 62
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板