Advertisement

Collision-Induced Coherence in Four Wave Light Mixing

  • N. Bloembergen
  • A. R. Bogdan
  • M. W. Downer
Part of the Springer Series in Optical Sciences book series (SSOS, volume 30)

Abstract

The evolution of the density matrix of a material system under the influence of one or more traveling electromagnetic waves is central in determining the linear and nonlinear optical response. The role of spontaneous emission and collisional processes may, under certain conditions which apply to a rather large variety of experimental situations, be represented by phenomenological damping terms in the equations of motion for the diagonal and off-diagonal elements of the density matrix [1]. General expressions for the third order nonlinear susceptibility have been given by many authors [2–4]. The bookkeeping of the many terms occurring in third order perturbation theory may be systematized by the use df double-sided Feynman type diagrams [5,6,7]. It is important to consider explicitly the evolution of both bra vectors <ψ| and ket vectors |ψ> in the presence of damping. Authors who use only one sided diagrams irretrievably lose some terms which have physical significance. One must not calculate the evolution in the absence of damping, and then formally add the damping by considering some frequencies as complex quantities. In the latter case one always ends up with resonant denominators which contain only separations ωgn from the initially occupied state, ρ gg (o) =1, to states |n>. The correct expression also contains denominators with frequency separations ωnn, between two initially unoccupied excited states.

Keywords

Spontaneous Emission Helium Pressure Order Perturbation Theory Nonlinear Optical Response Satellite Resonance 
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.
    N. Bloembergen and Y.R. Shen, Phys. Rev. 133, A37 (1964).ADSCrossRefGoogle Scholar
  2. 2.
    N. Bloembergen, H.Lotem and R.T. Lynch, Indian J. Pure Appl. Phys. 16, 151 (1978).Google Scholar
  3. 3.
    S.A.J. Druet, B. Attal, T.K. Gustafson and J.P. Taran, Phys. Rev. A18, 1529 (1978).ADSCrossRefGoogle Scholar
  4. 4.
    J.L. Oudar and Y.R. Shen, Phys. Rev. A22, 1141 (1980).MathSciNetADSGoogle Scholar
  5. 5.
    C.J. Bordé, C.R. Acad. Sc. Paris, 282B, 341 (1976).Google Scholar
  6. 6.
    S.Y. Yee and T.K. Gustafson, Phys. Rev. A18, 1597 (1978).ADSCrossRefGoogle Scholar
  7. 7.
    S.A.J. Druet and J.P.E. Taran, in Progress in Quantum Electronics, ed. by J.H. Sanders and S. Stenholm, Pergamon Press, Oxford, to be published.Google Scholar
  8. 8.
    N. Bloembergen, Nonlinear Optics, Benjamin, New York, 1965, p. 29Google Scholar
  9. 9.
    T.W. Hänsch and P. Toschek, Zeits. Phys. 236, 213 (1970). See also T.W. Hänsch, in Nonlinear Spectroscopy, edited by N. Bloembergen, p. 17, North-Holland Pub. Amsterdam, 1977.Google Scholar
  10. 10.
    L.A. Carreira, L.P. Goss and Th.B. Malloy, J. Chem. Phys. 69, 855 (1978).ADSCrossRefGoogle Scholar
  11. 11.
    G.L. Eesley, Coherent Raman Spectroscopy, Pergamón Press, Oxford, 1981. Some statements at the end of Appendix 2 (pp.115–116) are questionable.Google Scholar
  12. 12.
    N. Bloembergen, in Laser Spectroscopy IV, ed. by H. Walther, K.W. Rothe Springer Series in Optical Sciences, Vol. 21 ( Springer Berlin, Heidelberg, New York 1979 ) p. 340.Google Scholar
  13. 13.
    Y. Prior, A.R. Bogdan, M. Dagenais and N. Bloembergen, Phys. Rev. Lett. 46, 111 (1981).ADSCrossRefGoogle Scholar
  14. 14.
    A.R.Bogdan, Y. Prior and N. Bloembergen, Opt. Lett. 6, 82 (1981).Google Scholar
  15. 15.
    A.R. Bogdan, M. Downer and N. Bloembergen, Phys. Rev. A24, (1981).Google Scholar
  16. 16.
    A.R. Bogdan, M.W. Downer and N. Bloembergen, Opt. Lett. 6, (1981).Google Scholar
  17. 17.
    Y. Prior, Appt. Opt. 19, 1741 (1980).ADSCrossRefGoogle Scholar
  18. J.A. Shirley, R.J. Hall and A.C. Eckbreth, Opt. Lett. 5, 380 (1980).ADSCrossRefGoogle Scholar
  19. S. Chandra, A. Compaan and E. Wiener-Avnean, Appl. Phys. Lett. 33, 867 (1978).ADSCrossRefGoogle Scholar
  20. 18.
    J.P. Woerdman and M.F.H. Schuurmans, Opt. Lett. 6, 239 (1981), and references quoted therein.Google Scholar
  21. 19.
    P.F.Liao, J.E. Bjorkholm and P.R. Berman, Phys. Rev. A20, 1489 (1979)Google Scholar
  22. 20.
    T.W. Mossberg, F. Whittaker, R. Kachru and S.R. Hartmann, Phys. Rev. A22, 1962 (1980).MathSciNetADSCrossRefGoogle Scholar
  23. 21.
    A.R. Bogdan, Ph.D. thesis, Harvard University, 1981 (unpublished).Google Scholar
  24. 22.
    J. Herman and M. Landmann, Opt. Comm. 29, 172 (1979).ADSCrossRefGoogle Scholar
  25. 23.
    A. Lau, R. König and M. Pfeiffer, Opt. Comm. 32, 75 (1980).ADSCrossRefGoogle Scholar
  26. 24.
    M. Dagenais, Phys. Rev. A (1981).Google Scholar
  27. 25.
    M. Grynberg, J. de Physique, Paris, (1981). See also this volume.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • N. Bloembergen
    • 1
  • A. R. Bogdan
    • 1
  • M. W. Downer
    • 1
  1. 1.Division of Applied SciencesmHarvard UniversityCambridgeUSA

Personalised recommendations