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激光谐振腔内相位各向异性会引起频率分裂, 两分裂模的频差大小由表现出的相位延迟所决定. 对于腔内相位延迟较小的He-Ne激光器, 两分裂模很接近, 处于烧孔重叠区, 存在模式竞争而不能同时振荡, 形成隐频率分裂. 同时, 使得激光器两正交偏振方向上的相邻级纵模产生固定的变动量, 其大小等于隐频率分裂量的2倍. 如果沿激光偏振方向施加横向磁场, Ne原子谱线发生横向Zeeman分裂, 增益原子分成两群, 分别为平行于磁场和垂直于磁场方向偏振的光提供增益, 大大减弱模竞争, 使得激光器的两分裂模可同时振荡并测得频差. 在谐振腔内放入倾斜的石英晶体片或半波片, 由两种方法分别测量频率分裂量并进行比较. 实验表明两种方法测量的结果均与理论计算相符, 平均相对偏差不超过1%. 据此可以准确得到Zeeman双频激光器的频差大小, 并为半波片测量提供了新方法.Phase anisotropy in laser resonant cavity will bring about an influence on laser frequency and polarization, such as laser frequency splitting, of which the frequency difference is determined by their introduced phase retardation. For a helium-neon laser with a small phase retardation in the cavity, the two split modes are very close to each other whose burned holes are overlapped. Then only one mode oscillates while the other is always in lock-in state due to strong mode competition, which forms hidden frequency split. Meanwhile the spacing between adjacent longitudinal modes deviates from original value and produces a certain variation equal to twice the hidden splitting frequency difference. As a result the longitudinal modes spacing variation is dominated by the phase retardation. On the other hand, by applying transverse magnetic field to a laser tube along the polarization direction, the neon atoms will undergo transverse Zeeman effect and be divided into two groups to provide the gain for polarized light beams parallel to the magnetic field and perpendicular to the magnetic field respectively. Then the laser mode competition is greatly weakened so that the two split modes can oscillate simultaneously to obtain the frequency difference. In order to make profound study of the consistency between longitudinal mode spacing variation and splitting mode frequency difference in the presence of transverse magnetic field, the samples of tilted quartz plate or half wave plate is placed into laser cavity to produce phase retardation. By the two mentioned methods, the splitting frequency difference varying with phase retardation of samples is deduced to make a comparison. Two measurements show that the average relative deviation is less than 1%, while the experimental results accord with theoretical analyses quite well. In this way splitting frequency difference of Zeeman dual-frequency laser can be determined accurately, and a new method to measure the phase retardation of half wave plate is provided.
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Keywords:
- Zeeman laser /
- anisotropy /
- frequency splitting /
- laser longitudinal mode
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图 2 He-Ne激光器产生隐频率分裂原理
Fig. 2. Principle of implicit frequency splitting of He-Ne laser.
图 3 相邻纵模形成的光拍频谱图
Fig. 3. Beat frequency spectrum of adjacent longitudinal mode spacing.
图 4 双折射-Zeeman激光器实验装置结构图
Fig. 4. Schematic design of birefringence-Zeeman laser experimental setup.
图 5 激光频率分裂量随石英晶体倾角的变化
Fig. 5. Laser splitting frequency difference varies with tilted angle of quartz plate.
图 6 两种方法测得分裂模频差的相对偏差
Fig. 6. Relative deviation of splitting modes frequency difference with two methods.
表 1 半波片相位延迟测量结果
Table 1. Measurement of phase retardation of half wave plate.
待测波片 BZFS方法测得分裂频差$\Delta {v_{\rm{L}}}$/MHz LMSC方法测得相邻级纵模间隔 BZFS方法测量${\phi _1}$/(°) LMSC方法测量${\phi _2}$/(°) ${\varDelta _1}$/MHz ${\varDelta _2}$/MHz 1# 6.02 722.18 710.10 178.487 178.482 2# 4.9 711.13 721.08 181.232 181.252 3# 11.17 727.08 705.03 177.192 177.227 
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[1] Bretenaker F, Floch A L 1990 IEEE J. Quantum. Electron. 26 1451
Google Scholar
[2] Voitovich A P, Svirina L P, Severikov V N 1991 Opt. Commun. 80 435
Google Scholar
[3] Travagnin M, van Exter M P, Jansen van Doorn A K, Woerdman J P 1996 Phys. Rev. A 54 1647
Google Scholar
[4] Travagnin M 1997 Phys. Rev. A 56 4094
Google Scholar
[5] Schreiber T, Roser F, Schmidt O, Limpert J, Iliew R, Lederer F, Petersson A, Jacobsen C, Hansen K P, Broeng J, Tünnermann A 2005 Opt. Express 13 7621
Google Scholar
[6] Khandokhin P A, Ievlev I V, Lebedeva Y S, Mukhin I B, Palashov O V, Khazanov E A 2011 Quantum. Electron. 41 103
Google Scholar
[7] Khandokhin P A, Mamaev Y A 2015 Quantum. Electron. 45 128
Google Scholar
[8] Fördös T, Jaffrès H, Postava K, Seghilani M S, Garnache A, Pištora J, Drouhin H J 2017 Phys. Rev. A 96 043828
Google Scholar
[9] Litvin I A 2013 Opt. Express 21 10706
Google Scholar
[10] Mehdi A, Julien F, Alexandre J, Ghaya B, Daniel D, Jean-Marie G 2018 Opt. Express 26 6739
Google Scholar
[11] Petrovskiy V N, Prokopova N M, Protsenko E D, Yermachenko V M 2007 Laser Phys. Lett. 4 191
Google Scholar
[12] Oron R, Blit S, Davidson N, Friesem A A, Bomzon Z, Hasman E 2000 Appl. Phys. Lett. 77 3322
Google Scholar
[13] Jansen van Doorn AK, van Exter M P, Woerdman J P 1998 IEEE Quantum. Electron. 34 700
Google Scholar
[14] Wu Y, Zhang S L, Li Y 2013 Opt. Express 21 13684
Google Scholar
[15] Oram R J, Latimer I D, Spoor S P, Bocking S 1993 J. Phys. D 26 1169
Google Scholar
[16] Zhang S L, Wu M X, Jin G F 1990 Appl. Opt. 29 1265
Google Scholar
[17] Zhang S L, Holzapfel W 2013 Orthogonal Polarization in Lasers: Physical Phenomena and Engineering Applications (Berlin: Wiley and Tsinghua University Press) pp113−115
[18] Mamaev Y A, Khandokhin P A 2011 IEEE Quantum. Electron. 41 571
Google Scholar
[19] 陈恺, 祝连庆, 牛海莎, 孟阔, 董明利 2019 物理学报 68 104201
Google Scholar
Chen K, Zhu L Q, Niu H S, Meng K, Dong M L 2019 Acta Phys. Sin. 68 104201
Google Scholar
[20] Liu W X, Liu M, Zhang S L 2008 Appl. Opt. 47 5562
Google Scholar
[21] Holzapfel W, Settgast W 1989 Appl. Opt. 28 4585
Google Scholar
[22] Holzapfel W, Neuschaefer-Rube S, Kobusch M 2000 Measurement 28 277
Google Scholar
[23] Ren C, Yang X T, Zhang S L 2012 Chin. Phys. Lett. 29 054204
Google Scholar
[24] Hu Z H, Harding K, Huang P S, Zhang S L, Yoshizawa T 2010 Proc. SPIE 7855 711
[25] Fei L G, Li Y, Zong X B, Zhang S L 2005 Opt. Commun. 249 255
Google Scholar
[26] Zhou L F, Zhang S L, Huang Y, Guo H 2008 Laser Phys. 18 1517
Google Scholar
[27] 朱守深, 张书练, 刘维新, 牛海莎 2014 物理学报 63 064201
Google Scholar
Zhu S S, Zhang S L, Liu W X, Niu H S 2014 Acta Phys. Sin. 63 064201
Google Scholar
[28] Zong X B, Liu W X, Zhang S L 2005 Chin. Phys. Lett. 22 1906
Google Scholar
[29] Guo J H, Shen S, Jiang J H, Zhang S L 1996 Acta Opt. Sin. 16 716
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