Abstract

We present the results of a series of numerical experiments on the propagation of pairs of coupled short optical pulses in media with in-homogeneous broadening. The main results apply to propagation in three-level media in the V configuration.

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References

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  1. A. Rahman and J. H. Eberly, "Theory of shape-preserving short pulses in inhomogeneously broadened three-level media," Phys. Rev. A 58, R805 (1998).
    [CrossRef]
  2. A. Rahman, "Optical pulse propagation in V-type media," submitted for publication.
  3. L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover Publications, Inc., New York, 1987).
  4. S. L. McCall and E. L. Hahn, "Self-induced transparency," Phys. Rev. 183, 457 (1969).
    [CrossRef]
  5. For a recent new derivation of the Area Theorem in two-level media, see J. H. Eberly, "Area Theorem rederived," Opt. Express 2, 173 (1998); http://epubs.osa.org/oearchive/source/4295.htm
    [CrossRef] [PubMed]
  6. G. L. Lamb, Jr., "Analytical descriptions of ultrashort optical pulse propagation in a resonant medium," Rev. Mod. Phys. 43, 99 (1971).
    [CrossRef]
  7. G. L. Lamb, Jr., "Coherent-optical-pulse propagation as an inverse problem," Phys. Rev. A 9, 422 (1974).
    [CrossRef]
  8. R. J. Cook and B. W. Shore, "Coherent dynamics of N-level atoms and molecules. III. An analytically soluble periodic case," Phys. Rev. A 20, 539 (1979).
    [CrossRef]
  9. C. E. Carroll and F. T. Hioe, "Analytic solutions for three-state systems with overlapping pulses," Phys. Rev. A 42, 1522 (1990).
    [CrossRef] [PubMed]
  10. M. J. Konopnicki and J. H. Eberly, "Simultaneous propagation of short different-wavelength optical pulses," Phys. Rev. A 24, 2567 (1981).
    [CrossRef]

Other (10)

A. Rahman and J. H. Eberly, "Theory of shape-preserving short pulses in inhomogeneously broadened three-level media," Phys. Rev. A 58, R805 (1998).
[CrossRef]

A. Rahman, "Optical pulse propagation in V-type media," submitted for publication.

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

S. L. McCall and E. L. Hahn, "Self-induced transparency," Phys. Rev. 183, 457 (1969).
[CrossRef]

For a recent new derivation of the Area Theorem in two-level media, see J. H. Eberly, "Area Theorem rederived," Opt. Express 2, 173 (1998); http://epubs.osa.org/oearchive/source/4295.htm
[CrossRef] [PubMed]

G. L. Lamb, Jr., "Analytical descriptions of ultrashort optical pulse propagation in a resonant medium," Rev. Mod. Phys. 43, 99 (1971).
[CrossRef]

G. L. Lamb, Jr., "Coherent-optical-pulse propagation as an inverse problem," Phys. Rev. A 9, 422 (1974).
[CrossRef]

R. J. Cook and B. W. Shore, "Coherent dynamics of N-level atoms and molecules. III. An analytically soluble periodic case," Phys. Rev. A 20, 539 (1979).
[CrossRef]

C. E. Carroll and F. T. Hioe, "Analytic solutions for three-state systems with overlapping pulses," Phys. Rev. A 42, 1522 (1990).
[CrossRef] [PubMed]

M. J. Konopnicki and J. H. Eberly, "Simultaneous propagation of short different-wavelength optical pulses," Phys. Rev. A 24, 2567 (1981).
[CrossRef]

Supplementary Material (5)

» Media 1: MOV (312 KB)     
» Media 2: MOV (398 KB)     
» Media 3: MOV (400 KB)     
» Media 4: MOV (522 KB)     
» Media 5: MOV (461 KB)     

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Figures (6)

Figure 1.
Figure 1.

Schematic diagram of a V-type three-level atom and a two-level atom. The pulses Ω a and Ω b (driving transitions 1–2 and 2–3 respectively) are in two-photon resonance with intermediate detuning Δ in the V-type medium. The pulse Ω drives the 1–2 transition in the two-level medium.

Figure 2.
Figure 2.

(312KB) Snapshot of a frame of a movie showing the changing shape of an initially nearly square pulse as it propagates in a two-level medium. The pulse shape (≡ ΩT2*) is plotted as a function of time T (≡ τ/T2*) and space Z (≡ μζT2*)-The inset shows the pulse area as a function of space Z.

Figure 3.
Figure 3.

(398KB) Snapshot of a frame of a movie showing changing pulse shape during propagation in a V-type medium. The pulse shapes (≡ Ω a T2*, Ω b T2*) are plotted as a function of time T (≡ τ/T2*) and space Z (≡ μζT2*). The inset shows the pulse areas as a function of space Z.

Figure 4.
Figure 4.

(400KB) Snapshot of a frame of a movie showing changing pulse shape during propagation in a V-type medium. The pulse shapes (≡ Ω a T2*, Ω b T2*) are plotted as a function of time T (≡ τ/T2*) and space Z (≡ μζT2*). The inset shows the pulse areas as a function of space Z.

Figure 5.
Figure 5.

(522KB) Snapshot of a frame of a movie showing changing pulse shape during propagation in a V-type medium. The pulse shapes (≡ Ω a T2*, Ω b T2*) are plotted as a function of time T (≡ τ/T2*) and space Z (≡ μζT2*). The inset shows the pulse areas as a function of space Z.

Figure 6.
Figure 6.

(462KB) Snapshot of a frame of a movie showing changing pulse shape during a pulse collision in a V-type medium. The pulse shapes (≡ Ω a T2*, Ω b T2*) are plotted as a function of time T (≡ τ/T2*) and space Z (≡ μζT2*). The inset shows the pulse areas as a function of space Z.

Equations (17)

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E = x ̂ ε a ( z , t ) e i ( k a z ω a t ) + x ̂ ε b ( z , t ) e i ( k b z ω b t ) + c . c . ,
i τ C 1 = Δ C 1 1 2 Ω a C 2
i τ C 2 = 1 2 Ω a * C 1 1 2 Ω b * C 3
i τ C 3 = Δ C 3 1 2 Ω b C 2
ζ Ω a = C 2 * C 1 g ( Δ ) d Δ
ζ Ω b = C 2 * C 3 g ( Δ ) d Δ
C 1 ( ζ , 0 ) = 0 , C 2 ( ζ , 0 ) = 1 , C 3 ( ζ , 0 ) = 0 .
θ ( ζ ) = Ω ( ζ , τ ) .
ζ θ ( ζ ) = α 2 sin θ ( ζ ) ,
Ω ( ζ , τ ) 2 τ p sech ( τ τ p ) ,
Ω b ( 0 , τ ) = r Ω a ( 0 , τ ) ,
Ω b ( ζ , τ ) = r Ω a ( ζ , τ )
C 3 ( ζ , τ ) = r C 1 ( ζ , τ ) .
ζ θ a 2 + θ b 2 = α 2 sin θ a 2 + θ b 2 ,
Ω a ( ζ , τ ) 2 τ p 1 + r 2 sech ( τ τ p )
Ω b ( ζ , τ ) 2 r τ p 1 + r 2 sech ( τ τ p ) .
A 2 + B 2 = 4 τ p 2

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