Abstract

We compute the spectral distributions of the transmitted and reflected signals from an extended optically dense superradiant amplifier. We show that, if the amplifier length is in the neighborhood of an integer multiple of the resonance transition half-wavelength, the frequency shift in the spectral distributions of the transmitted and reflected signals are modified by the Dynamical Lorentz Shift. The broken spatial inversion symmetry, manifested through an asymmetrical distribution of the population difference with respect to a spatial inversion around the midpoint of the sample, is shown to be at the origin of this spectral asymmetry in these so-called asymmetrical transition domains.

© 1997 Optical Society of America

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References

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  1. H. A. Lorentz,Theory of Electrons (Dover, New york, 2nd ed., 1952). Sections 117-124 and note 54.
  2. R. Friedberg, S. R. Hartmann, and J. T. Manassah, “Frequency shifts in emission and absorption by resonant systems of two-level atoms”, Phys. Rep. C 7, 101 (1973).
    [CrossRef]
  3. J.T. Manassah, “Statistical quantum electrodynamics of resonant atoms”, Phys. Rep. 101, 359 (1983).
    [CrossRef]
  4. 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]
  5. K. J. Boller, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency”, Phys. Rev. Lett. 66, 2593 (1991).
    [CrossRef] [PubMed]
  6. J. E. Field, K. H. Hahn, and S. E. Harris, “Observation of electromagnetically induced transparency in collisionally broadened lead vapor”, Phys. Rev. Lett. 67, 3062 (1991).
    [CrossRef] [PubMed]
  7. V. Malyshev and E. C. Jarque, “Optical hysteresis and instabilities inside the polariton bandgap”, J. Opt. Soc. Am. 12, 1868 (1995).
    [CrossRef]
  8. M. G. Benedict and E. D. Trifonov, “Coherent reflection as superradiation from the boundary of a resonant medium”, Phys. Rev. A 38, 2854 (1988).
    [CrossRef] [PubMed]
  9. M. G. Benedict, V. A. Malyshev, E. D. Trifonov, and I. Zaitsev, “Reflection and transmission of ultrafast light pulses through a thin resonant medium: LFC”, Phys. Rev. A. 43, 3854 (1991).
    [CrossRef]
  10. J. T. Manassah and B. Gross, “Pulse reflectivitry at a dense dielectric-gas interface” Opt. Commun. 131, 408 (1996).
    [CrossRef]
  11. R. Friedberg, S. R. Hartmann, and J. T. Manassah, “Intensity-dependent spectral reflectivity of a dense gas-dielectric interface”, Phys. Rev. 42, 5573 (1990).
    [CrossRef]
  12. R. Friedberg, S. R. Hartmann, and J. T. Manassah, “Effects of the dynamic Lorentz shift on four-wave parametric interactions in a strongly driven two-level system”, Phys. Rev. 42, 494 (1990).
    [CrossRef]
  13. R. Friedberg, S. R. Hartmann, and J. T. Manassah, “Dynamical Lorentz shift revealed via nonlinear multiwave excitation”, J. Phys. B: At. Mol. Opt. Phys. 24, 3981 (1991).
    [CrossRef]
  14. 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]
  15. J. T. Manassah and B. Gross, “Superradiant amplification in an optically dense gas”, Opt. Commun. (1997) in print.
    [CrossRef]
  16. A. Omont, ”Remarques sur la theorie de l’elargissement Holtsmark des raies de resonance optique”, C. R. Acad. Sci. (Paris) 262, 190 (1966).
  17. Y. A. Vdovin and V. M. Galitskii, “Dielectric constant of a gas of resonant atoms”, Zh. Eksp. Teor. Fiz. 52, 1345 (1967). [JETP 25, 894 (1967)]

1996 (1)

J. T. Manassah and B. Gross, “Pulse reflectivitry at a dense dielectric-gas interface” Opt. Commun. 131, 408 (1996).
[CrossRef]

1995 (1)

V. Malyshev and E. C. Jarque, “Optical hysteresis and instabilities inside the polariton bandgap”, J. Opt. Soc. Am. 12, 1868 (1995).
[CrossRef]

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]

1991 (5)

K. J. Boller, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency”, Phys. Rev. Lett. 66, 2593 (1991).
[CrossRef] [PubMed]

J. E. Field, K. H. Hahn, and S. E. Harris, “Observation of electromagnetically induced transparency in collisionally broadened lead vapor”, Phys. Rev. Lett. 67, 3062 (1991).
[CrossRef] [PubMed]

R. Friedberg, S. R. Hartmann, and J. T. Manassah, “Dynamical Lorentz shift revealed via nonlinear multiwave excitation”, J. Phys. B: At. Mol. Opt. Phys. 24, 3981 (1991).
[CrossRef]

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]

M. G. Benedict, V. A. Malyshev, E. D. Trifonov, and I. Zaitsev, “Reflection and transmission of ultrafast light pulses through a thin resonant medium: LFC”, Phys. Rev. A. 43, 3854 (1991).
[CrossRef]

1990 (2)

R. Friedberg, S. R. Hartmann, and J. T. Manassah, “Intensity-dependent spectral reflectivity of a dense gas-dielectric interface”, Phys. Rev. 42, 5573 (1990).
[CrossRef]

R. Friedberg, S. R. Hartmann, and J. T. Manassah, “Effects of the dynamic Lorentz shift on four-wave parametric interactions in a strongly driven two-level system”, Phys. Rev. 42, 494 (1990).
[CrossRef]

1988 (1)

M. G. Benedict and E. D. Trifonov, “Coherent reflection as superradiation from the boundary of a resonant medium”, Phys. Rev. A 38, 2854 (1988).
[CrossRef] [PubMed]

1983 (1)

J.T. Manassah, “Statistical quantum electrodynamics of resonant atoms”, Phys. Rep. 101, 359 (1983).
[CrossRef]

1973 (1)

R. Friedberg, S. R. Hartmann, and J. T. Manassah, “Frequency shifts in emission and absorption by resonant systems of two-level atoms”, Phys. Rep. C 7, 101 (1973).
[CrossRef]

1967 (1)

Y. A. Vdovin and V. M. Galitskii, “Dielectric constant of a gas of resonant atoms”, Zh. Eksp. Teor. Fiz. 52, 1345 (1967). [JETP 25, 894 (1967)]

1966 (1)

A. Omont, ”Remarques sur la theorie de l’elargissement Holtsmark des raies de resonance optique”, C. R. Acad. Sci. (Paris) 262, 190 (1966).

Benedict, M. G.

M. G. Benedict, V. A. Malyshev, E. D. Trifonov, and I. Zaitsev, “Reflection and transmission of ultrafast light pulses through a thin resonant medium: LFC”, Phys. Rev. A. 43, 3854 (1991).
[CrossRef]

M. G. Benedict and E. D. Trifonov, “Coherent reflection as superradiation from the boundary of a resonant medium”, Phys. Rev. A 38, 2854 (1988).
[CrossRef] [PubMed]

Boller, K. J.

K. J. Boller, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency”, Phys. Rev. Lett. 66, 2593 (1991).
[CrossRef] [PubMed]

Bowden, C. M.

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]

Boyd, R. W.

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]

Dowling, J. P.

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]

Field, J. E.

J. E. Field, K. H. Hahn, and S. E. Harris, “Observation of electromagnetically induced transparency in collisionally broadened lead vapor”, Phys. Rev. Lett. 67, 3062 (1991).
[CrossRef] [PubMed]

Friedberg, R.

R. Friedberg, S. R. Hartmann, and J. T. Manassah, “Dynamical Lorentz shift revealed via nonlinear multiwave excitation”, J. Phys. B: At. Mol. Opt. Phys. 24, 3981 (1991).
[CrossRef]

R. Friedberg, S. R. Hartmann, and J. T. Manassah, “Effects of the dynamic Lorentz shift on four-wave parametric interactions in a strongly driven two-level system”, Phys. Rev. 42, 494 (1990).
[CrossRef]

R. Friedberg, S. R. Hartmann, and J. T. Manassah, “Intensity-dependent spectral reflectivity of a dense gas-dielectric interface”, Phys. Rev. 42, 5573 (1990).
[CrossRef]

R. Friedberg, S. R. Hartmann, and J. T. Manassah, “Frequency shifts in emission and absorption by resonant systems of two-level atoms”, Phys. Rep. C 7, 101 (1973).
[CrossRef]

Galitskii, V. M.

Y. A. Vdovin and V. M. Galitskii, “Dielectric constant of a gas of resonant atoms”, Zh. Eksp. Teor. Fiz. 52, 1345 (1967). [JETP 25, 894 (1967)]

Gross, B.

J. T. Manassah and B. Gross, “Pulse reflectivitry at a dense dielectric-gas interface” Opt. Commun. 131, 408 (1996).
[CrossRef]

J. T. Manassah and B. Gross, “Superradiant amplification in an optically dense gas”, Opt. Commun. (1997) in print.
[CrossRef]

Hahn, K. H.

J. E. Field, K. H. Hahn, and S. E. Harris, “Observation of electromagnetically induced transparency in collisionally broadened lead vapor”, Phys. Rev. Lett. 67, 3062 (1991).
[CrossRef] [PubMed]

Harris, S. E.

J. E. Field, K. H. Hahn, and S. E. Harris, “Observation of electromagnetically induced transparency in collisionally broadened lead vapor”, Phys. Rev. Lett. 67, 3062 (1991).
[CrossRef] [PubMed]

K. J. Boller, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency”, Phys. Rev. Lett. 66, 2593 (1991).
[CrossRef] [PubMed]

Hartmann, S. R.

R. Friedberg, S. R. Hartmann, and J. T. Manassah, “Dynamical Lorentz shift revealed via nonlinear multiwave excitation”, J. Phys. B: At. Mol. Opt. Phys. 24, 3981 (1991).
[CrossRef]

R. Friedberg, S. R. Hartmann, and J. T. Manassah, “Effects of the dynamic Lorentz shift on four-wave parametric interactions in a strongly driven two-level system”, Phys. Rev. 42, 494 (1990).
[CrossRef]

R. Friedberg, S. R. Hartmann, and J. T. Manassah, “Intensity-dependent spectral reflectivity of a dense gas-dielectric interface”, Phys. Rev. 42, 5573 (1990).
[CrossRef]

R. Friedberg, S. R. Hartmann, and J. T. Manassah, “Frequency shifts in emission and absorption by resonant systems of two-level atoms”, Phys. Rep. C 7, 101 (1973).
[CrossRef]

Imamoglu, A.

K. J. Boller, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency”, Phys. Rev. Lett. 66, 2593 (1991).
[CrossRef] [PubMed]

Jarque, E. C.

V. Malyshev and E. C. Jarque, “Optical hysteresis and instabilities inside the polariton bandgap”, J. Opt. Soc. Am. 12, 1868 (1995).
[CrossRef]

Lorentz, H. A.

H. A. Lorentz,Theory of Electrons (Dover, New york, 2nd ed., 1952). Sections 117-124 and note 54.

Maki, J. J.

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]

Malcuit, M. S.

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]

Malyshev, V.

V. Malyshev and E. C. Jarque, “Optical hysteresis and instabilities inside the polariton bandgap”, J. Opt. Soc. Am. 12, 1868 (1995).
[CrossRef]

Malyshev, V. A.

M. G. Benedict, V. A. Malyshev, E. D. Trifonov, and I. Zaitsev, “Reflection and transmission of ultrafast light pulses through a thin resonant medium: LFC”, Phys. Rev. A. 43, 3854 (1991).
[CrossRef]

Manassah, J. T.

J. T. Manassah and B. Gross, “Pulse reflectivitry at a dense dielectric-gas interface” Opt. Commun. 131, 408 (1996).
[CrossRef]

R. Friedberg, S. R. Hartmann, and J. T. Manassah, “Dynamical Lorentz shift revealed via nonlinear multiwave excitation”, J. Phys. B: At. Mol. Opt. Phys. 24, 3981 (1991).
[CrossRef]

R. Friedberg, S. R. Hartmann, and J. T. Manassah, “Effects of the dynamic Lorentz shift on four-wave parametric interactions in a strongly driven two-level system”, Phys. Rev. 42, 494 (1990).
[CrossRef]

R. Friedberg, S. R. Hartmann, and J. T. Manassah, “Intensity-dependent spectral reflectivity of a dense gas-dielectric interface”, Phys. Rev. 42, 5573 (1990).
[CrossRef]

R. Friedberg, S. R. Hartmann, and J. T. Manassah, “Frequency shifts in emission and absorption by resonant systems of two-level atoms”, Phys. Rep. C 7, 101 (1973).
[CrossRef]

J. T. Manassah and B. Gross, “Superradiant amplification in an optically dense gas”, Opt. Commun. (1997) in print.
[CrossRef]

Manassah, J.T.

J.T. Manassah, “Statistical quantum electrodynamics of resonant atoms”, Phys. Rep. 101, 359 (1983).
[CrossRef]

Omont, A.

A. Omont, ”Remarques sur la theorie de l’elargissement Holtsmark des raies de resonance optique”, C. R. Acad. Sci. (Paris) 262, 190 (1966).

Sipe, J. E.

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]

Trifonov, E. D.

M. G. Benedict, V. A. Malyshev, E. D. Trifonov, and I. Zaitsev, “Reflection and transmission of ultrafast light pulses through a thin resonant medium: LFC”, Phys. Rev. A. 43, 3854 (1991).
[CrossRef]

M. G. Benedict and E. D. Trifonov, “Coherent reflection as superradiation from the boundary of a resonant medium”, Phys. Rev. A 38, 2854 (1988).
[CrossRef] [PubMed]

Vdovin, Y. A.

Y. A. Vdovin and V. M. Galitskii, “Dielectric constant of a gas of resonant atoms”, Zh. Eksp. Teor. Fiz. 52, 1345 (1967). [JETP 25, 894 (1967)]

Zaitsev, I.

M. G. Benedict, V. A. Malyshev, E. D. Trifonov, and I. Zaitsev, “Reflection and transmission of ultrafast light pulses through a thin resonant medium: LFC”, Phys. Rev. A. 43, 3854 (1991).
[CrossRef]

C. R. Acad. Sci. (Paris) (1)

A. Omont, ”Remarques sur la theorie de l’elargissement Holtsmark des raies de resonance optique”, C. R. Acad. Sci. (Paris) 262, 190 (1966).

J. Opt. Soc. Am. (1)

V. Malyshev and E. C. Jarque, “Optical hysteresis and instabilities inside the polariton bandgap”, J. Opt. Soc. Am. 12, 1868 (1995).
[CrossRef]

J. Phys. B: At. Mol. Opt. Phys. (1)

R. Friedberg, S. R. Hartmann, and J. T. Manassah, “Dynamical Lorentz shift revealed via nonlinear multiwave excitation”, J. Phys. B: At. Mol. Opt. Phys. 24, 3981 (1991).
[CrossRef]

Opt. Commun. (1)

J. T. Manassah and B. Gross, “Pulse reflectivitry at a dense dielectric-gas interface” Opt. Commun. 131, 408 (1996).
[CrossRef]

Phys. Rep. (1)

J.T. Manassah, “Statistical quantum electrodynamics of resonant atoms”, Phys. Rep. 101, 359 (1983).
[CrossRef]

Phys. Rep. C (1)

R. Friedberg, S. R. Hartmann, and J. T. Manassah, “Frequency shifts in emission and absorption by resonant systems of two-level atoms”, Phys. Rep. C 7, 101 (1973).
[CrossRef]

Phys. Rev. (2)

R. Friedberg, S. R. Hartmann, and J. T. Manassah, “Intensity-dependent spectral reflectivity of a dense gas-dielectric interface”, Phys. Rev. 42, 5573 (1990).
[CrossRef]

R. Friedberg, S. R. Hartmann, and J. T. Manassah, “Effects of the dynamic Lorentz shift on four-wave parametric interactions in a strongly driven two-level system”, Phys. Rev. 42, 494 (1990).
[CrossRef]

Phys. Rev. A (2)

M. G. Benedict and E. D. Trifonov, “Coherent reflection as superradiation from the boundary of a resonant medium”, Phys. Rev. A 38, 2854 (1988).
[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]

Phys. Rev. A. (1)

M. G. Benedict, V. A. Malyshev, E. D. Trifonov, and I. Zaitsev, “Reflection and transmission of ultrafast light pulses through a thin resonant medium: LFC”, Phys. Rev. A. 43, 3854 (1991).
[CrossRef]

Phys. Rev. Lett. (3)

K. J. Boller, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency”, Phys. Rev. Lett. 66, 2593 (1991).
[CrossRef] [PubMed]

J. E. Field, K. H. Hahn, and S. E. Harris, “Observation of electromagnetically induced transparency in collisionally broadened lead vapor”, Phys. Rev. Lett. 67, 3062 (1991).
[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]

Zh. Eksp. Teor. Fiz. (1)

Y. A. Vdovin and V. M. Galitskii, “Dielectric constant of a gas of resonant atoms”, Zh. Eksp. Teor. Fiz. 52, 1345 (1967). [JETP 25, 894 (1967)]

Other (2)

J. T. Manassah and B. Gross, “Superradiant amplification in an optically dense gas”, Opt. Commun. (1997) in print.
[CrossRef]

H. A. Lorentz,Theory of Electrons (Dover, New york, 2nd ed., 1952). Sections 117-124 and note 54.

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Figures (6)

Fig. 1.
Fig. 1.

The spatio-temporal dependence of the field and atomic variables are plotted for a typical value of L = (p + ¼)λ, T 1 = 30 ns , T2* = 300 ps , T 2 = 100 ps , τ = 30 ps.

Fig. 2.
Fig. 2.

The normalized field amplitude is plotted as a function of z / L , at the value of U corresponding to the location of the maximum of the transmitted field for different values of the transverse relaxation time. T 1 = 30 ns , T2* = 300 ps , τ = 30 ps, L = 5.25 λ

Fig. 3.
Fig. 3.

The normalized field amplitude is plotted as a function of z / L, at the value of U corresponding to the location of the maximum of the transmitted field for values of the sample length within the same symmetry sector.

Fig. 4.
Fig. 4.

The spatio-temporal dependence of the field and atomic variables are plotted for sample length within an asymmetrical transition region.

Fig. 5.
Fig. 5.

The time-integrated field energy flux inside the resonant medium, normalized to the initially stored energy density in the atomic system, is plotted as a function of z / L , for different values of the sample length within the asymmetrical transition region centered at L = 4.5 λ.

Fig. 6.
Fig. 6.

The difference in the values of the first moment of the transmitted and reflected fields spectral distributions, between the models including and excluding the Local Field Corrections, is plotted as a function of L / λ

Equations (15)

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i p t = [ ( ω o ω c ) n ω L + ω D i γ 2 ] p n d 2 2 h E
i n t = 1 h [ p * E p E * ] + i γ 1 ( 1 n )
χ U = [ i [ ( Ω o Ω c ) n Ω L + Δ ] + γ 2 T 2 * ] χ + inϕ 2
n U = i [ χ * ϕ χ ϕ * ] + γ 1 T 2 * ( 1 n )
ϕ = d E T 2 * h ; χ = p d ; U = t T 2 * ; Ω o , c , L = ω o , c , L T 2 * ; Δ = ω D T 2 * .
2 ϕ z ¯ 2 + ϕ + 2 i Ω c ϕ U + 2 B χ Δ = 0
g ( Δ ) = 1 2 π exp ( Δ 2 2 )
ϕ ( z ¯ , U ) = ϕ in ( z ¯ = 0 , U ) exp ( i z ¯ ) + i B 0 L ¯ exp ( i z ¯ z ¯ ' ) χ z ¯ U Δ Δ d z ¯ '
ϕ in ( z ¯ = 0 , U ) = ϕ in 0 exp ( U 2 ( τ T 2 * ) 2 )
χ ( z ̅ , U = 0 , Δ ) = 0
n ( z ̅ , U = 0 , Δ ) = 1
r = η + n r η n r
ϕ refl ( z ¯ = 0 , U ) = ϕ ( z ¯ = 0 , U ) ϕ in ( z ¯ = 0 , U ) = + i B 0 L ¯ exp ( i z ¯ ' ) χ ( z ¯ ' , U , Δ ) Δ d z ¯ '
ϕ ( L 2 z , U ) = ϕ ( L 2 + z , U ) for L = ( p 1 4 ) λ
ϕ ( L 2 z , U ) = ϕ ( L 2 + z , U ) for L = ( p + 1 4 ) λ

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