Skip to main content
SpringerLink
Log in

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

  • Published:
Applied Physics B Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. A.D. Ludlow, M.M. Boyd, J. Ye, E. Peik, P.O. Schmidt, Optical atmoic clocks. Rev. Mod. Phys. 87, 637 (2015)

    Article  ADS  Google Scholar 

  2. B.P. Abbott et al., Observation of gravitational waves from a binary black hole merger. Phys. Rev. Lett. 116, 061102 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  3. W. Demtröder, Laser Spectroscopy: Basic Concepts and Instrumentation (Springer Science and Business Media, New York, 2003)

    Book  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

  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)

    Article  ADS  Google Scholar 

  9. M. Gehrtz, G.C. Bjorklund, E.A. Whittaker, Quantum-limited laser frequency-modulation spectroscopy. J. Opt. Soc. Am. B 2, 1510–1526 (1985)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  Google Scholar 

  15. E.D. Black, An introduction to Pound-Drever-Hall laser frequency stabilization. Am. J. Phys. 69, 79–87 (2001)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  17. F. Bondu, O. Debieu, Accurate measurement method of Fabry–Perot cavity parameters via optical transfer function. Appl. Opt. 46, 2611–2614 (2007)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  26. F. Acernese et al., Measurement of the optical parameters of the Virgo interferometer. Appl. Opt. 46, 3466–3484 (2007)

    Article  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

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).

Author information

Authors and Affiliations

  1. MOE Key Laboratory of Fundamental Physical Quantities Measurement, Hubei Key Laboratory of Gravitation and Quantum Physics, School of Physics, Huazhong University of Science and Technology, Wuhan, 430074, People’s Republic of China

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

Authors
  1. Xiaohui Shi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jie Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xiaoyi Zeng
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xiaolong Lü
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Kui Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Jing Xi
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Yanxia Ye
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Zehuang Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Jie Zhang or Zehuang Lu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shi, X., Zhang, J., Zeng, X. et al. Suppression of residual amplitude modulation effects in Pound–Drever–Hall locking. Appl. Phys. B 124, 153 (2018). https://doi.org/10.1007/s00340-018-7021-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00340-018-7021-y

Search

Navigation