Non-Hermitian ring laser gyroscopes with enhanced Sagnac sensitivity

Abstract

Gyroscopes are essential to many diverse applications associated with navigation, positioning and inertial sensing1. In general, most optical gyroscopes rely on the Sagnac effect—a relativistically induced phase shift that scales linearly with the rotational velocity2,3. In ring laser gyroscopes (RLGs), this shift manifests as a resonance splitting in the emission spectrum, which can be detected as a beat frequency4. The need for ever more precise RLGs has fuelled research activities aimed at boosting the sensitivity of RLGs beyond the limits dictated by geometrical constraints, including attempts to use either dispersive or nonlinear effects5,6,7,8. Here we establish and experimentally demonstrate a method using non-Hermitian singularities, or exceptional points, to enhance the Sagnac scale factor9,10,11,12,13. By exploiting the increased rotational sensitivity of RLGs in the vicinity of an exceptional point, we enhance the resonance splitting by up to a factor of 20. Our results pave the way towards the next generation of ultrasensitive and compact RLGs and provide a practical approach for the development of other classes of integrated sensor.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Fig. 1: Conceptual illustrations comparing the eigenvalue surfaces associated with Hermitian and non-Hermitian two-level systems.
Fig. 2: Principle of operation of an EP-based He–Ne RLG.
Fig. 3: Bifurcations of complex eigenfrequencies and sensitivity enhancement of EP-based RLG around an EP.
Fig. 4: Measured beat frequency and sensitivity enhancement factor versus rotation rate.
Fig. 5: Transfer functions and estimated rotation rates.

Data availability

All data that support the findings of this study are available within the paper and the Supplementary Information and are available from the corresponding author upon reasonable request.

References

  1. 1.

    Armenise, M. N., Ciminelli, C., Dell’Olio, F. & Passaro, V. M. Advances in Gyroscope Technologies (Springer, 2010).

  2. 2.

    Post, E. J. Sagnac effect. Rev. Mod. Phys. 39, 475–493 (1967).

  3. 3.

    Chow, W. W. et al. The ring laser gyro. Rev. Mod. Phys. 57, 61–104 (1985).

  4. 4.

    Macek, W. M. & Davis, D. T. M. Jr Rotation rate sensing with traveling-wave ring lasers. Appl. Phys. Lett. 2, 67–68 (1963).

  5. 5.

    Boyd, R. W. Slow and fast light: fundamentals and applications. J. Mod. Opt. 56, 1908–1915 (2009).

  6. 6.

    Shahriar, M. S. et al. Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light. Phys. Rev. A 75, 053807 (2007).

  7. 7.

    Smith, D. D., Chang, H., Arissian, L. & Diels, J. C. Dispersion-enhanced laser gyroscope. Phys. Rev. A 78, 053824 (2008).

  8. 8.

    Kaplan, A. E. & Meystre, P. Enhancement of the Sagnac effect due to nonlinearly induced nonreciprocity. Opt. Lett. 6, 590–592 (1981).

  9. 9.

    Hodaei, H. et al. Enhanced sensitivity at higher-order exceptional points. Nature 548, 187–191 (2017); erratum 551, 658–191 (2017).

  10. 10.

    Chen, W., Özdemir, Ş. K., Zhao, G., Wiersig, J. & Yang, L. Exceptional points enhance sensing in an optical microcavity. Nature 548, 192–196 (2017).

  11. 11.

    Ren, J. et al. Ultrasensitive micro-scale parity-time-symmetric ring laser gyroscope. Opt. Lett. 42, 1556–1559 (2017).

  12. 12.

    Sunada, S. Large Sagnac frequency splitting in a ring resonator operating at an exceptional point. Phys. Rev. A 96, 033842 (2017).

  13. 13.

    Grant, M. J. & Digonnet, M. J. F. Loss-gain coupled ring resonator gyroscope. In Proc. SPIE Optical, Opto-Atomic, and Entanglement-Enhanced Precision Metrology Vol. 10934 (SPIE, 2019).

  14. 14.

    Vahala, K. J. Optical microcavities. Nature 424, 839–846 (2003).

  15. 15.

    Vollmer, F. & Arnold, S. Whispering-gallery-mode biosensing: label-free detection down to single molecules. Nat. Methods 5, 591–596 (2008).

  16. 16.

    Lu, T. et al. High sensitivity nanoparticle detection using optical microcavities. Proc. Natl Acad. Sci. USA 108, 5976–5979 (2011).

  17. 17.

    Liang, W. et al. Resonant microphotonic gyroscope. Optica 4, 114–117 (2017).

  18. 18.

    Makris, K. G., El-Ganainy, R., Christodoulides, D. N. & Musslimani, Z. H. Beam dynamics in PT symmetric optical lattices. Phys. Rev. Lett, 100, 103904 (2008).

  19. 19.

    Klaiman, S., Gunther, U. & Moiseyev, N. Visualization of branch points in PT-symmetric waveguides. Phys. Rev. Lett, 101, 080402 (2008).

  20. 20.

    Moiseyev, N. Non-Hermitian Quantum Mechanics (Cambridge Univ. Press, 2011).

  21. 21.

    Wiersig, J. Enhancing the sensitivity of frequency and energy splitting detection by using exceptional points: application to microcavity sensors for single-particle detection. Phys. Rev. Lett. 112, 203901 (2014).

  22. 22.

    El-Ganainy, R. et al. Non-Hermitian physics and PT symmetry. Nat. Phys. 14, 11–19 (2018).

  23. 23.

    Yariv, A. & Yeh, P. Photonics: Optical Electronics in Modern Communications (Oxford Univ. Press, 2006).

  24. 24.

    Khajavikhan, M., John, K. & Leger, J. R. Experimental measurements of supermodes in superposition architectures for coherent laser beam combining. IEEE J. Quantum Electron. 46, 1221–1231 (2010).

  25. 25.

    Hu, J., Sun, X., Agarwal, A. & Kimerling, L. C. Design guidelines for optical resonator biochemical sensors. J. Opt. Soc. Am. B 26, 1032–1041 (2009).

  26. 26.

    LIGO Scientific and Virgo Collaboration. GW170104: observation of a 50-solar-mass binary black hole coalescence at redshift 0.2. Phys. Rev. Lett. 118, 221101 (2017).

  27. 27.

    Collett, M. J., Loudon, R. & Gardiner, C. W. Quantum theory of optical homodyne and heterodyne detection. J. Mod. Opt. 34, 881–902 (1987).

  28. 28.

    Mortensen, N. A. et al. Fluctuations and noise-limited sensing near the exceptional point of parity-time-symmetric resonator systems. Optica 5, 1342–1346 (2018).

  29. 29.

    Zhang, M. et al. Quantum noise theory of exceptional point amplifying sensors. Phys. Rev. Lett. 123, 180501 (2019).

  30. 30.

    De Carlo, M., De Leonardis, F. & Passaro, V. M. Design rules of a microscale PT-symmetric optical gyroscope using group IV platform. J. Light. Technol. 36, 3261–3268 (2018).

Download references

Acknowledgements

We acknowledge support from the US Air Force Office of Scientific Research (FA9550-14-1-0037), Office of Naval Research (N00014-16-1-2640, N00014-18-1-2347, N00014-19-1-2052), National Science Foundation (ECCS1454531, DMR-1420620, ECCS1757025), Army Research Office (W911NF-16-1-0013, W911NF-17-1-0481), US–Israel Binational Science Foundation (BSF) (2016381), DARPA (D18AP00058, HR00111820042, HR00111820038) and the European Commission Project ‘Non-Hermitian Quantum Wave Engineering’ (NHQWAVE, MSCA-RISE 691209). We thank W. Luhs for help in setting up the gyroscope and for performing some of the initial measurements, S. Milady, S. Rotter and K. Vahala for technical discussions, and S. Rotter for supporting this project through funding for A.S.

Author information

All authors contributed equally to this work.

Correspondence to Mercedeh Khajavikhan.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Peer review information Nature thanks Chia Wei Hsu and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Supplementary information

Supplementary Information

This file contains information on analytical calculations of the beat frequency for Hermitian and non-Hermitian ring laser gyroscopes using linear and nonlinear coupled mode theory and Jones calculus

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Hokmabadi, M.P., Schumer, A., Christodoulides, D.N. et al. Non-Hermitian ring laser gyroscopes with enhanced Sagnac sensitivity. Nature 576, 70–74 (2019). https://doi.org/10.1038/s41586-019-1780-4

Download citation

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.