Abstract

Random optical-pulse polarization switching along an active optical medium in the Λ configuration with spatially disordered occupation numbers of its lower energy sublevel pair is described using the idealized integrable Maxwell–Bloch model. Analytical results describing the light polarization-switching statistics for the single self-induced transparency pulse are compared with statistics obtained from direct Monte Carlo numerical simulations.

© 2013 Optical Society of America

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References

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  1. S. E. Harris, Phys. Rev. Lett. 62, 1033 (1989).
    [CrossRef]
  2. L. N. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, Nature 397, 594 (1999).
    [CrossRef]
  3. A. M. Basharov, S. O. Elyutin, A. I. Maimistov, and Y. M. Sklyarov, Phys Rep. 191, 1 (1990).
    [CrossRef]
  4. A. I. Maimistov, Sov. J. Quantum Electron. 14, 385 (1984).
    [CrossRef]
  5. A. I. Maimistov and Y. M. Sklyarov, Opt. Spectrosc. 59, 459 (1985).
  6. J. A. Byrne, I. R. Gabitov, and G. Kovačič, Phys. D 186, 69 (2003).
    [CrossRef]
  7. E. P. Atkins, P. R. Kramer, G. Kovačič, and I. R. Gabitov, Phys. Rev. A 85, 043834 (2012).
    [CrossRef]
  8. M. J. Konopnicki and J. H. Eberly, Phys. Rev. A 24, 2567 (1981).
    [CrossRef]
  9. L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover, 1987).
  10. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).

2012 (1)

E. P. Atkins, P. R. Kramer, G. Kovačič, and I. R. Gabitov, Phys. Rev. A 85, 043834 (2012).
[CrossRef]

2003 (1)

J. A. Byrne, I. R. Gabitov, and G. Kovačič, Phys. D 186, 69 (2003).
[CrossRef]

1999 (1)

L. N. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, Nature 397, 594 (1999).
[CrossRef]

1990 (1)

A. M. Basharov, S. O. Elyutin, A. I. Maimistov, and Y. M. Sklyarov, Phys Rep. 191, 1 (1990).
[CrossRef]

1989 (1)

S. E. Harris, Phys. Rev. Lett. 62, 1033 (1989).
[CrossRef]

1985 (1)

A. I. Maimistov and Y. M. Sklyarov, Opt. Spectrosc. 59, 459 (1985).

1984 (1)

A. I. Maimistov, Sov. J. Quantum Electron. 14, 385 (1984).
[CrossRef]

1981 (1)

M. J. Konopnicki and J. H. Eberly, Phys. Rev. A 24, 2567 (1981).
[CrossRef]

Allen, L.

L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover, 1987).

Atkins, E. P.

E. P. Atkins, P. R. Kramer, G. Kovačič, and I. R. Gabitov, Phys. Rev. A 85, 043834 (2012).
[CrossRef]

Basharov, A. M.

A. M. Basharov, S. O. Elyutin, A. I. Maimistov, and Y. M. Sklyarov, Phys Rep. 191, 1 (1990).
[CrossRef]

Behroozi, C. H.

L. N. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, Nature 397, 594 (1999).
[CrossRef]

Byrne, J. A.

J. A. Byrne, I. R. Gabitov, and G. Kovačič, Phys. D 186, 69 (2003).
[CrossRef]

Dutton, Z.

L. N. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, Nature 397, 594 (1999).
[CrossRef]

Eberly, J. H.

M. J. Konopnicki and J. H. Eberly, Phys. Rev. A 24, 2567 (1981).
[CrossRef]

L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover, 1987).

Elyutin, S. O.

A. M. Basharov, S. O. Elyutin, A. I. Maimistov, and Y. M. Sklyarov, Phys Rep. 191, 1 (1990).
[CrossRef]

Gabitov, I. R.

E. P. Atkins, P. R. Kramer, G. Kovačič, and I. R. Gabitov, Phys. Rev. A 85, 043834 (2012).
[CrossRef]

J. A. Byrne, I. R. Gabitov, and G. Kovačič, Phys. D 186, 69 (2003).
[CrossRef]

Harris, S. E.

L. N. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, Nature 397, 594 (1999).
[CrossRef]

S. E. Harris, Phys. Rev. Lett. 62, 1033 (1989).
[CrossRef]

Hau, L. N.

L. N. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, Nature 397, 594 (1999).
[CrossRef]

Konopnicki, M. J.

M. J. Konopnicki and J. H. Eberly, Phys. Rev. A 24, 2567 (1981).
[CrossRef]

Kovacic, G.

E. P. Atkins, P. R. Kramer, G. Kovačič, and I. R. Gabitov, Phys. Rev. A 85, 043834 (2012).
[CrossRef]

J. A. Byrne, I. R. Gabitov, and G. Kovačič, Phys. D 186, 69 (2003).
[CrossRef]

Kramer, P. R.

E. P. Atkins, P. R. Kramer, G. Kovačič, and I. R. Gabitov, Phys. Rev. A 85, 043834 (2012).
[CrossRef]

Maimistov, A. I.

A. M. Basharov, S. O. Elyutin, A. I. Maimistov, and Y. M. Sklyarov, Phys Rep. 191, 1 (1990).
[CrossRef]

A. I. Maimistov and Y. M. Sklyarov, Opt. Spectrosc. 59, 459 (1985).

A. I. Maimistov, Sov. J. Quantum Electron. 14, 385 (1984).
[CrossRef]

Sklyarov, Y. M.

A. M. Basharov, S. O. Elyutin, A. I. Maimistov, and Y. M. Sklyarov, Phys Rep. 191, 1 (1990).
[CrossRef]

A. I. Maimistov and Y. M. Sklyarov, Opt. Spectrosc. 59, 459 (1985).

Wolf, E.

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).

Nature (1)

L. N. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, Nature 397, 594 (1999).
[CrossRef]

Opt. Spectrosc. (1)

A. I. Maimistov and Y. M. Sklyarov, Opt. Spectrosc. 59, 459 (1985).

Phys Rep. (1)

A. M. Basharov, S. O. Elyutin, A. I. Maimistov, and Y. M. Sklyarov, Phys Rep. 191, 1 (1990).
[CrossRef]

Phys. D (1)

J. A. Byrne, I. R. Gabitov, and G. Kovačič, Phys. D 186, 69 (2003).
[CrossRef]

Phys. Rev. A (2)

E. P. Atkins, P. R. Kramer, G. Kovačič, and I. R. Gabitov, Phys. Rev. A 85, 043834 (2012).
[CrossRef]

M. J. Konopnicki and J. H. Eberly, Phys. Rev. A 24, 2567 (1981).
[CrossRef]

Phys. Rev. Lett. (1)

S. E. Harris, Phys. Rev. Lett. 62, 1033 (1989).
[CrossRef]

Sov. J. Quantum Electron. (1)

A. I. Maimistov, Sov. J. Quantum Electron. 14, 385 (1984).
[CrossRef]

Other (2)

L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover, 1987).

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).

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Figures (3)

Fig. 1.
Fig. 1.

PDF pψ(x;s), with β=1/3, γ=1/3, ε=0, and d+=d=i; theoretical (black lines) and results from 1600 simulations (gray lines, green online). Left: b=0 and a=0.75. Right: b=0.75 and a=0.5.

Fig. 2.
Fig. 2.

PDF pη(x;s), with β=1/3, γ=1/3, ε=0, and d+=d=i; theoretical (black lines) and results from 1600 simulations (gray lines, green online). Left: b=0 and a=0.75. Right: b=0.75 and a=0.5.

Fig. 3.
Fig. 3.

Comparison of exit time statistics between analytical formulas and results from numerical simulations when (left) no bias, b=0, a=0.75, and (right) b=0.75, a=0.5. For both, β=1/3, γ=1/3, ε=0, and d+=d=i.

Equations (15)

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tE±+xE±=ρ±g(ν)dν,
tρ+2iλρ+=[E+(Nn+)Eμ*]/2,
tρ2iλρ=[E(Nn)E+μ]/2,
tμ=[E+*ρ+Eρ+*]/2,
tN=[E+ρ+*+E+*ρ++Eρ*+E*ρ]/2,
tn±=[E±ρ±*+E±*ρ±]/2.
E±(x,t)=4iβG±(x)eiΘ±(x,t)sech[2β(tx)+τx+12ln|d+||d|2β2+12lncosh(2τA(x)+ln|d+||d|)],
A(x)=0xα(ξ)dξ
limtn±(x,t,λ)=[1±α(x)]/20.
σ+iτ=g(ν)8(γ+iβν)dν,
α(x)=b,[α(x)b][α(x)b]=a2δ(xx),
pXtra(x)=2L/πx3n=(4n+1)e(4n+1)2L/2x,
pXint(x)=2L/πx3[n=0(4n+2)e(4n+2)2L/2xn=14ne16n2L/2x],
pX(x)=(|b|/a2πx3)exp[b2(x)2/2a2x],
pXfluc(x)=(|b|/a2πx)exp(b2x/2a2).

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