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

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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.

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Authors and contacts

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).

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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.

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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

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

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

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

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