Abstract

We argue that in nonlinear optical systems with atoms randomly distributed in crystals or amorphous hosts one should go beyond the Clausius-Mossoti limit in order to take into account the effect of local field fluctuations induced by configurational disorder in atom position. This effect is analyzed by means of a random local mean field approach with neglect of correlations between dipole moments of different atoms. The formalism is applied to 3-level Λ type systems with quantum coherence possessing an absorptionless index of refraction and lasing without inversion. We show that the effect of configurational fluctuations results in the suppression of the atom susceptibility compared with the predictions based on the Clausius-Mossoti equation.

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References

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  1. J.D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).
  2. C. Kittel, Solid State Theory ( Dover Publ., New York, 1986).
  3. H.A. Lorentz, The Theory of Electrons (Teubner, Leipzig, 1909)
  4. R. Friedberg, S.R. Hartmann and J.T. Manassah, "Frequency Shift in Emission and Absorption by Resonant systems of Two-Level Atoms", Phys. Rep. 7, 101 (1973).
    [CrossRef]
  5. C.M. Bowden and J.P. Dowling, "Near Dipole-Dipole Effects in Dense Media: Generalized Maxwell-Bloch Equations", Phys. Rev. A 47, 1247 (1993).
    [CrossRef] [PubMed]
  6. J.T. Manassah, "Statistical Quantum Electrodynamics of Resonant Atoms", Phys. Rep. 101, 359 (1983).
    [CrossRef]
  7. Y. Ben-Aryeh, C.M. Bowden and J.C. Englund, "Intrinsic Optical Bistability in Collection of Spatially Distributed Two-Level Atoms", Phys.Rev. A 34, 3917 (1986).
    [CrossRef] [PubMed]
  8. R. Friedberg and S. R. Hartman, and J.T. Manassah, "Eect of Local Field Correction on a Strongly Pumped Resonance", Phys. Rev. A 40, 2446 (1989).
    [CrossRef] [PubMed]
  9. J.J. Maki, M.S. Malcuit, J.E. Sipe, and R.W. Boyd, "Linear and Nonlinear Optical Measurements of the Lorentz Local Field", Phys. Rev. Lett. 67, 972 (1991).
    [CrossRef] [PubMed]
  10. J.P.Dowling and C.M. Bowden, "Near Dipole-Dipole Eects in Lasing without Inversion: An Enhancement of Gain and Absorptionless Index of Refraction", Phys. Rev. Lett. 70, 1421 (1993).
    [CrossRef] [PubMed]
  11. A. Manka, J. P. Dowling,and C.M. Bowden, "Piezophotonic Switching Due to Local Field Eects in a Coherently Prepared Medium of Three-Level Atoms", Phys. Rev. Lett. 73 , 1789 (1994).
    [CrossRef] [PubMed]

  12. [CrossRef]
  13. C.M. Bowden, S. Sinch, and G. Agraval, "Laser instabilities and chaos in inhomogeneously broadened dense media", J. Mod. Opt. 42, 101 (1995).
    [CrossRef]
  14. O. Kocharovskaya, "Amplication and Lasing without Inversion", Phys. Rep. 219, 175 (1992).
    [CrossRef]
  15. M.O. Scully, "From Lasers and Masers to Phaseonium and Phasers", Phys. Rep. 219, 191 (1992).
    [CrossRef]
  16. M. Fleischhauer, C.H. Keitel, M.O. Scully, C. Su, and S.-Y. Zhu, "Resonantly Enhanced Refractive Index without Absorption via Atomic Coherence", Phys. Rev. A 46, 1468 (1992).
    [CrossRef] [PubMed]
  17. K. Binder and A.P. Young, "Spin Glasses", Rev. Mod. Phys. 58,801 (1986).
    [CrossRef]
  18. M.W. Klein, C. Held, and E. Zuro, "Dipole Interactions Among Polar Defects: a Self-Consistent Theory with Application to OH Impurities in KCL", Phys. Rev. B 13, 3576 (1976).
    [CrossRef]
  19. H. Margenau, "Pressure Broadenning of Spectral Lines", Phys. Rev. 43, 129 (1933).
    [CrossRef]
  20. B.E. Vugmeister and M.D. Glinchuk, "Dipole Glass and Ferroelectricity in Random Site electric Dipole Systems" Rev. Mod. Phys. 62, 993 (1990).
    [CrossRef]
  21. B.E.Vugmeister and H. Rabitz, "Eect of Local Field Fluctuations on Orientational in Random Site Dipole Systems", J. Stat. Phys. 88, 477 (1997).
    [CrossRef]
  22. P.W. Miloni and P.L. Knight, "Retardation in the Resonant Interaction of Two Identical Atoms", Phys. Rev. A 10, 1076 (1974).
    [CrossRef]
  23. Y. Ben-Aryeh and S. Ruschin, "Cooperative Decay of a Linear Chain of Molecules Including Explicit Spatial Dependence", Physica A 88, 362 (1977).
    [CrossRef]
  24. B.E. Vugmeister and H. Rabitz, "NonequilibriumSpin Glass State in Nonlinear Optical Systems with Coherence", Phys. Lett. 232,129 (1997).
    [CrossRef]
  25. R.R. Mosley, B.D. Sinclair, and M.H. Dunn, "Local Field Eect in the Three-level Atom", Opt. Commun. 108, 247 (1994).

Other (25)

J.D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).

C. Kittel, Solid State Theory ( Dover Publ., New York, 1986).

H.A. Lorentz, The Theory of Electrons (Teubner, Leipzig, 1909)

R. Friedberg, S.R. Hartmann and J.T. Manassah, "Frequency Shift in Emission and Absorption by Resonant systems of Two-Level Atoms", Phys. Rep. 7, 101 (1973).
[CrossRef]

C.M. Bowden and J.P. Dowling, "Near Dipole-Dipole Effects in Dense Media: Generalized Maxwell-Bloch Equations", Phys. Rev. A 47, 1247 (1993).
[CrossRef] [PubMed]

J.T. Manassah, "Statistical Quantum Electrodynamics of Resonant Atoms", Phys. Rep. 101, 359 (1983).
[CrossRef]

Y. Ben-Aryeh, C.M. Bowden and J.C. Englund, "Intrinsic Optical Bistability in Collection of Spatially Distributed Two-Level Atoms", Phys.Rev. A 34, 3917 (1986).
[CrossRef] [PubMed]

R. Friedberg and S. R. Hartman, and J.T. Manassah, "Eect of Local Field Correction on a Strongly Pumped Resonance", Phys. Rev. A 40, 2446 (1989).
[CrossRef] [PubMed]

J.J. Maki, M.S. Malcuit, J.E. Sipe, and R.W. Boyd, "Linear and Nonlinear Optical Measurements of the Lorentz Local Field", Phys. Rev. Lett. 67, 972 (1991).
[CrossRef] [PubMed]

J.P.Dowling and C.M. Bowden, "Near Dipole-Dipole Eects in Lasing without Inversion: An Enhancement of Gain and Absorptionless Index of Refraction", Phys. Rev. Lett. 70, 1421 (1993).
[CrossRef] [PubMed]

A. Manka, J. P. Dowling,and C.M. Bowden, "Piezophotonic Switching Due to Local Field Eects in a Coherently Prepared Medium of Three-Level Atoms", Phys. Rev. Lett. 73 , 1789 (1994).
[CrossRef] [PubMed]


[CrossRef]

C.M. Bowden, S. Sinch, and G. Agraval, "Laser instabilities and chaos in inhomogeneously broadened dense media", J. Mod. Opt. 42, 101 (1995).
[CrossRef]

O. Kocharovskaya, "Amplication and Lasing without Inversion", Phys. Rep. 219, 175 (1992).
[CrossRef]

M.O. Scully, "From Lasers and Masers to Phaseonium and Phasers", Phys. Rep. 219, 191 (1992).
[CrossRef]

M. Fleischhauer, C.H. Keitel, M.O. Scully, C. Su, and S.-Y. Zhu, "Resonantly Enhanced Refractive Index without Absorption via Atomic Coherence", Phys. Rev. A 46, 1468 (1992).
[CrossRef] [PubMed]

K. Binder and A.P. Young, "Spin Glasses", Rev. Mod. Phys. 58,801 (1986).
[CrossRef]

M.W. Klein, C. Held, and E. Zuro, "Dipole Interactions Among Polar Defects: a Self-Consistent Theory with Application to OH Impurities in KCL", Phys. Rev. B 13, 3576 (1976).
[CrossRef]

H. Margenau, "Pressure Broadenning of Spectral Lines", Phys. Rev. 43, 129 (1933).
[CrossRef]

B.E. Vugmeister and M.D. Glinchuk, "Dipole Glass and Ferroelectricity in Random Site electric Dipole Systems" Rev. Mod. Phys. 62, 993 (1990).
[CrossRef]

B.E.Vugmeister and H. Rabitz, "Eect of Local Field Fluctuations on Orientational in Random Site Dipole Systems", J. Stat. Phys. 88, 477 (1997).
[CrossRef]

P.W. Miloni and P.L. Knight, "Retardation in the Resonant Interaction of Two Identical Atoms", Phys. Rev. A 10, 1076 (1974).
[CrossRef]

Y. Ben-Aryeh and S. Ruschin, "Cooperative Decay of a Linear Chain of Molecules Including Explicit Spatial Dependence", Physica A 88, 362 (1977).
[CrossRef]

B.E. Vugmeister and H. Rabitz, "NonequilibriumSpin Glass State in Nonlinear Optical Systems with Coherence", Phys. Lett. 232,129 (1997).
[CrossRef]

R.R. Mosley, B.D. Sinclair, and M.H. Dunn, "Local Field Eect in the Three-level Atom", Opt. Commun. 108, 247 (1994).

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Figures (3)

Figure 1:
Figure 1:

Real (1) and imaginary (2) part of the susceptibility χ e of non-interacting atoms9

Figure 2:
Figure 2:

Real (1) and imaginary (2) part of the susceptibility χ DD obtained from Eqs.(11)–(14)

Figure 3:
Figure 3:

Real (1) and imaginary (2) part of the susceptibility χ DD given by the Clausius-Mossoti equation5

Equations (14)

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E L ( t ) = E ( t ) + 4 π 3 P ( t )
P ( ω ) = n α ( ω ) E L ( ω ) .
χ DD = 4 πnα 1 4 π 3 χ e 1 1 3 χ e .
P = 1 V 0 i N < μ ̂ i ¯ > n m i ¯
m i = α E iL ,
E iL = j J ij m j + E ex .
J ij J ( r ij ) = 3 ( n ij ) x 2 1 r ij 3 .
E iL MF = E ex + j J ij m j ¯ = E ex + P d r J ( r ) .
E iL = E + 4 π 3 P + e i ,
e i = j J ˜ ij m j ; J ˜ ij = J ij 1 V 0 d r J ( r ) .
χDD = κ e 1 1 3 κ e ,
κ e = de χ e ( e ) f ( e ) .
f ( e ) = 1 π δ δ 2 + e 2 ; δ = 5.1 μnM .
M = 1 μ de χ ' e ( e ) e f ( e , M )

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