Abstract

We investigate local-field effects in nonlinear optical materials composed of two species of atoms. One species of atom is assumed to be near resonance with an applied field and is modeled as a two-level system while the other species of atom is assumed to be in the linear regime. If the near dipole-dipole interaction between two-level atoms is negligible, the usual local- field enhancement of the field is obtained. For the case in which near-dipole-dipole interactions are significant due to a high density of two-level atoms, local-field effects associated with the presence of a optically linear material component lead to local-field enhancement of the near dipole-dipole interaction, intrinsic cooperative decays, and coherence exchange processes.

© 1997 Optical Society of America

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References

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  1. 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]
  2. F. A. Hopf, C. M. Bowden, and W. Louisell, “Mirrorless optical bistability with the use of the local-field correction,”Phys. Rev. A 29, 2591 (1984).
    [Crossref]
  3. M. E. Crenshaw and C. M. Bowden, “Quasiadiabatic Following Approximation for a Dense Medium of Two-Level Atoms,” Phys. Rev. Lett. 69, 3475 (1992).
    [Crossref] [PubMed]
  4. A. S. Manka, J. P. Dowling, C. M. Bowden, and M. Fleishhauer, “Piezophotonic Switching Due to Local Field Effects in a Coherently Prepared Medium of Three-Level Atoms,” Phys. Rev. Lett. 73, 1789 (1994).
    [Crossref] [PubMed]
  5. D. Marcuse, Principles of Quantum Electronics, (Academic Press, Orlando, FL, 1980), pg. 307.
  6. N. Bloembergen, Nonlinear Optics (W. A. Benjamin, New York, 1964).
  7. M. P. Hehlen, H. U. Güdel, Q. Shu, J. Rai, S. Rai, and S. C. Rand, “Cooperative Bistability in Dense, Excited Atomic Systems” Phys. Rev. Lett. 73, 1103 (1994).
    [Crossref] [PubMed]
  8. M. Born and E. Wolf, Principles of Optics, Sixth Ed., (Pergamon Press, Oxford, 1991).
  9. R. Friedberg, S. R. Hartmann, and J. T. Manassah, “Effect of local-field correction on a strongly pumped resonance,” Phys. Rev. A 40, 2446 (1989).
    [Crossref] [PubMed]
  10. M. E. Crenshaw, M. Scalora, and C. M. Bowden, “Ultrafast Intrinsic Optical Swithcin in a Dense Medium of Two-Level Atoms,” Phys. Rev. Lett. 68, 911 (1992).
    [Crossref] [PubMed]
  11. L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms, (Wiley, New York, 1975), (republished by Dover, NY, 1987).
  12. M. Sargent III, M. O. Scully, and W. E. Lamb, Laser Physics, (Addison-Wesley, NY, 1987).

1994 (2)

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

M. P. Hehlen, H. U. Güdel, Q. Shu, J. Rai, S. Rai, and S. C. Rand, “Cooperative Bistability in Dense, Excited Atomic Systems” Phys. Rev. Lett. 73, 1103 (1994).
[Crossref] [PubMed]

1993 (1)

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]

1992 (2)

M. E. Crenshaw and C. M. Bowden, “Quasiadiabatic Following Approximation for a Dense Medium of Two-Level Atoms,” Phys. Rev. Lett. 69, 3475 (1992).
[Crossref] [PubMed]

M. E. Crenshaw, M. Scalora, and C. M. Bowden, “Ultrafast Intrinsic Optical Swithcin in a Dense Medium of Two-Level Atoms,” Phys. Rev. Lett. 68, 911 (1992).
[Crossref] [PubMed]

1989 (1)

R. Friedberg, S. R. Hartmann, and J. T. Manassah, “Effect of local-field correction on a strongly pumped resonance,” Phys. Rev. A 40, 2446 (1989).
[Crossref] [PubMed]

1984 (1)

F. A. Hopf, C. M. Bowden, and W. Louisell, “Mirrorless optical bistability with the use of the local-field correction,”Phys. Rev. A 29, 2591 (1984).
[Crossref]

1964 (1)

N. Bloembergen, Nonlinear Optics (W. A. Benjamin, New York, 1964).

Allen, L.

L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms, (Wiley, New York, 1975), (republished by Dover, NY, 1987).

Bloembergen, N.

N. Bloembergen, Nonlinear Optics (W. A. Benjamin, New York, 1964).

Born, M.

M. Born and E. Wolf, Principles of Optics, Sixth Ed., (Pergamon Press, Oxford, 1991).

Bowden, C. M.

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

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]

M. E. Crenshaw and C. M. Bowden, “Quasiadiabatic Following Approximation for a Dense Medium of Two-Level Atoms,” Phys. Rev. Lett. 69, 3475 (1992).
[Crossref] [PubMed]

M. E. Crenshaw, M. Scalora, and C. M. Bowden, “Ultrafast Intrinsic Optical Swithcin in a Dense Medium of Two-Level Atoms,” Phys. Rev. Lett. 68, 911 (1992).
[Crossref] [PubMed]

F. A. Hopf, C. M. Bowden, and W. Louisell, “Mirrorless optical bistability with the use of the local-field correction,”Phys. Rev. A 29, 2591 (1984).
[Crossref]

Crenshaw, M. E.

M. E. Crenshaw and C. M. Bowden, “Quasiadiabatic Following Approximation for a Dense Medium of Two-Level Atoms,” Phys. Rev. Lett. 69, 3475 (1992).
[Crossref] [PubMed]

M. E. Crenshaw, M. Scalora, and C. M. Bowden, “Ultrafast Intrinsic Optical Swithcin in a Dense Medium of Two-Level Atoms,” Phys. Rev. Lett. 68, 911 (1992).
[Crossref] [PubMed]

Dowling, J. P.

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

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]

Eberly, J. H.

L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms, (Wiley, New York, 1975), (republished by Dover, NY, 1987).

Fleishhauer, M.

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

Friedberg, R.

R. Friedberg, S. R. Hartmann, and J. T. Manassah, “Effect of local-field correction on a strongly pumped resonance,” Phys. Rev. A 40, 2446 (1989).
[Crossref] [PubMed]

Güdel, H. U.

M. P. Hehlen, H. U. Güdel, Q. Shu, J. Rai, S. Rai, and S. C. Rand, “Cooperative Bistability in Dense, Excited Atomic Systems” Phys. Rev. Lett. 73, 1103 (1994).
[Crossref] [PubMed]

Hartmann, S. R.

R. Friedberg, S. R. Hartmann, and J. T. Manassah, “Effect of local-field correction on a strongly pumped resonance,” Phys. Rev. A 40, 2446 (1989).
[Crossref] [PubMed]

Hehlen, M. P.

M. P. Hehlen, H. U. Güdel, Q. Shu, J. Rai, S. Rai, and S. C. Rand, “Cooperative Bistability in Dense, Excited Atomic Systems” Phys. Rev. Lett. 73, 1103 (1994).
[Crossref] [PubMed]

Hopf, F. A.

F. A. Hopf, C. M. Bowden, and W. Louisell, “Mirrorless optical bistability with the use of the local-field correction,”Phys. Rev. A 29, 2591 (1984).
[Crossref]

Lamb, W. E.

M. Sargent III, M. O. Scully, and W. E. Lamb, Laser Physics, (Addison-Wesley, NY, 1987).

Louisell, W.

F. A. Hopf, C. M. Bowden, and W. Louisell, “Mirrorless optical bistability with the use of the local-field correction,”Phys. Rev. A 29, 2591 (1984).
[Crossref]

Manassah, J. T.

R. Friedberg, S. R. Hartmann, and J. T. Manassah, “Effect of local-field correction on a strongly pumped resonance,” Phys. Rev. A 40, 2446 (1989).
[Crossref] [PubMed]

Manka, A. S.

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

Marcuse, D.

D. Marcuse, Principles of Quantum Electronics, (Academic Press, Orlando, FL, 1980), pg. 307.

Rai, J.

M. P. Hehlen, H. U. Güdel, Q. Shu, J. Rai, S. Rai, and S. C. Rand, “Cooperative Bistability in Dense, Excited Atomic Systems” Phys. Rev. Lett. 73, 1103 (1994).
[Crossref] [PubMed]

Rai, S.

M. P. Hehlen, H. U. Güdel, Q. Shu, J. Rai, S. Rai, and S. C. Rand, “Cooperative Bistability in Dense, Excited Atomic Systems” Phys. Rev. Lett. 73, 1103 (1994).
[Crossref] [PubMed]

Rand, S. C.

M. P. Hehlen, H. U. Güdel, Q. Shu, J. Rai, S. Rai, and S. C. Rand, “Cooperative Bistability in Dense, Excited Atomic Systems” Phys. Rev. Lett. 73, 1103 (1994).
[Crossref] [PubMed]

Sargent III, M.

M. Sargent III, M. O. Scully, and W. E. Lamb, Laser Physics, (Addison-Wesley, NY, 1987).

Scalora, M.

M. E. Crenshaw, M. Scalora, and C. M. Bowden, “Ultrafast Intrinsic Optical Swithcin in a Dense Medium of Two-Level Atoms,” Phys. Rev. Lett. 68, 911 (1992).
[Crossref] [PubMed]

Scully, M. O.

M. Sargent III, M. O. Scully, and W. E. Lamb, Laser Physics, (Addison-Wesley, NY, 1987).

Shu, Q.

M. P. Hehlen, H. U. Güdel, Q. Shu, J. Rai, S. Rai, and S. C. Rand, “Cooperative Bistability in Dense, Excited Atomic Systems” Phys. Rev. Lett. 73, 1103 (1994).
[Crossref] [PubMed]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, Sixth Ed., (Pergamon Press, Oxford, 1991).

Phys. Rev. A (3)

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]

F. A. Hopf, C. M. Bowden, and W. Louisell, “Mirrorless optical bistability with the use of the local-field correction,”Phys. Rev. A 29, 2591 (1984).
[Crossref]

R. Friedberg, S. R. Hartmann, and J. T. Manassah, “Effect of local-field correction on a strongly pumped resonance,” Phys. Rev. A 40, 2446 (1989).
[Crossref] [PubMed]

Phys. Rev. Lett. (4)

M. E. Crenshaw, M. Scalora, and C. M. Bowden, “Ultrafast Intrinsic Optical Swithcin in a Dense Medium of Two-Level Atoms,” Phys. Rev. Lett. 68, 911 (1992).
[Crossref] [PubMed]

M. E. Crenshaw and C. M. Bowden, “Quasiadiabatic Following Approximation for a Dense Medium of Two-Level Atoms,” Phys. Rev. Lett. 69, 3475 (1992).
[Crossref] [PubMed]

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

M. P. Hehlen, H. U. Güdel, Q. Shu, J. Rai, S. Rai, and S. C. Rand, “Cooperative Bistability in Dense, Excited Atomic Systems” Phys. Rev. Lett. 73, 1103 (1994).
[Crossref] [PubMed]

Other (5)

M. Born and E. Wolf, Principles of Optics, Sixth Ed., (Pergamon Press, Oxford, 1991).

D. Marcuse, Principles of Quantum Electronics, (Academic Press, Orlando, FL, 1980), pg. 307.

N. Bloembergen, Nonlinear Optics (W. A. Benjamin, New York, 1964).

L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms, (Wiley, New York, 1975), (republished by Dover, NY, 1987).

M. Sargent III, M. O. Scully, and W. E. Lamb, Laser Physics, (Addison-Wesley, NY, 1987).

Supplementary Material (6)

» Media 1: GIF (8 KB)     
» Media 2: GIF (6 KB)     
» Media 3: GIF (11 KB)     
» Media 4: GIF (12 KB)     
» Media 5: GIF (20 KB)     
» Media 6: GIF (19 KB)     

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Figures (3)

Figure 1:
Figure 1:

(a) Vapor cell: Dilute atomic vapors near resonance can be modeled as two-level systems in a vacuum. At low densities, the interaction between atoms is negligible, and it is sufficient to consider the interaction of a single particle with the field when developing equations of motion. (b) Dense medium: At high densities, the particles interact via the electromagnetic field. The Lorentz local-field condition (LLFC) leads to the Clausius - Mossotti - Lorentz - Lorenz (CMLL) relation for linearly polarizable particles and to near dipole-dipole interaction for two-level systems. (c) Multicomponent medium with dilute nonlinear component: We consider optically nonlinear condensed mater comprised of two polarizable components. If the density of nonlinear particles is sufficiently low then interaction between the nonlinear particles is negligible. (d) Dense nonlinear multicomponent media: When near dipole-dipole interactions are significant due to a high density of two-level atoms, local-field effe associated with the presence of an optically linear material component lead to local-field enhancement of the NDD interaction, local cooperative decays, and coherence exchange processes. [Media 1] [Media 2] [Media 3] [Media 4]

Figure 2:
Figure 2:

Calculation of the near field: Individual dipoles are used in the calculation of E near. In cubic symmetry E near = 0, but here the symmetry of the lattice is altered by the presence of a second species. [Media 5]

Figure 3:
Figure 3:

Transition from microscopic to macroscopic variables: The transition from microscopic to macroscopic variables is obtained by integrating over a large number of particles. For a dense multi-component medium, all species of particles are included in the volume of integration. [Media 6]

Equations (15)

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E L = E + i ( 4 π 3 + sL i ) P i = E + i 4 π 3 η i P i ,
ε L = ε + 4 π 3 ( η α 𝑝 lin + η 𝑝 res ) = ε + 4 π 3 η α α N α ε L + 4 π 3 η 𝑝 res
4 π η α α N α 3 = ε 1 ε 1 + 3 / η α
ε L = ( ε + 4 π 3 η 𝑝 res ) ,
l = ε bg 1 + 3 / η α 3 .
ω t = ħ ( ε L * r 21 ε L r 21 * )
r 21 t = i Δ r 21 ε L 2 ħ ω .
R 21 t = i ( Δ W ) R 21 2 ħ ℓεW γ R 21
W t = ħ ( * ε * R 21 ε R 21 * ) 2 i ( * ) R 21 2 γ ( W W eq ) ,
R 21 t = i ( Δ r ∊W ) R 21 + i ∊W R 21 2 ħ ℓεW γ R 21
W t = ħ ( * ε * R 21 ℓε R 21 * ) 4 i R 21 2 γ ( W W eq ) ,
R 21 t = i ( Δ ∊W ) R 21 i 2 Ω W i 2 ω p 2 3 X ¯ W γ R 21
W t = i ( Ω * R 21 Ω R 21 * ) i ω p 2 3 ( X ¯ * R 21 X ¯ R 21 * ) γ ( W W eq )
2 X ¯ t 2 + ( γ 2 ) X ¯ t + ( ω b 2 ω 2 ω p 2 / 3 iωγ ) X ¯ = ( Ω + 2 R 21 ) ,
X ¯ = Ω + 2 R 21 ω b 2 ω 2 ω p 2 / 3 iωγ ,

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