摘要
窄线宽稳频激光器在高灵敏高分辨率激光光谱、基本物理常数的测定等领域有着广泛的应用,同时又是作为未来时间频率标准的光钟的必要组成部分。为了获得频率稳定且线宽窄的激光,通常采用Pound-Drever-Hall(PDH)技术将激光频率锁定在高精细度光学谐振腔的共振频率上。因而被锁定激光的频率稳定度由参考腔光程长度的稳定度及伺服锁定系统综合决定,研究表明环境振动及温度变化对参考腔光程长度的影响已成为限制激光线宽进入Hz及亚Hz量级的主要因素。
本文致力于研究光学谐振腔由振动引起的弹性形变,采用了有限元分析法对环境振动导致谐振腔光程长度的变化进行了定量计算和数值分析。通过优化设计腔体及选取合适的支撑方式来补偿腔体形变,降低腔体光程长度对振动的敏感度。
对水平侧向支撑的圆柱形和长方形这两种常见驻波腔在竖直振动加速度作用下的形变进行了数值计算,通过调整优化支撑方式及位置,使得光程长度对振动的敏感度降低到25kHz/ms~(-2);计算了竖直放置的圆锥形腔体的振动敏感度,发现在结构对称的情况下,其形变量仍存在一定的不对称性,通过微调腔体支撑面上下部分的质量分布来补偿形变,理论上获得腔体光程长度对振动免疫的设计方案。
首次提出了在PDH稳频中采用具有隔离反馈光特性的环形腔用于提供频率参考标准的设想。通过对环形腔体在不同支撑方式下振动形变的数值计算,发现对于不同宽度的支撑面,都对应存在一个支撑位置,使得腔体的光程变化量为零,即对振动免疫,这一结论为光学谐振腔的振动免疫设计提供了有价值的参考。
通过对采用振动免疫圆锥形参考腔的理论计算结果与实验系统测试结果进行比较,验证了此研究方法的有效性。
Stable and narrow-linewidth lasers are essential in the development of optical clocks that will serve as future optical frequency standards. Furthermore, they have important applications in many other fields such as high-precision laser spectroscopy and fundamental physics tests. To achieve superior stability, a free-running laser is usually servo-locked to the resonance of an optical cavity. Therefore, the remaining instability of the locked laser is a combination of the instability of the length of the frequency reference itself and the defects of the servo-locking system. It is shown that environmental vibrations and temperature fluctuations are the dominant factures which degrade the stability of the optical length of the cavity and limit the laser linewidth into Hertz or sub-Hertz level.
In this paper, a detailed numerical analysis of optical cavities is performed for state-of-the-art laser stabilization. Elastic deformation due to vibrations of the cavities with different shapes and mounting methods is quantitatively analyzed using finite element analysis. We show that with modified cavity geometry and suitable mounting schemes it is feasible to minimize the susceptibility of the optical length to vibrational perturbations.
For linear cavities, simulation results of the optical length to vibrations are obtained by removing material form the underside of a cylindrical cavity and a rectangular one for the purpose of deformation compensation. A sensitivity of vertical vibrations of 25 kHz/ms~(-2) is achieved. By vertically supporting a tapered cavity at its midplane, we find that the deformation is still asymmetrical to the supporting surface even when the structure is symmetrical to it. After delicately adjusting the weight distribution to compensate the vertical deformation, the vibrational sensitivity is reduced to zero.
Ring cavities which have the characteristic of avoiding optical feedback effects are proposed to serve as the frequency references in the PDH laser stabilization system for the first time. A series of research and analysis of vibration sensitivity of a ring cavity is given. By adjusting the position of supporting beams, we show that the optical path can remain unchanged at a certain supporting position for each beam width, which means that ring cavities can also obtain low vibration sensitivities as linear cavities. The results discussed here offer experimental parameters that can be adjusted to achieve vibration immune conditions and provide theoretical support for the experiments.
By comparing the test result of the stable and narrow-linewidth laser system with a modified tapered cavity as its frequency reference to the theoretical result, validity of this research is then verified.
引文
1. B. C. Young, F. C. Cruz, W. M. Itano, and J. C. Bergquist, Phys. Rev. Lett. 82, 3799(1999).
2. S. A. Diddams et al., Science 293, 825 (2001).
3. H. S. Margolis et al., Science 306, 1355 (2004).
4. M. Takamoto, F. L. Hong, R. Higashi, and H. Katori, Nature 435, 321 (2005).
5. H. Stoehr, F. Mensing, J. Helmcke, and U. Sterr, Opt. Lett. 31, 736 (2006).
6. M. M. Boyd et al., Science 314, 1430 (2006).
7. A. D. Ludlow, X. Huang, M. Notcutt, T. Zanon-Willette, S. M. Foreman, M. M. Boyd, S. Blatt, and J. Ye, Opt. Lett. 32, 641 (2007).
8. L. S. Ma, Opt. Photon. News 18, 42 (2007).
9. V. A. Dzuba and V. V. Flambaum, Phys. Rev. A 61, 034502 (2000).
10. S. N. Lea, Rep. Prog. Phys. 70, 1473 (2007).
11. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
12. M. Notcutt, L. S. Ma, J. Ye, and J. L. Hall, Opt. Lett. 30, 1815 (2005).
13. T. Nazarova, F. Riehle, and U. Sterr, Appl. Phys. B 83, 531 (2006).
14. S. A. Webster, M. Oxborrow, and P. Gill, Phys. Rev. A 75, 011801(R) (2007).
15. J. Hough et al., The Detection of Gravitational Waves, edited by D. G. Blair (Cambridge University Press, UK, 1991)
16. F. J. Raab, S. E. Whitcomb, Technical Report LIGO-T920004-00-R, 1992.
17. K. Numata, A. Kemery, and J. Camp, Phys. Rev. Lett. 93, 250602 (2004).
18. L. S. Chen, J. L. Hall, and J. Ye, Phys. Rev. A 74, 053801 (2006).
19. Schenzle and Devoe, Phys.Rev.A, 1982, 25: 2606-2621
20. K. Nakagawa and A. S. Shelkovnikov, Appl. Phys. 1994, 33(27):6383-6386
21. Ch. Salomon, D. Hils, J. L. Hall, J. Opt. Soc. Am. B Vol.5, No.8 (1988)
22.N.M.Sampas,E.K.Gustafson,R.L.Byer.Opt.Lett.1983,18(12):947-949
23.A.Y.Nevsky,M.Eichenseer,J.von Zanthier,and H.Walther,Opt.Commun.210,91(2002)
24.S.A.Webster,M.Oxborrow,and P.Gill,Opt.Lett.29,1497(2004)
25.Eric D.Black,Am.J.Phys.January 2001,69(1):79-87
26.J.Hough,D.Hils,M.D.Rayman.Appl.Phys.B 33,179-185(1984)
27.S.A.Webster,M.Oxborrow,and P.Gill,Opt.Lett.29,1497(2004).
28.J.Hough,D.Hils,M.D.Rayman.Appl.Phys.B 33,179-185(1984)
29.毕志毅,丁良恩,马龙生,郑一善.光学谐振腔反射特性的光外差探测[J].华东师范大学学报.1989,第三期:41-46
30.毕志毅.位相调制光外差光谱技术的研究及应用.上海:华东师范大学,(1986)
31.陈扬骎,杨晓华.光谱测量技术,华东师范大学出版社,(2006)
32.赵凯华,钟锡华.光学,北京大学出版社,上册(1982)
33.陈钰清,王静环.激光原理,浙江大学出版社,(1992)
34.Whittaker E.A.,Gehrtz M.and Bjorklund G.C.J.Opt.Soc.Am.B 2 1320,(1985)