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基于电光晶体马赫-曾德(M-Z)干涉仪的载波包络相位偏移频率(carrier-envelop offset frequency, f0)调节方法是一种新颖的f0调节方法. 该方法通过改变脉冲包络而不改变载波频率实现对f0信号的调节. 本文对该方法所涉及的偏振控制装置进行了仿真, 分析了其中波片光轴偏差对输出激光偏振方向和偏振度的影响. 在实验上提出了一种光轴校准方法以减小波片光轴偏差带来的影响, 并对比了抽运电流调节方法和基于电光晶体M-Z干涉仪的f0调节方法对f0信号和光梳与激光拍频信号(beat note, fb)的影响. 实验结果表明改变抽运电流, 在f0调节量为9 MHz的情况下, 对fb影响为7 MHz. 而在相同f0调节量下, 电光晶体M-Z干涉仪f0调节方法对fb 的影响为0.2 MHz, 仅为抽运电流对fb影响的1/35, 从而验证了基于电光晶体M-Z干涉仪的f0调节方法可以有效降低对fb的干扰, 为利用fb锁定重复频率(repetition rate, fr), 进而实现光梳梳齿线宽的压窄提供了一种技术手段.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 3568Google 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 635Google 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 5102Google Scholar
[4] Udem T, Reichert J, Holzwarth R, Hänsch T W 1999 Opt. Lett. 24 881Google Scholar
[5] Hachisu H, Petit G, Nakagawa F, Hanado Y, Ido T 2017 Opt. Express 25 8511Google 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 3707Google 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 065004Google 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 033201Google Scholar
[11] Yamanaka K, Ohmae N, Ushijima I, Takamoto M, Katori H 2015 Phys. Rev. Lett. 114 230801Google 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 7891Google Scholar
[13] Coddington I, Swann W C, Newbury N R 2008 Phys. Rev. Lett. 100 013902Google Scholar
[14] Lee C C, Mohr C, Bethge J, Suzuki S, Fermann M E, Hartl I, Schibli T R 2012 Opt. Lett. 37 3084Google Scholar
[15] McFerran J J, Swann W C, Washburn B R, Newbury N R 2006 Opt. Lett. 31 1997Google 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 113904Google Scholar
[17] Hudson D D, Holman K W, Jones R J, Cundiff S T, Ye J, Jones D J 2005 Opt. Lett. 30 2948Google Scholar
[18] Iwakuni K, Inaba H, Nakajima Y, Kobayashi T, Hosaka K, Onae A, Hong F L 2012 Opt. Express 20 13769Google Scholar
[19] Nakamura T, Tani S, Ito I, Kobayashi Y 2017 Opt. Express 25 4994Google Scholar
[20] Hundertmark H, Wandt D, Fallnich C, Haverkamp N, Telle H 2004 Opt. Express 12 770Google Scholar
[21] Koke S, Grebing C, Frei H, Anderson A, Assion A, Steinmeyer G 2010 Nat. Photonics 4 462Google Scholar
[22] Newbury N R, Washburn B R 2005 IEEE J. Quantum Electron. 41 1388Google 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 064202Google 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 030601Google Scholar
[26] Ma Y X, Meng F, Wang Y, Wang A M, Zhang Z G 2019 Chin. Opt. Lett. 17 041402Google 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 074203Google Scholar
Cao S Y, Lin B K, Yuan X D, Ding Y J, Meng F, Fang Z J 2021 Acta Phys. Sin. 70 074203Google Scholar
[28] 曹士英, 孟飞, 方占军, 李天初 2012 物理学报 61 064208Google Scholar
Cao S Y, Meng F, Fang Z J, Li T C 2012 Acta Phys. Sin. 61 064208Google Scholar
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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Fig. 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 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
Fig. 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.
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° -
[1] Udem T, Reichert J, Holzwarth R, Hänsch T W 1999 Phys. Rev. Lett. 82 3568Google 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 635Google 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 5102Google Scholar
[4] Udem T, Reichert J, Holzwarth R, Hänsch T W 1999 Opt. Lett. 24 881Google Scholar
[5] Hachisu H, Petit G, Nakagawa F, Hanado Y, Ido T 2017 Opt. Express 25 8511Google 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 3707Google 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 065004Google 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 033201Google Scholar
[11] Yamanaka K, Ohmae N, Ushijima I, Takamoto M, Katori H 2015 Phys. Rev. Lett. 114 230801Google 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 7891Google Scholar
[13] Coddington I, Swann W C, Newbury N R 2008 Phys. Rev. Lett. 100 013902Google Scholar
[14] Lee C C, Mohr C, Bethge J, Suzuki S, Fermann M E, Hartl I, Schibli T R 2012 Opt. Lett. 37 3084Google Scholar
[15] McFerran J J, Swann W C, Washburn B R, Newbury N R 2006 Opt. Lett. 31 1997Google 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 113904Google Scholar
[17] Hudson D D, Holman K W, Jones R J, Cundiff S T, Ye J, Jones D J 2005 Opt. Lett. 30 2948Google Scholar
[18] Iwakuni K, Inaba H, Nakajima Y, Kobayashi T, Hosaka K, Onae A, Hong F L 2012 Opt. Express 20 13769Google Scholar
[19] Nakamura T, Tani S, Ito I, Kobayashi Y 2017 Opt. Express 25 4994Google Scholar
[20] Hundertmark H, Wandt D, Fallnich C, Haverkamp N, Telle H 2004 Opt. Express 12 770Google Scholar
[21] Koke S, Grebing C, Frei H, Anderson A, Assion A, Steinmeyer G 2010 Nat. Photonics 4 462Google Scholar
[22] Newbury N R, Washburn B R 2005 IEEE J. Quantum Electron. 41 1388Google 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 064202Google 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 030601Google Scholar
[26] Ma Y X, Meng F, Wang Y, Wang A M, Zhang Z G 2019 Chin. Opt. Lett. 17 041402Google 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 074203Google Scholar
Cao S Y, Lin B K, Yuan X D, Ding Y J, Meng F, Fang Z J 2021 Acta Phys. Sin. 70 074203Google Scholar
[28] 曹士英, 孟飞, 方占军, 李天初 2012 物理学报 61 064208Google Scholar
Cao S Y, Meng F, Fang Z J, Li T C 2012 Acta Phys. Sin. 61 064208Google Scholar
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