Quantum mechanism method for self-mixing
interference effects in LD pumped laser
Zhang Yong*①~⑥Yao Jian-quan①，③~⑥Xu Ke-xin ①Wang Peng①，③~⑥
①College of Precision Instrument and Opto-Electronics Engineering,
Institute of Laser and Optoelectronics, TianjinUniversity, Tianjin (300072) P.R.China
②College of Science ,Hebei University of Technology, Tianjin (300130)P.R.China
③Cooperated Institute of Nankai University and Tianjin University
④Key Lab. of OPtoelectric Information Science and Technology ,Ministry of Education
⑤State Key Lab. of Laser Technology(HuazhongUniversity of Science and Technology)
⑥State Key Lab of Tunable (GAS)Laser Technology on Defense Science and Technology
(HarbinUniversity of Technology)
Tel: 022-27407676 Fax: 022-27406436 Email Add.:
Abstract
Self-mixing interference effectsin the LD pumped green laser are observed. Then small disturbance theory is used for the first time to analysis the quantumbehaviors in the laser. The cavity system without feedback is considered to be the initial status function, the influence of feedback is considered to be the disturbance. The interaction Hamilton is deduced finally.
Keywords: quantum mechanism method, LD pumped,green laser, self-mixing interference, small disturbance theory,quantumbehaviors,cavity system,initial status function,influence of feedback,interaction Hamilton
1. INTRODUCTION
Self-mixing interference effects have been widely studied since it was discovered in 1960s [1-5]. By analyzing the feedback signals, one can know some information such as displacement, position and moving velocity of the target. Therefore, it becomes a new domain in microcosmic measurement. But to our knowledge, theories on self-mixing interference effects are still not perfect. We tried to do some work about it.We first observed the interference signals of strong (the reflectivity of the target is 89.6% at 532nm) and weak feedback (the reflectivity of the target is 4.9% at 532nm). Each casewe observed the signals of the length of external cavity (the distance between the laser cavity and the target)of22cm and 1.4cm respectively. And then by using small disturbance theory, we deduced the interaction Hamilton.
2. EXPERIMENTAL OBSERVATION
The experimental setup of self-mixing interference was shown in figure 1. The experimental settings including the laser source (the central wavelength was 532nm), the target and a photon detector.
We observed self-mixing interference effects signals of strong and weak feedback
2.1 Strong feedback
We took the length of Lext for 20cm and 5cm，respectively. As shown below.
2.1.1 Lext=20cm
We can see from the experimental result that, the intensity of the signals of higher current (higher than 0.90A) were low, while that of lowercurrent (about 0.65A) were about 200 times of the former. The threshold current of the laser was 0.585A. According to the results, we can drew the conclusion that: We can get the strongest interference effect at the working current I=1.11Ith.Based on this, we put forward for the first time the idea that deducing the matter of self-mixing interference effect using small disturbance theory. We did this work in section 3.
In figure 2 the units of x-axis are 5ms/Div and different current different units in y-axis for each curve as shown in the figure.
2.1.2 Lext=5cm
Also in figure 3 the units of x-axis are 5ms/Div and different current different units in y-axis for each curve as shown in the figure.
2.2 Weak feedback
In this part, we took the length of Lext for 25cm only. We can see the similarityresults to that of strong feedback.As shown below.
Different current different units in x-axis and in y-axis for each curve as shown in the figure.
3. THEORYITICAL ANALYSIS USING SMALL DISTURBANCE THEORY
In discussingthis, we took the intra-cavity system for basic state function, took the feedback for small disturbance.
Real time Schrodinger equation presented system information
（1）
where,was the Hamilton functorof the laser system. It can be written as.
The wave function can be expanded as latent function of ground state function:
（2）
where,and werelatent functionand energy value of .
（3）
where,.The expanding coefficientwas related to the transition probability of electron from ground state to higher states at . And
In order to obtain the wave function, we should know the form of the function of the disturbance.We denoted the vector field of electromagnetism field, themomentum functor , we got:
(4)
For traveling wave:
， （5）
where stands for the x-axial projection of the unit vector，is the amplitude intensity of electric field. Then 。
Based on Maxwell equations, we got:
（6）
where was the vertical part of, . Thus the energy density can be written as: （7）
Regarding , we got:
（8）
At last we obtained the Hamilton functor
（9）
Using this Hamilton functor, we can calculate the wave function of disturbance, and thereby know the distributing probability of photons.
4. CONCLUSIONS
The experimental results showed that: near the threshold current,different initial external cavity length, different current be when the signals reached the maximum value, strong feedback changed some characters of the cavity, thus changed the threshold current. The disturbance of the optical feedback of steady target had little effect on the intra-cavity. But if we move or shake the target, the signals were still obvious. Indicating that moving or shaking the target arose stronger disturbance. Therefore the interferometer shouldwork near the threshold current in order to obtain stronger signals while measuring distance. The intensity of the signals of higher current waslow, while that of lowercurrent were about 200 times of the former. We can get the strongest interference effect at the working current I=1.11Ith. In the next stage, we willdiscuss the problem in-depth.
ACKNOWLEDGEMENTS
This work is supported by Cooperated Institute of Nankai University and TianjinUniversity,
Key Lab. of OPtoelectric Information Science and Technology, Ministry of Education
State Key Lab. of Laser Technology (HuazhongUniversity of Science and Technology)
State Key Lab of Tunable (GAS) Laser Technology on Defence Science and Technology
(HarbinUniversity of Technology)
REFERENCES
1. Edson T. Shimizu. Directional Discrimination in the Self-mixing Type Laser Doppler Velocimeter. Appl.Opt.,26(2): 4541-4544 ,1987
2.Paone, N., Scalise, L. Advances in self-mixing vibrometry, Proceedings of SPIE - The International Society for Optical Engineering, v 4204:103-114,2001
3. Yu Yan-guang, Ye Hui-ying Yao Jian-quan. Self-mixing interference effects in a multi-mode LD:Experimental observation and theoretical analysis. J. of Optoelectronics Laser,13(11):1190-1193, 2002
4. Yong Zhang,Yanguang Yu, Jianquan Yao, Peng Wang, Jin Chen. Analysis of self-mixing interference signals in LD pumped solid-state lasers using fast Fourier transform technique. Proceedings of SPIE - The International Society for Optical Engineering v 4919 p 488-492 0277-786X, 2002
5. ZHANG Yong，YAO Jian-quan，WANG Peng，YU Yan-guang，CHEN Jin，Study on self-mixing interference effects in the LD pumped multi-mode solid-state laser, Transactions of Tianjin University, Vol.9, No.4, P261-263, 2003
*contact. Zhang Yong, e-mail: ; phone: 022-27407676; fax: 022-27406436; Address: College of Precision Instrument and Opto-Electronics Engineering, Optoelectronic Information Science and Technology Laboratory, Tianjin University, Tianjin (300072) China; College of Science, Hebei University of Technology, Tianjin (300130) P.R.China
Proc. of SPIE Vol. 5628 1