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Dynamics of Dissipative Temporal Solitons

Part of the Lecture Notes in Physics book series (LNP,volume 661)

Abstract

The properties and the dynamics of localized structures, frequently termed solitary waves or solitons, define, to a large extent, the behavior of the relevant nonlinear system [1]. Thus, it is a crucial and fundamental issue of nonlinear dynamics to fully characterize these objects in various conservative and dissipative nonlinear environments. Apart from this fundamental point of view, solitons (henceforth we adopt this term, even for localized solutions of non-integrable systems) exhibit a remarkable potential for applications, particularly if optical systems are considered. Regarding the type of localization, one can distinguish between temporal and spatial solitons. Spatial solitons are self-confined beams, which are shape-invariant upon propagation. (For an overview, see [2, 3]). It can be anticipated that they could play a vital role in all-optical processing and logic, since we can use their complex collision behavior [4]. Temporal solitons, on the other hand, represent shapeinvariant (or breathing) pulses. It is now common belief that robust temporal solitons will play a major role as elementary units (bits) of information in future all-optical networks [5, 6]. Until now, the main emphasis has been on temporal and spatial soliton families in conservative systems, where energy is conserved. Recently, another class of solitons, which are characterized by a permanent energy exchange with their environment, has attracted much attention. These solitons are termed dissipative solitons or auto-solitons. They emerge as a result of a balance between linear (delocalization and losses) and nonlinear (self-phase modulation and gain/loss saturation) effects. Except for very few cases [7], they form zero-parameter families and their features are entirely fixed by the underlying optical system. Cavity solitons form a prominent type. They appear as spatially-localized transverse peaks in transmission or reflection, e.g. from a Fabry-Perot cavity. They rely strongly on the nonlinear interaction of forward and backward propagating fields, where cavity (radiation) losses are compensated for by gain or an external holding beam. Cavity solitons have been observed in Fabry-Perot cavities and single mirror feedback setups (for an overview see [8]). In contrast, propagating dissipative solitons consist of forward-propagating fields only. Recently, the existence of both stable temporal [9] and spatial propagating dissipative solitons [10] was experimentally demonstrated. It is evident that the study of dissipative solitons is of great practical relevance, because most real optical systems are dissipative by nature.

Keywords

  • Soliton Solution
  • Saturable Absorber
  • Group Velocity Dispersion
  • Timing Jitter
  • Spatial Soliton

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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REFERENCES

  1. M. C. Cross and P. C. Hohenberg, Rev. Mod. Phys., 65, 851 (1993).

    CrossRef  Google Scholar 

  2. S. Trillo and W. Torruellas (eds.),Spatial Solitons, Springer Series on Optical Sciences, vol. 82, (Springer, Berlin, Heidelberg, New York, 2001).

    Google Scholar 

  3. F. Lederer (ed.), Feature Issue on Spatial Solitons, IEEE J. Quantum Electron., 39, 1 (2003).

    Google Scholar 

  4. G. I. Stegeman and M. Segev, Science., 286, 1518 (1999).

    Google Scholar 

  5. A. Hasegawa and Y. Kodama, Solitons in Optical Communications, (Clarendon Press, Oxford 1995).

    Google Scholar 

  6. Y. A. Kivshar and G. P. Agrawal, Optical Solitons. From Fibers to Photonic Crystals,(Academic Press, Amsterdam, 2003).

    Google Scholar 

  7. N. Akhmediev and A. Ankiewicz, Solitons: nonlinear pulses and beams, (Chapman & Hall, London, 1997).

    Google Scholar 

  8. L. A. Lugiato (ed.), Feature Issue on Cavity Solitons, IEEE J. Quantum Electron., 39, 193 (2003).

    Google Scholar 

  9. Z. Bakonyi, D. Michaelis, U. Peschel, G. Onishchukov, and F. Lederer, J. Opt. Soc. Am. B 19, 487 (2002).

    Google Scholar 

  10. E. Ultanir, G. I. Stegeman, D. Michaelis, C. H. Lange, and F. Lederer, Phys. Rev. Lett. 90, 253903 (2003).

    Google Scholar 

  11. N. J. Smith and N. J. Doran, Electron. Lett., 30, 1084 (2000).

    Google Scholar 

  12. G. Agrawal and N. Olson, IEEE J. Quantum Electron., QE-25, 2297 (1989).

    Google Scholar 

  13. S. Wabnitz, Opt. Lett., 20, 1979 (1995).

    Google Scholar 

  14. S. K. Turitsyn, Phys. Rev. E, 20, R3125 (1996).

    Google Scholar 

  15. A. Mecozzi, Opt. Lett., 20, 1616 (1995).

    Google Scholar 

  16. V. S. Grigoryan, Opt. Lett., 21, 1882 (1996).

    Google Scholar 

  17. S. Fauve and O. Thual, Phys. Rev. Lett., 64, 282 (1990).

    Google Scholar 

  18. W. van Saarloos and P. C. Hohenberg, Phys. Rev. Lett., 64, 749 (1990).

    Google Scholar 

  19. S. Longhi, Phys. Scr., 56, 611 (1997).

    Google Scholar 

  20. K. Staliunas, V. Sanchez-Morcillo, Opt. Commun., 139, 306 (1997).

    Google Scholar 

  21. M. Tlidi, P. Mandel, R. Lefever, Phys. Rev. Lett., 73, 640 (1994).

    CrossRef  Google Scholar 

  22. W. J. Firth and A. J. Scroggie, Phys. Rev. Lett., 76, 1623 (1996).

    CrossRef  Google Scholar 

  23. S. Trillo, M. Haelterman, and A. Sheppard, Opt. Lett. 22, 1514 (1997).

    Google Scholar 

  24. K. Staliunas and V. J. Sanchez-Morcillo, Phys. Rev. A, 57, 1454 (1998).

    Google Scholar 

  25. U. Peschel, D. Michaelis, C. Etrich, and F. Lederer, Phys. Rev. E, 58, R27435 (1998).

    Google Scholar 

  26. R. Gallego, M. San Miguel, and R. Toral, Phys. Rev. E, 61, 2241 (2000).

    Google Scholar 

  27. Z. Bakonyi, G. Onishchukov, C. Knöll, M. Gölles, and F. Lederer, Electron. Lett., 36, 1790 (2000).

    Google Scholar 

  28. A. Hasegawa and Y. Kodama, Opt. Lett., 15, 1443 (1990).

    Google Scholar 

  29. N. Akhmediev, M. J. Lederer, and B. Luther-Davis, Phys. Rev. E, 57, 3664 (1998).

    Google Scholar 

  30. F. Mitschke, C. Boden, W. Lange, and P. Mandel, Opt. Comm., 71, 385 (1989).

    Google Scholar 

  31. J. Danckaert, G. Vitrant, R. Reinisch, and M. Georgiou, Phys. Rev. A, 48, 2324 (1993).

    Google Scholar 

  32. J. P. Gordon and H. A. Haus, Opt. Lett., 11, 665 (1986).

    Google Scholar 

  33. Y. Kodama and A. Hasegawa, Opt. Lett., 17, 31 (1992).

    Google Scholar 

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Peschel, U., Michaelis, D., Bakonyi, Z., Onishchukov, G., Lederer, F. Dynamics of Dissipative Temporal Solitons. In: Akhmediev, N., Ankiewicz, A. (eds) Dissipative Solitons. Lecture Notes in Physics, vol 661. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10928028_7

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