Applied Physics B

, 124:153 | Cite as

Suppression of residual amplitude modulation effects in Pound–Drever–Hall locking

  • Xiaohui Shi
  • Jie Zhang
  • Xiaoyi Zeng
  • Xiaolong Lü
  • Kui Liu
  • Jing Xi
  • Yanxia Ye
  • Zehuang Lu


Residual amplitude modulation (RAM) effects in Pound–Drever–Hall (PDH) locking are analyzed in this paper. The suppression of the RAM effect in PDH locking has been investigated by many groups, but the effect of cavity response has not been fully considered. Frequency shifts caused by RAM in PDH locking are found to be both related to the amplitude of the RAM and to the cavity’s mode matching and impedance matching. We measure the RAM-to-frequency conversion coefficients at different coupling efficiencies. The result agrees well with our theoretical model. According to our analysis, the RAM effect in principle can be fully suppressed by choosing proper impedance-matching parameters and mode coupling efficiency, and we give several examples to demonstrate the potential of full suppression of the RAM effect through proper design of cavities.



We thank Prof. Zhongkun Hu and Prof. Minkang Zhou for the help of laser phase locking. The project is partially supported by the National Key R&D Program of China (Grant No. 2017YFA0304400) and the National Natural Science Foundation of China (Grant Nos. 91536116, 91336213, and 11774108).


  1. 1.
    A.D. Ludlow, M.M. Boyd, J. Ye, E. Peik, P.O. Schmidt, Optical atmoic clocks. Rev. Mod. Phys. 87, 637 (2015)ADSCrossRefGoogle Scholar
  2. 2.
    B.P. Abbott et al., Observation of gravitational waves from a binary black hole merger. Phys. Rev. Lett. 116, 061102 (2016)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    W. Demtröder, Laser Spectroscopy: Basic Concepts and Instrumentation (Springer Science and Business Media, New York, 2003)CrossRefGoogle Scholar
  4. 4.
    R.W.P. Drever, J.L. Hall, F.V. Kowalski, J. Hough, G.M. Ford, A.J. Munley, H. Ward, Laser phase and frequency stabilization using an optical resonator. Appl. Phys. B. 31, 97–105 (1983)ADSCrossRefGoogle Scholar
  5. 5.
    D.G. Matei, T. Legero, S. Häfner, C. Grebing, R. Weyrich, W. Zhang, L. Sonderhouse, J.M. Robinson, J. Ye, F. Riehle, U. Sterr, \(1.5\, \mu \text{ m }\) lasers with sub-10 mHz linewidth. Phys. Rev. Lett. 118, 263202 (2017)ADSCrossRefGoogle Scholar
  6. 6.
    W. Zhang, M.J. Martin, C. Benk, J.L. Hall, J. Ye, C. Hagemann, T. Legero, U. Sterr, F. Riehle, G.D. Cole, M. Aspelmeyer, Reduction of residual ampltude modulation to \(1\times 10^{-6}\) for frequency modulation and laser stabilization. Opt. Lett. 39, 1980–1983 (2014)ADSCrossRefGoogle Scholar
  7. 7.
    J.L. Hall, W. Zhang, J. Ye, in Accurate Removal of RAM from FM Laser Beams. International Frequency Control Symposium (IEEE), pp. 713–716 (2015)Google Scholar
  8. 8.
    N.C. Wong, J.L. Hall, Servo control of amplitude modulation in frequency-modulation spectrospectry: demonstration of shot-noise-limited detection. J. Opt. Soc. Am. B 2, 1527–1533 (1985)ADSCrossRefGoogle Scholar
  9. 9.
    M. Gehrtz, G.C. Bjorklund, E.A. Whittaker, Quantum-limited laser frequency-modulation spectroscopy. J. Opt. Soc. Am. B 2, 1510–1526 (1985)ADSCrossRefGoogle Scholar
  10. 10.
    L.F. Li, F. Liu, C. Wang, L.S. Chen, Measurement and control of residual amplitude modulation in optical phase modulation. Rev. Sci. Instrum. 83, 043111 (2012)ADSCrossRefGoogle Scholar
  11. 11.
    J. Keller, S. Ignatovich, S.A. Webster, T.E. Mehistäubler, Simple vibration-insensitive cavity for laser stabilization at the \(10^{-16}\) level. Appl. Phys. B 116, 203–210 (2014)ADSCrossRefGoogle Scholar
  12. 12.
    Z.X. Li, W.G. Ma, W.H. Yang, Y.J. Wang, Y.H. Zheng, Reduction of zero baseline drift of the Pound–Drever–Hall error signal with a wedged electro-optical crystal for squeezed state generation. Opt. Lett. 41, 3331–3334 (2016)ADSCrossRefGoogle Scholar
  13. 13.
    Z.Y. Tai, L.L. Yan, Y.Y. Zhang, X.F. Zhang, W.G. Guo, S.G. Zhang, H.F. Jiang, Electro-optic modulator with ultra-low residual amplitude modulation for frequency modulation and laser stabilization. Opt. Lett. 41, 5584–5587 (2016)ADSCrossRefGoogle Scholar
  14. 14.
    D.G. Matei, T. Legero, C. Grebing, S. Häfner, C. Lisdat, R. Weyrich, W. Zhang, L. Sonderhouse, J.M. Robinson, F. Riehle, J. Ye, U. Sterr, A second generation of low thermal noise cryogenic silicon resonators. J. Phys. Conf. Ser. 723, 012031 (2016)CrossRefGoogle Scholar
  15. 15.
    E.D. Black, An introduction to Pound-Drever-Hall laser frequency stabilization. Am. J. Phys. 69, 79–87 (2001)ADSCrossRefGoogle Scholar
  16. 16.
    H. Shen, L.F. Li, J. Bi, J. Wang, L.S. Chen, Systematic and quantitative analysis of residual amplitude modulation in Pound–Drever–Hall frequency stabilization. Phys. Rev. A 92, 063809 (2015)ADSCrossRefGoogle Scholar
  17. 17.
    F. Bondu, O. Debieu, Accurate measurement method of Fabry–Perot cavity parameters via optical transfer function. Appl. Opt. 46, 2611–2614 (2007)ADSCrossRefGoogle Scholar
  18. 18.
    T. Kessler, C. Hagemann, C. Grebing, T. Legero, U. Sterr, F. Riehle, M.J. Martin, L. Chen, J. Ye, A sub-40-mHz-linewidth laser based on a silicon single-crystal optical cavity. Nat. Photon. 6, 687–692 (2012)ADSCrossRefGoogle Scholar
  19. 19.
    J. Zhang, X.H. Shi, X.Y. Zeng, X.L. Lü, K. Deng, Z.H. Lu, Characterization of electrical noise limits in ultra-stable laser systems. Rev. Sci. Instrum. 87, 123105 (2016)ADSCrossRefGoogle Scholar
  20. 20.
    J. Zhang, W. Wu, X.H. Shi, X.Y. Zeng, K. Deng, Z.H. Lu, Design verification of large time constant thermal shields for optical reference cavities. Rev. Sci. Instrum. 87, 023104 (2016)ADSCrossRefGoogle Scholar
  21. 21.
    X.Y. Zeng, Y.X. Ye, X.H. Shi, Z.Y. Wang, K. Deng, J. Zhang, Z.H. Lu, Thermal noise limited higher-order mode locking of a reference cavity. Opt. Lett. 43, 1690–1693 (2018)ADSCrossRefGoogle Scholar
  22. 22.
    N. Uehara, A. Ueda, K. Ueda, H. Sekiguchi, T. Mitake, K. Nakamura, I. Kataoka, Ultralow-loss mirror of the parts-in-\(10^6\) level at 1064 nm. Opt. Lett. 20, 530–532 (1995)ADSCrossRefGoogle Scholar
  23. 23.
    N. Uehara, K. Ueda, Accurate measurement of ultralow loss in a high-finesse Fabry–Perot interferometer using the frequency response functions. Appl. Phys. B. 61, 9–15 (1995)ADSCrossRefGoogle Scholar
  24. 24.
    Z.K. Hu, B.L. Sun, X.C. Duan, M.K. Zhou, L.L. Chen, S. Zhan, Q.Z. Zhang, J. Luo, Demonstration of an ultrahigh-sensitivity atom-interferometry absolute gravimeter. Phys. Rev. A 88, 043610 (2013)ADSCrossRefGoogle Scholar
  25. 25.
    B.J.J. Slagmolen, M.B. Gray, K.G. Baigent, D.E. McClelland, Phase-sensitive reflection technique for characterization of a Fabry–Perot interferometer. Appl. Opt. 39, 3638–3643 (2000)ADSCrossRefGoogle Scholar
  26. 26.
    F. Acernese et al., Measurement of the optical parameters of the Virgo interferometer. Appl. Opt. 46, 3466–3484 (2007)CrossRefGoogle Scholar
  27. 27.
    J.H. Chow, I.C.M. Littler, D.S. Rabeling, D.E. McClelland, M.B. Gray, Using active resonator impedance matching for shot-noise limited, cavity enhanced amplitude modulated laser absorption spectroscopy. Opt. Express 16, 7726–7738 (2014)ADSCrossRefGoogle Scholar
  28. 28.
    G. Mueller, Qp Z. Shu, R. Adhikari, D.B. Tanner, D. Reitze, Determination and optimization of mode matching into optical cavities by heterodyne detection. Opt. Lett. 25, 266–268 (2000)ADSCrossRefGoogle Scholar
  29. 29.
    D.S. Rabeling, J.H. Chow, M.B. Gray, D.E. McClelland, Experimental demonstration of impedance match locking and control for coupled resonators. Opt. Express 18, 9314–9323 (2014)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.MOE Key Laboratory of Fundamental Physical Quantities Measurement, Hubei Key Laboratory of Gravitation and Quantum Physics, School of PhysicsHuazhong University of Science and TechnologyWuhanPeople’s Republic of China

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