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Electro-optic-modulator (EOM) based Mach-Zehnder (M-Z) interferometer is a novel method of controlling the carrier envelope offset frequency (f0). It is achieved by adjusting the envelop of the pulse, while keeping the carrier frequency unchanged. In this paper, the polarization control device involved in this method is simulated, and the influences caused by the deviation of the optical axis of the wave plate on the polarization direction and the degree of output laser are analyzed. An optical axis calibration method is proposed to reduce the influence caused by the deviation of optical axis of wave plate. The effects of pump current and EOM based M-Z interferometer on f0 and the beat note (fb) between the comb and the laser are compared with each other. The experimental results show that the effect of changing the pump current on fb is 7 MHz, when the f0 adjustment quantity is 9 MHz. Under the same f0 adjustment quantity, the influence of EOM based M-Z interferometer on fb is 0.2 MHz, which is only 1/35 of the influence of pump current. Therefore, it is verified that EOM based M-Z interferometer can effectively reduce the interference to fb. It provides a technical means to narrow the line width of optical comb by using fb to lock repetition rate (fr) .
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Keywords:
- Mach-Zehnder interferometer /
- offset frequency /
- narrow linewidth /
- optical frequency comb
[1] Udem T, Reichert J, Holzwarth R, Hänsch T W 1999 Phys. Rev. Lett. 82 3568
Google Scholar
[2] Jones D J, Diddams S A, Ranka J K, Stentz A, Windeler R S, Hall J L, Cundiff S T 2000 Science 288 635
Google Scholar
[3] Diddams S A, Jones D J, Ye J, Cundiff S T, Hall J L, Ranka J K, Windeler R S, Holzwarth R, Udem T, Hänsch T W 2000 Phys. Rev. Lett. 84 5102
Google Scholar
[4] Udem T, Reichert J, Holzwarth R, Hänsch T W 1999 Opt. Lett. 24 881
Google Scholar
[5] Hachisu H, Petit G, Nakagawa F, Hanado Y, Ido T 2017 Opt. Express 25 8511
Google Scholar
[6] Schliesser A, Brehm M, Keilmann F, van der Weide D 2005 Opt. Express 13 9029
[7] Millo J, Boudot R, Lours M, Bourgeois P Y, Luiten A N, Coq Y Le, Kersalé Y, Santarelli G 2009 Opt. Lett. 34 3707
Google Scholar
[8] Coddington I, Swann W C, Nenadovic L, Newbury N R 2009 Nat. Photonics 3 351
[9] Bothwell T, Kedar D, Oelker E, Robinson J M, Bromley S L, Tew W L, Ye J, Kennedy C J 2019 Metrologia 56 065004
Google Scholar
[10] Brewer S M, Chen J S, Hankin A M, Clements E R, Chou C W, Wineland D J, Hume D B, Leibrandt D R 2019 Phys. Rev. Lett. 123 033201
Google Scholar
[11] Yamanaka K, Ohmae N, Ushijima I, Takamoto M, Katori H 2015 Phys. Rev. Lett. 114 230801
Google Scholar
[12] Inaba H, Hosaka K, Yasuda M, Nakajima Y, Iwakuni K, Akamatsu D, Okubo S, Kohno T, Onae A, Hong F L 2013 Opt. Express 21 7891
Google Scholar
[13] Coddington I, Swann W C, Newbury N R 2008 Phys. Rev. Lett. 100 013902
Google Scholar
[14] Lee C C, Mohr C, Bethge J, Suzuki S, Fermann M E, Hartl I, Schibli T R 2012 Opt. Lett. 37 3084
Google Scholar
[15] McFerran J J, Swann W C, Washburn B R, Newbury N R 2006 Opt. Lett. 31 1997
Google Scholar
[16] Corwin K L, Newbury N R, Dudley J M, Coen S, Diddams S A, Weber K, Windeler R S 2003 Phys. Rev. Lett. 90 113904
Google Scholar
[17] Hudson D D, Holman K W, Jones R J, Cundiff S T, Ye J, Jones D J 2005 Opt. Lett. 30 2948
Google Scholar
[18] Iwakuni K, Inaba H, Nakajima Y, Kobayashi T, Hosaka K, Onae A, Hong F L 2012 Opt. Express 20 13769
Google Scholar
[19] Nakamura T, Tani S, Ito I, Kobayashi Y 2017 Opt. Express 25 4994
Google Scholar
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Google Scholar
[21] Koke S, Grebing C, Frei H, Anderson A, Assion A, Steinmeyer G 2010 Nat. Photonics 4 462
Google Scholar
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Google Scholar
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Google Scholar
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[28] 曹士英, 孟飞, 方占军, 李天初 2012 物理学报 61 064208
Google Scholar
Cao S Y, Meng F, Fang Z J, Li T C 2012 Acta Phys. Sin. 61 064208
Google Scholar
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图 1 脉冲包络与载波示意图
Figure 1. Diagram of the envelope and carrier of a pulse.
图 2 基于电光晶体M-Z干涉仪的f0调节方法示意图 (a)基本原理图; (b)脉冲包络位置的演化图
Figure 2. Principal of the EOM based M-Z interferometer for controlling f0: (a) Principle of f0 control device; (b) evolution of the pulse envelope.
图 3 基于电光晶体的M-Z干涉仪示意图及光在其中的偏振方向
Figure 3. Diagram of experimental device of the EOM based M-Z interferometer for controlling f0 and the polarization of the light that travels along it.
图 4 偏振控制装置结构图, 其中QWP为1/4波片, 实线为QWP和EOM快轴, 虚线为QWP和EOM慢轴,
$ \alpha $ 为入射光偏振方向与x轴夹角,$ \beta $ 为出射光偏振方向与x轴夹角Figure 4. Structure of PCD, where, QWP is quarter-wave plate, the solid lines are the fast axes of QWP and EOM, the dotted lines are the slow axes of QWP and EOM,
$ \alpha $ is the angle between the polarization of the incident light and the x-axis,$ \beta $ is the angle between the polarization of the output light and the x-axis.
图 5 器件光轴存在偏离的情况 (a)第一个1/4波片光轴发生偏离; (b)第二个1/4波片光轴发生偏离; (c) EOM光轴发生偏离
Figure 5. Influence of the deviation of the optical axis on the polarization: (a) Deviation of the first QWP optical axis; (b) deviation of the second QWP optical axis; (c) deviation of the EOM optical axis.
图 6 1/4波片光轴校准示意图
Figure 6. Schematic of QWP optical axis alignment.
图 7 光经过偏振控制装置后的偏振方向偏离角
Figure 7. Deviation angle of the light after passing through polarization control device.
图 8 实验采用的锁模激光器结构图. LD, 抽运源; EDF, 掺铒增益光纤; WDM, 波分复用器; COL, 准直器; HWP, 1/2波片; FR, 法拉第旋光器; ISO, 隔离器; M, 反射镜
Figure 8. Diagram of the mode-locked laser: LD, pump laser; EDF, Er-doped fiber; WDM, 980 nm/1550 nm wavelength division multiplexing; COL, collimator; HWP, half wave plate; FR, Faraday rotator; ISO, optical isolator; M, reflective mirror.
图 9 有无f0调节装置光谱对比
Figure 9. Comparison of the spectrum with and without f0 control device.
图 10 电光晶体M-Z干涉仪f0调节装置对f0、 fb 和 fr 频率影响 (a) f0; (b) fb; (c) fr
Figure 10. Influence of the EOM based M-Z interferometer on f0, fb and fr: (a) f0; (b) fb; (c) fr.
图 11 抽运电流对f0、 fb 和 fr 频率影响 (a) f0; (b) fb; (c) fr
Figure 11. Influence of the pump current on f0, fb and fr: (a) f0; (b) fb; (c) fr .
图 12 PZT对f0和 fr 频率影响 (a) f0; (b) fr
Figure 12. Influence of PZT on f0 and fr: (a) f0; (b) fr .
表 1 1/4波片光轴校准数据
Table 1. Alignment data of the QWPs.
1st QWP 2nd QWP 3th QWP 4th QWP A side 2.23° 3.81° 3.75° 2.35° B side 2.23° 3.79° 3.69° 2.42° 
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[1] Udem T, Reichert J, Holzwarth R, Hänsch T W 1999 Phys. Rev. Lett. 82 3568
Google Scholar
[2] Jones D J, Diddams S A, Ranka J K, Stentz A, Windeler R S, Hall J L, Cundiff S T 2000 Science 288 635
Google Scholar
[3] Diddams S A, Jones D J, Ye J, Cundiff S T, Hall J L, Ranka J K, Windeler R S, Holzwarth R, Udem T, Hänsch T W 2000 Phys. Rev. Lett. 84 5102
Google Scholar
[4] Udem T, Reichert J, Holzwarth R, Hänsch T W 1999 Opt. Lett. 24 881
Google Scholar
[5] Hachisu H, Petit G, Nakagawa F, Hanado Y, Ido T 2017 Opt. Express 25 8511
Google Scholar
[6] Schliesser A, Brehm M, Keilmann F, van der Weide D 2005 Opt. Express 13 9029
[7] Millo J, Boudot R, Lours M, Bourgeois P Y, Luiten A N, Coq Y Le, Kersalé Y, Santarelli G 2009 Opt. Lett. 34 3707
Google Scholar
[8] Coddington I, Swann W C, Nenadovic L, Newbury N R 2009 Nat. Photonics 3 351
[9] Bothwell T, Kedar D, Oelker E, Robinson J M, Bromley S L, Tew W L, Ye J, Kennedy C J 2019 Metrologia 56 065004
Google Scholar
[10] Brewer S M, Chen J S, Hankin A M, Clements E R, Chou C W, Wineland D J, Hume D B, Leibrandt D R 2019 Phys. Rev. Lett. 123 033201
Google Scholar
[11] Yamanaka K, Ohmae N, Ushijima I, Takamoto M, Katori H 2015 Phys. Rev. Lett. 114 230801
Google Scholar
[12] Inaba H, Hosaka K, Yasuda M, Nakajima Y, Iwakuni K, Akamatsu D, Okubo S, Kohno T, Onae A, Hong F L 2013 Opt. Express 21 7891
Google Scholar
[13] Coddington I, Swann W C, Newbury N R 2008 Phys. Rev. Lett. 100 013902
Google Scholar
[14] Lee C C, Mohr C, Bethge J, Suzuki S, Fermann M E, Hartl I, Schibli T R 2012 Opt. Lett. 37 3084
Google Scholar
[15] McFerran J J, Swann W C, Washburn B R, Newbury N R 2006 Opt. Lett. 31 1997
Google Scholar
[16] Corwin K L, Newbury N R, Dudley J M, Coen S, Diddams S A, Weber K, Windeler R S 2003 Phys. Rev. Lett. 90 113904
Google Scholar
[17] Hudson D D, Holman K W, Jones R J, Cundiff S T, Ye J, Jones D J 2005 Opt. Lett. 30 2948
Google Scholar
[18] Iwakuni K, Inaba H, Nakajima Y, Kobayashi T, Hosaka K, Onae A, Hong F L 2012 Opt. Express 20 13769
Google Scholar
[19] Nakamura T, Tani S, Ito I, Kobayashi Y 2017 Opt. Express 25 4994
Google Scholar
[20] Hundertmark H, Wandt D, Fallnich C, Haverkamp N, Telle H 2004 Opt. Express 12 770
Google Scholar
[21] Koke S, Grebing C, Frei H, Anderson A, Assion A, Steinmeyer G 2010 Nat. Photonics 4 462
Google Scholar
[22] Newbury N R, Washburn B R 2005 IEEE J. Quantum Electron. 41 1388
Google Scholar
[23] Hänsel W, Giunta M, Lezius M, Fischer M, Holzwarth R 2017 Conference on Lasers and Electro-Optics San Jose, United States, May 14-19, 2017 pSF1C.5
[24] Ning K, Hou L, Fan S T, Yan L L, Zhang Y Y, Rao B J, Zhang X F, Zhang S G, Jiang H F 2020 Chin. Phys. Lett. 37 064202
Google Scholar
[25] Wang H B, Han H N, Zhang Z Y, Shao X D, Zhu J F, Wei Z Y 2020 Chin. Phys. B 29 030601
Google Scholar
[26] Ma Y X, Meng F, Wang Y, Wang A M, Zhang Z G 2019 Chin. Opt. Lett. 17 041402
Google Scholar
[27] 曹士英, 林百科, 袁小迪, 丁永今, 孟飞, 方占军 2021 物理学报 70 074203
Google Scholar
Cao S Y, Lin B K, Yuan X D, Ding Y J, Meng F, Fang Z J 2021 Acta Phys. Sin. 70 074203
Google Scholar
[28] 曹士英, 孟飞, 方占军, 李天初 2012 物理学报 61 064208
Google Scholar
Cao S Y, Meng F, Fang Z J, Li T C 2012 Acta Phys. Sin. 61 064208
Google Scholar
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