The European Physical Journal D

, Volume 58, Issue 2, pp 235–242 | Cite as

Nonlocal feedback in nonlinear systems

Focus point issue on Laser dynamics and nonlinear photonics

Abstract

A shifted or misaligned feedback loop gives rise to a two-point nonlocality that is the spatial analog of a temporal delay. Important consequences of this nonlocal coupling have been found both in diffusive and in diffractive systems, and include convective instabilities, independent tuning of phase and group velocities, as well as amplification, chirping and even splitting of localized perturbations. Analytical predictions about these nonlocal systems as well as their spatio-temporal dynamics are discussed in one and two transverse dimensions and in presence of noise.

Keywords

Group Velocity Transverse Dimension Convective Instability Localize Perturbation Phase Pattern 

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References

  1. M. Santagiustina, P. Colet, M. San Miguel, D. Walgraef, Phys. Rev. Lett. 79, 3633 (1997) Google Scholar
  2. M. Santagiustina, P. Colet, M. San Miguel, D. Walgraef, Phys. Rev. E 58, 3843 (1998) Google Scholar
  3. M. Santagiustina, P. Colet, M. San Miguel, D. Walgraef, Opt. Lett. 23, 1167 (1998) Google Scholar
  4. M. Taki, N. Ouarzazi, H. Ward, P. Glorieux, J. Opt. Soc. Am. B 17, 997 (2000) Google Scholar
  5. J.M. Chomaz, Phys. Rev. Lett. 69, 1931 (1992) Google Scholar
  6. K.L. Babcock, G. Ahlers, D.S. Cannell, Phys. Rev. Lett. 67, 3388 (1991) Google Scholar
  7. P. Gondret, P. Ern, L. Meignin, M. Rabaud, Phys. Rev. Lett. 82, 1442 (1999) Google Scholar
  8. R.J. Briggs, Electron-Stream Interaction with Plasmas (MIT, Cambridge, MA, 1964) Google Scholar
  9. N. Mitarai, H. Nakanishi, Phys. Rev. Lett. 85, 1766 (2000) Google Scholar
  10. E. Louvergneaux, C. Szwaj, G. Agez, P. Glorieux, M. Taki, Phys. Rev. Lett. 93, 101801 (2004) Google Scholar
  11. A. Mussot, E. Louvergneaux, N. Akhmediev, F. Reynaud, L. Delage, M. Taki, Phys. Rev. Lett. 101, 113904 (2008) Google Scholar
  12. F. Papoff, R. Zambrini, Phys. Rev. Lett. 94, 243903 (2005) Google Scholar
  13. P. Ramazza, S. Ducci, F. Arecchi, Phys. Rev. Lett. 81, 4128 (1998) Google Scholar
  14. S. Rankin, E. Yao, F. Papoff, Phys. Rev. A 68, 013821 (2003) Google Scholar
  15. L. Pastur, U. Bortolozzo, P. Ramazza, Phys. Rev. E 69, 016210 (2004) Google Scholar
  16. J.P. Seipenbusch, T. Ackemann, B.B.B. Schäpers, W. Lange, Phys. Rev. A 56, R4401 (1997) Google Scholar
  17. G. Agez, P. Glorieux, M. Taki, E. Louvergneaux, Phys. Rev. A 74, 043814 (2006) Google Scholar
  18. R. Zambrini, F. Papoff, Phys. Rev. Lett. 99, 063907 (2007) Google Scholar
  19. F. Arecchi, S. Boccaletti, P. Ramazza, Phys. Rep. 318, 1 (1999) Google Scholar
  20. Foundations of Systems Biology, edited by H. Kitano (MIT, Boston, 2001) Google Scholar
  21. G.F. Franklin et al., Feedback Control of Dynamic Systems (Prentice Hall, 2002) Google Scholar
  22. C. Evain, C. Szwaj, S. Bielawski, M. Hosaka, A. Mochihashi, M. Katoh, M.-E. Couprie, Phys. Rev. Lett. 102, 134501 (2009) Google Scholar
  23. P. Coullet, L. Gill, F. Rocca, Opt. Commun. 73, 403 (1989) Google Scholar
  24. P. Kockaert, P. Tassin, G.V. der Sande, I. Veretennicoff, M. Tlidi, Phys. Rev. A 74, 033822 (2006) Google Scholar
  25. D.A. Martin, M. Hoyuelos, Phys. Rev. E 80, 056601 (2009) Google Scholar
  26. A. Dunlop, W. Firth, E. Wright, Opt. Commun. 138, 211 (1997) Google Scholar
  27. F. Papoff, R. Zambrini, Phys. Rev. A 79, 033811 (2009) Google Scholar
  28. R. Zambrini, F. Papoff, Phys. Rev. E 73, 016611 (2006) Google Scholar
  29. F. Papoff, G. D'Alessandro, G.-L. Oppo, Phys. Rev. Lett. 100, 123905 (2008) Google Scholar
  30. G. D'Alessandro, C.B. Laforet, Opt. Lett. 34, 614 (2009) Google Scholar
  31. G. D'Alessandro, F. Papoff, Phys. Rev. A 80, 023804 (2009) Google Scholar
  32. C. Cossu, J.M. Chomaz, Phys. Rev. Lett. 78, 4387 (2007) Google Scholar
  33. R. Zambrini, M.S. Miguel, Phys. Rev. A 66, 023807 (2002) Google Scholar
  34. R. Zambrini, S. Barnett, P. Colet, M.S. Miguel, Phys. Rev. A 65, 023813 (2002) Google Scholar
  35. R. Zambrini, M.S. Miguel, C. Durniak, M. Taki, Phys. Rev. E 72, R025603 (2005) Google Scholar
  36. P.K. Jakobsen, J. Lega, Q. Feng, M. Staley, J.V. Moloney, A.C. Newell, Phys. Rev. A 49, 4189 (1994) Google Scholar
  37. R. Toral, A. Chakrabarti, Comput. Phys. Commun. 74, 327 (1993) Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.IFISC (CSIC-UIB), Campus Universitat Illes BalearsPalma de MallorcaSpain
  2. 2.SUPA, Department of PhysicsUniversity of StrathclydeGlasgowUK

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