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Experimental observation of symmetry-breaking nonlinear modes in an active ring

Nature volume 426, pages 159–162 (2003)Cite this article

Abstract

Solitons are large-amplitude, spatially confined wave packets in nonlinear media. They occur in a wide range of physical systems, such as water surfaces, optical fibres, plasmas, Bose–Einstein condensates and magnetically ordered media1,2. A distinguishing feature of soliton behaviour that is common to all systems, is that they propagate without a change in shape owing to the stabilizing effect of the particular nonlinearity involved1,3. When the propagation path is closed, modes consisting of one or several solitons may rotate around the ring, the topology of which imposes additional constraints on their allowed frequencies and phases4,5. Here we measure the mode spectrum of spin-wave solitons in a nonlinear active ring constructed from a magnetic ferrite film. Several unusual symmetry-breaking soliton-like modes are found, such as ‘Möbius’ solitons, which break the fundamental symmetry of 2π-periodicity in the phase change acquired per loop: a Möbius soliton needs to travel twice around the ring to meet the initial phase condition.

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Figure 1: Schematic layout of the active ring based on an yttrium iron garnet film as the nonlinear medium for spin-wave propagation and the experimental arrangement for observation of nonlinear modes in the ring.
Figure 2: Waveforms of the modes observed in the ring.
Figure 3: Waveforms of the one-soliton modes in the experiments with two sequences of the pumping pulses.

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References

  1. Remoissenet, M. Waves Called Solitons: Concepts and Experiments (Springer, Berlin/Heidelberg, 1994)

    Book  Google Scholar 

  2. Khaykovich, L. et al. Formation of a matter-wave bright soliton. Science 296, 1290–1293 (2002)

    Article  ADS  CAS  Google Scholar 

  3. Agrawal, G. P. Nonlinear Fiber Optics (Academic, San Diego, 1995)

    MATH  Google Scholar 

  4. Carr, L. D., Clark, C. W. & Reinhardt, W. P. Stationary solutions of the one-dimensional nonlinear Schrödinger equation. I. Case of repulsive nonlinearity. Phys. Rev. A 62, 063610 (2000)

    Article  ADS  Google Scholar 

  5. Carr, L. D., Clark, C. W. & Reinhardt, W. P. Stationary solutions of the one-dimensional nonlinear Schrödinger equation. II. Case of attractive nonlinearity. Phys. Rev. A 62, 063611 (2000)

    Article  ADS  Google Scholar 

  6. Liu, X., Qian, L. J. & Wise, F. W. Generation of optical spatiotemporal solitons. Phys. Rev. Lett. 82, 4631–4634 (1999)

    Article  ADS  CAS  Google Scholar 

  7. Bauer, M. et al. Observation of spatiotemporal self-focusing of spin waves in magnetic films. Phys. Rev. Lett. 81, 3769–3772 (1998)

    Article  ADS  CAS  Google Scholar 

  8. Kivshar, Y. S. & Malomed, B. A. Dynamics of solitons in nearly integrable systems. Rev. Mod. Phys. 61, 763–915 (1989)

    Article  ADS  Google Scholar 

  9. Li, Z., Li, L., Tian, H., Zhou, G. & Spatschek, K. H. Chirped femtosecond solitonlike laser pulse form with self-frequency shift. Phys. Rev. Lett. 89, 263901 (2002)

    Article  ADS  Google Scholar 

  10. Kalinikos, B. A., Scott, M. M. & Patton, C. E. Self-generation of fundamental dark solitons in magnetic films. Phys. Rev. Lett. 84, 4697–4700 (2000)

    Article  ADS  CAS  Google Scholar 

  11. Kalinikos, B. A., Kovshikov, N. G., Kostylev, M. P. & Benner, H. Self-generation of spin-wave envelope soliton trains with different periods. JETP Lett. 76, 253–257 (2002)

    Article  ADS  CAS  Google Scholar 

  12. Kalinikos, B. A., Kovshikov, N. G. & Patton, C. E. Self-generation of microwave magnetic envelope soliton trains in yttrium iron garnet thin films. Phys. Rev. Lett. 80, 4301–4304 (1998)

    Article  ADS  CAS  Google Scholar 

  13. Steinmeyer, G., Sutter, D. H., Gallmann, L., Matuschek, N. & Keller, U. Frontiers in ultrashort pulse generation: Pushing the limits in linear and nonlinear optics. Science 286, 1507–1512 (1999)

    Article  CAS  Google Scholar 

  14. Bagada, A. V., Melkov, G. A., Serga, A. A. & Slavin, A. N. Parametric interaction of dipolar spin wave solitons with localized electromagnetic pumping. Phys. Rev. Lett. 79, 2137–2140 (1997)

    Article  ADS  CAS  Google Scholar 

  15. Kolodin, P. A. et al. Amplification of microwave magnetic envelope solitons in thin yttrium iron garnet films by parallel pumping. Phys. Rev. Lett. 80, 1976–1979 (1998)

    Article  ADS  CAS  Google Scholar 

  16. Melkov, G. A. et al. Nonadiabatic interaction of a propagating wave packet with localized parametric pumping. Phys. Rev. E 63, 066607 (2001)

    Article  ADS  CAS  Google Scholar 

  17. Nash, J. M., Kabos, P., Staudinger, R. & Patton, C. E. Phase profiles of microwave magnetic envelope solitons. J. Appl. Phys. 83, 2689–2699 (1998)

    Article  ADS  CAS  Google Scholar 

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Acknowledgements

Support by the Deutsche Forschungsgemeinschaft is gratefully acknowledged. We also thank J.D. Comins for a careful reading of the manuscript.

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Authors and Affiliations

  1. Fachbereich Physik and Forschungsschwerpunkt MINAS, Technische Universität Kaiserslautern, Erwin-Schrödinger-Straße 56, Kaiserslautern, 67663, Germany

    Sergej O. Demokritov, Alexander A. Serga, Vladislav E. Demidov & Burkard Hillebrands

  2. St Petersburg Electrotechnical University, St Petersburg, 197376, Russia

    Michail P. Kostylev & Boris A. Kalinikos

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  1. Sergej O. Demokritov
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  2. Alexander A. Serga
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  3. Vladislav E. Demidov
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  4. Burkard Hillebrands
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  5. Michail P. Kostylev
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  6. Boris A. Kalinikos
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Correspondence to Sergej O. Demokritov.

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Demokritov, S., Serga, A., Demidov, V. et al. Experimental observation of symmetry-breaking nonlinear modes in an active ring. Nature 426, 159–162 (2003). https://doi.org/10.1038/nature02042

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