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Enhancement of nonlinear response using vibrational resonance in a nonlinear oscillator; sum and difference frequency generation

  • Debapriya Das
  • Deb Shankar Ray
Regular Article

Abstract

We consider the second order response for nonlinear processes at the sum and difference frequencies of a nonlinear centrosymmetric system to a weak low frequency field excitation in presence of a strong rapidly varying time-periodic field. It is shown that the rapidly varying field breaks the centre of symmetry of the potential and shifts the steady state in such a way that the system becomes susceptible to weak field excitation at an optimal strength of the high frequency field. The magnitude nonlinear response to the weak field is of the order of the linear response in sharp contrast to the usual three-wave mixing processes traditionally carried out in strong laser fields.

Keywords

Statistical and Nonlinear Physics 

References

  1. 1.
    P.A. Franken, A.E. Hill, C.W. Peters, G. Weinreich, Phys. Rev. Lett. 7, 118 (1961) ADSCrossRefGoogle Scholar
  2. 2.
    J.A. Armstrong, N. Bloembergen, J. Ducuing, P.S. Pershan, Phys. Rev. 127, 1918 (1962) ADSCrossRefGoogle Scholar
  3. 3.
    R.W. Boyd, Nonlinear optics, 3rd edn. (Academic Press, New York, 2008) Google Scholar
  4. 4.
    A. Yariv, Optical electronics (Oxford University Press, 1990) Google Scholar
  5. 5.
    P. Landa, P. McClintock, J. Phys. A 33, L433 (2000) ADSCrossRefGoogle Scholar
  6. 6.
    A.A. Zaikin, L. López, J.P. Baltanás, J. Kurths, M.A.F. Sanjuán, Phys. Rev. E 66, 011106 (2002) ADSCrossRefGoogle Scholar
  7. 7.
    J.P. Baltanás, L. López, I.I. Blechman, P.S. Landa, A. Zaikin, J. Kurths, M.A.F. Sanjuán, Phys. Rev. E 67, 066119 (2003) ADSCrossRefGoogle Scholar
  8. 8.
    V.N. Chizhevsky, E. Smeu, G. Giacomelli, Phys. Rev. Lett. 91, 220602 (2003) ADSCrossRefGoogle Scholar
  9. 9.
    I.I. Blekhman, P.S. Landa, Int. J. Nonlinear Mech. 39, 421 (2004) ADSCrossRefGoogle Scholar
  10. 10.
    V.N. Chizhevsky, G. Giacomelli, Phys. Rev. E 77, 051126 (2008) ADSCrossRefGoogle Scholar
  11. 11.
    V.N. Chizhevsky, Opt. Lett. 37, 4386 (2012) ADSCrossRefGoogle Scholar
  12. 12.
    C. Jeevarathinam, S. Rajasekar, M.A.F. Sanjuán, Phys. Rev. E 83, 066205 (2011) ADSCrossRefGoogle Scholar
  13. 13.
    W. Can-Jun, Chin. Phys. Lett. 28, 090504 (2011) CrossRefGoogle Scholar
  14. 14.
    J. Casado-Pascual, J.P. Baltanás, Phys. Rev. E 69, 046108 (2004) ADSCrossRefGoogle Scholar
  15. 15.
    V.N. Chizhevsky, G. Giacomelli, Phys. Rev. E 73, 022103 (2006) ADSCrossRefGoogle Scholar
  16. 16.
    S. Ghosh, D.S. Ray, Phys. Rev. E 88, 042904 (2013) ADSCrossRefGoogle Scholar
  17. 17.
    V.N. Chizhevsky, Phys. Rev. E 89, 062914 (2014) ADSCrossRefGoogle Scholar
  18. 18.
    S. Ghosh, D.S. Ray, Eur. Phys. J. B 88, 23 (2015) ADSCrossRefGoogle Scholar
  19. 19.
    R. Benzi, A. Sutera, A. Vulpiani, J. Phys. A: Math. Gen. 14,L453 (1981) ADSCrossRefGoogle Scholar
  20. 20.
    B. McNamara, K. Wiesenfeld, R. Roy, Phys. Rev. Lett. 60, 2626 (1988) ADSCrossRefGoogle Scholar
  21. 21.
    C.R. Doering, J.C. Gadoua, Phys. Rev. Lett. 69, 2318 (1992) ADSCrossRefGoogle Scholar
  22. 22.
    M. Marchi, F. Marchesoni, L. Gammaitoni, E. Menichella-Saetta, S. Santucci, Phys. Rev. E 54, 3479 (1996) ADSCrossRefGoogle Scholar
  23. 23.
    L. Gammaitoni, F. Marchesoni, E. Menichella-Saetta, S. Santucci, Phys. Rev. Lett. 62, 349 (1989) ADSCrossRefGoogle Scholar
  24. 24.
    V.I. Melnikov, Phys. Rev. E 48, 2481 (1993) ADSCrossRefGoogle Scholar
  25. 25.
    L. Gammaitoni, P. Hänggi, P. Jung, F. Marchesoni, Rev. Mod. Phys. 70, 223 (1998) ADSCrossRefGoogle Scholar
  26. 26.
    R.N. Mantegna, B. Spagnolo, Phys. Rev. Lett. 84, 3025 (2000) ADSCrossRefGoogle Scholar
  27. 27.
    P.K. Ghosh, D.S. Ray, J. Chem. Phys. 125, 124102 (2006) ADSCrossRefGoogle Scholar
  28. 28.
    A. Fiasconaro, B. Spagnolo, Phys. Rev. E 83, 041122 (2011) ADSCrossRefGoogle Scholar
  29. 29.
    F. Sagués, J.M. Sancho, J. Garcĺa-Ojalvo, Rev. Mod. Phys. 79, 829 (2007) ADSCrossRefGoogle Scholar
  30. 30.
    J. Buceta, M. Ibañes, J.M. Sancho, K. Lindenberg, Phys. Rev. E 67, 021113 (2003) ADSCrossRefGoogle Scholar
  31. 31.
    A. Sanz-Anchelergues, A.M. Zhabotinsky, I.R. Epstein, A.P. Muñuzuri, Phys. Rev. E 63, 056124 (2001) ADSCrossRefGoogle Scholar
  32. 32.
    S. Dutta, S.S. Riaz, D.S. Ray, Phys. Rev. E 71, 036216 (2005) ADSCrossRefGoogle Scholar
  33. 33.
    D. Das, D.S. Ray, Phys. Rev. E 87, 062924 (2013) ADSCrossRefGoogle Scholar
  34. 34.
    B. Spagnoloa, A. La Barbera, Physica A 315, 114 (2002) ADSCrossRefGoogle Scholar
  35. 35.
    K. Horsthemke, R. Lefever, Phys. Lett. 64A, 19 (1977) ADSCrossRefGoogle Scholar
  36. 36.
    C. Van den Broeck, J.M.R. Parrondo, R. Toral, Phys. Rev. Lett. 73, 3395 (1994) ADSCrossRefGoogle Scholar
  37. 37.
    P.K. Ghosh, D. Barik, D.S. Ray, Phys. Lett. A 12, 342 (2005) Google Scholar
  38. 38.
    M. Borromeo, F. Marchesoni, Europhys. Lett. 68, 783 (2004) ADSCrossRefGoogle Scholar
  39. 39.
    M. Borromeo, F. Marchesoni, Phys. Rev. E 71, 031105 (2005) ADSCrossRefGoogle Scholar
  40. 40.
    M. Borromeo, S. Giusepponi, F. Marchesoni, Phys. Rev. E 74, 031121 (2006) ADSCrossRefGoogle Scholar
  41. 41.
    S. Savel’ev, F. Marchesoni, P. Hänggi, F. Nori, Europhys. Lett. 67, 179 (2004) ADSCrossRefGoogle Scholar
  42. 42.
    M.I. Dykman, P.V.E. McClintock, Nature 391, 344 (1998) ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Indian Association for the Cultivation of ScienceJadavpur, KolkataIndia

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