Quantum Noise Reduction and Instabilities in Nondegenerate Four-Wave-Mixing

  • M. Brambilla
  • F. Castelli
  • L. A. Lugiato
  • F. Prati
  • G. Strini
Part of the NATO ASI Series book series (NSSB, volume 282)

Abstract

Four-wave-mixing (FWM) is one of the basic mechanisms in nonlinear optics. We consider the interaction of a pump field of frequency ω l and two signal fields (or more precisely, a signal and an idler field) of frequencies ω 2 and ω 3 such that ω 2 + ω 3 = 2ω 1; hence the FWM process corresponds to the conversion of the two photons of frequency ω l into two photons with frequencies ω 2 and ω 3, and vice versa. Especially interesting is the case of a nonlinear material placed in a resonant optical cavity; the two signal fields, propagating along the longitudinal axis of the cavity, can be spontaneously generated by the pump field. The mechanism is basically as follows: the pump field saturates the medium and, under appropriate conditions, any probe field with a frequency lying in a suitable interval experiences gain1,2. In a cavity, the modes work as probe fields, and one can obtain that a mode has a frequency that lies in the gain region; in addition, the pump gives rise to a FWM coupling of the mode with another mode whose frequency lies on the other side with respect to the pump frequency 3,4. This process is an example of laser without inversion and has been experimentally realized few years ago5,6.

Keywords

Master Equation Quantum Noise Signal Field Time Correlation Function Input Field 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    B. R. Mollow, Phys. Rev. A 5:2217 (1972).CrossRefGoogle Scholar
  2. 2.
    F. Y. Wu, S. Ezekiel, M. Ducloy and B. R. Mollow, Phys. Rev. Lett. 38:1077 (1977).CrossRefGoogle Scholar
  3. 3.
    T. Fu and M. Sargent III, Opt. Lett. 4:366 (1979).CrossRefGoogle Scholar
  4. 4.
    R. W. Boyd, M. G. Raymer, P. Narum and D. I. Marten, Phys. Rev. A 24:411 (1981).CrossRefGoogle Scholar
  5. 5.
    D. Grandclement, G. Grynberg and M. Pinard, Phys. Rev. Lett. 59:40,44 (1987).CrossRefGoogle Scholar
  6. 6.
    G. Khitrova, J.F. Valley and H. M. Gibbs, Phys. Rev. Lett. 60:1126 (1988).CrossRefGoogle Scholar
  7. 7.
    R. Bonifacio and L. A. Lugiato, Lett. Nuovo Cimento 21:510 (1978).CrossRefGoogle Scholar
  8. 8.
    L. A. Lugiato, Opt. Comm. 33:108 (1980).CrossRefGoogle Scholar
  9. 9.
    R. Bonifacio, M. Gronchi and L. A. Lugiato, Opt. Comm. 30:129 (1979).CrossRefGoogle Scholar
  10. 10.
    M. Gronchi, V. Benza, L. A. Lugiato, P. Meystre and M. Sargent III, Phys. Rev. A 24:1419 (1981).CrossRefGoogle Scholar
  11. 11.
    L. A. Lugiato, V. Benza, L. M. Narducci and J. D. Farina, Z. Phys. B 49:351 (1983).CrossRefGoogle Scholar
  12. 12.
    L. A. Lugiato, in: Progress in Optics, vol XXI, ed. by E.Wolf, North-Holland, Amsterdam, p. 69 ff.Google Scholar
  13. 13.
    M. L. Asquini, L. A. Lugiato, H. J. Carmichael and L. M. Narducci, Phys. Rev. A 33:360 (1986).CrossRefGoogle Scholar
  14. 14.
    B. Segard and B. Macke, Phys. Rev. Lett. 60:412 (1988).CrossRefGoogle Scholar
  15. 15.
    B. Segard, B. Macke, L.A. Lugiato, F. Prati and M. Brambilla, Phys. Rev. A 39:706 (1989).Google Scholar
  16. 16.
    L. A. Lugiato, Z. Phys. B 41:85 (1981).MathSciNetCrossRefGoogle Scholar
  17. 17.
    L. A. Lugiato and F. Castelli, Z. Phys. B 64:375 (1986).CrossRefGoogle Scholar
  18. 18.
    H. P. Yuen and J. H. Shapiro, Opt. Lett. 4:334 (1979).CrossRefGoogle Scholar
  19. 19.
    P. Kumar and J. H. Shapiro, Phys. Rev. A 30:1568 (1984).CrossRefGoogle Scholar
  20. 20.
    M. D. Reid and D. F. Walls, Phys. Rev. A 31:1622 (1985)CrossRefGoogle Scholar
  21. R. E. Slusher, B. Yurke, P. Grangier, A. La Porta, D. F. Walls and M. D. Reid,Journ. Opt. Soc. Am. B4:1453 (1987).Google Scholar
  22. 21.
    M. D. Reid and D. F. Walls, Phys. Rev. A 34:4929 (1986).CrossRefGoogle Scholar
  23. 22.
    D. A. Holm and M. Sargent III, Phys. Rev. A 35:2150 (1987).CrossRefGoogle Scholar
  24. 23.
    C. M. Savage and D. F. Walls, J. Opt. Soc. Am. B 4:154 (1987)CrossRefGoogle Scholar
  25. 24.
    W. Zhang and D. F. Walls, Phys. Rev. A 41:6385 (1990).CrossRefGoogle Scholar
  26. 25.
    L. A. Lugiato, P. Galatola and L. M. Narducci, Opt. Comm. 76:276 (1990).CrossRefGoogle Scholar
  27. 26.
    W. Zhang and D. F. Walls, Opt. Comm in press.Google Scholar
  28. 27.
    B. C. Sanders and M. D. Reid, Phys. Rev. A in press.Google Scholar
  29. 28.
    Wang Kaige and L. A. Lugiato, Annalen der Physik, 200th anniversary issue, in press.Google Scholar
  30. 29.
    R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz and J. F. Valley, Phys. Rev. Lett. 55:2409 (1985).CrossRefGoogle Scholar
  31. 30.
    R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. De Voe and D. F. Walls, Phys. Rev. Lett. 57:691 (1986).CrossRefGoogle Scholar
  32. 31.
    M. W. Maeda, P. Kumar and J. H. Shapiro, Opt. Lett. 12:161 (1986).CrossRefGoogle Scholar
  33. 32.
    M. Vallet, M. Pinard and G. Grynberg, Europhys. Lett. 11:739 (1990).CrossRefGoogle Scholar
  34. 33.
    A. Heidmann, R. J. Horowicz, S. Reynaud, E. Giacobino, C. Fabre and G. Carry, Phys. Rev. Lett. 59:2555 (1987).CrossRefGoogle Scholar
  35. 34.
    S. Reynaud, C. Fabre and E. Giacobino, J. Opt. Soc. Am. B 4:1520 (1987).CrossRefGoogle Scholar
  36. 35.
    R. J. Glauber, Phys. Rev. 130:2529 (1963)MathSciNetCrossRefGoogle Scholar
  37. R. J. Glauber,Phys. Rev.131:2766 (1963).MathSciNetCrossRefGoogle Scholar
  38. 36.
    H. Haken, in: Laser Theory,Encyclopaedia der Physik, Vol. XXV/2c, ed. by L. Genzel, Springer-Verlag, Berlin 1970.Google Scholar
  39. 37.
    M. Brambilla, F. Castelli, L. A. Lugiato, F. Prati and G. Strini, submitted to Opt. Comm.Google Scholar
  40. 38.
    R. Bonifacio, M. Gronchi and L. A. Lugiato, Nuovo Cimento B 53:311 (1979).CrossRefGoogle Scholar
  41. 39.
    L. A. Lugiato, L. M. Narducci and R. Lefever, in: Lasers and Synergetics, ed. by R. Graham and A. Wunderlin, Springer-Verlag, Berlin 1987, pp 59,60.Google Scholar
  42. 40.
    P. Grangier, J. F. Roch and G. Roger, in: Proceedings of the ECOOSA Conference, Rome, November 7–9 1990, ed. by M. Bertolotti, Hilger, Bristol, in press.Google Scholar
  43. 41.
    H. M. Gibbs, S. L. McCall and N. C. Venkatesan, Phys. Rev. Lett. 36:113 (1976).CrossRefGoogle Scholar
  44. 42.
    M. Brambilla, F. Castelli, L. A. Lugiato, F. Prati and G. Strini, in: Proceedings of the ECOOSA Conference, Rome, November 7–9 1990, ed. by M. Bertolotti, Hilger, Bristol, in press.Google Scholar
  45. 43.
    R. Graham, Z. Phys. 210:319 (1968)CrossRefGoogle Scholar
  46. R. Graham,Z. Phys.211:469 (1968).CrossRefGoogle Scholar
  47. 44.
    M. Brambilla, F. Castelli, L. A. Lugiato, F. Prati and G. Strini, in preparation.Google Scholar
  48. 45.
    A. S. Lane, M. D. Reid and D. F. Walls, Phys. Rev. A 38:788 (1988).CrossRefGoogle Scholar
  49. 46.
    B. Yurke, Phys. Rev. A 29:408 (1984).MathSciNetCrossRefGoogle Scholar
  50. 47.
    M. J. Collett and C. W. Gardiner, Phys. Rev. A 30:1386 (1984)CrossRefGoogle Scholar
  51. M. J. Collett and D. F. Walls,Phys. Rev. A32:2887 (1985).MathSciNetGoogle Scholar
  52. 48.
    M. Brambilla, G. Strini, F. Castelli, L. A. Lugiato and F. Prati, in: Proceedings of the Conference Nonlinear Dynamics of Optical Systems, Afton, June 4–8 1990, ed. by N. Abraham, E. Garmire and P. Mandel, Optical Society of America, in press.Google Scholar

Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • M. Brambilla
    • 1
  • F. Castelli
    • 1
  • L. A. Lugiato
    • 1
  • F. Prati
    • 1
  • G. Strini
    • 1
  1. 1.Dipartimento di Fisica dell’ Università di MilanoMilanoItaly

Personalised recommendations