Abstract

We obtain the shape, phase, and spectral distribution of an ultrafast pulse propagating in a χ(5) medium (six-photon mixing). The calculation is performed in the plane-wave approximation for a dispersionless medium but with self-steepening present.

© 1988 Optical Society of America

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References

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  1. R. R. Alfano, S. L. Shapiro, Phys. Rev. Lett. 24, 592 (1970)
    [CrossRef]
  2. A. H. Nayfeh, Introduction to Perturbation Techniques (Wiley, New York, 1981).
  3. J. T. Manassah, M. A. Mustafa, R. R. Alfano, P. P. Ho, IEEE J. Quantum Electron. QE-22, 197 (1986).
    [CrossRef]
  4. F. De Martini, C. H. Townes, T. K. Gustafsson, P. L. Kelley, Phys. Rev. 164, 312 (1967); D. Anderson, M. Lisak, Phys. Rev. A 27, 1393 (1983).
    [CrossRef]
  5. A. Borshch, M. Brodin, V. Volkov, N. Kukhtarev, V. Starkov, J. Opt. Soc. Am. A 1, 40 (1984).
    [CrossRef]
  6. J. T. Manassah, M. A. Mustafa, “Phase, spectral shape, and frequency shift of a self-phase-modulated pulse,” Phys. Lett. (to be published).
  7. J. T. Manassah, M. A. Mustafa, Opt. Lett. 13, 752 (1988).
    [CrossRef] [PubMed]

1988 (1)

1986 (1)

J. T. Manassah, M. A. Mustafa, R. R. Alfano, P. P. Ho, IEEE J. Quantum Electron. QE-22, 197 (1986).
[CrossRef]

1984 (1)

1970 (1)

R. R. Alfano, S. L. Shapiro, Phys. Rev. Lett. 24, 592 (1970)
[CrossRef]

1967 (1)

F. De Martini, C. H. Townes, T. K. Gustafsson, P. L. Kelley, Phys. Rev. 164, 312 (1967); D. Anderson, M. Lisak, Phys. Rev. A 27, 1393 (1983).
[CrossRef]

Alfano, R. R.

J. T. Manassah, M. A. Mustafa, R. R. Alfano, P. P. Ho, IEEE J. Quantum Electron. QE-22, 197 (1986).
[CrossRef]

R. R. Alfano, S. L. Shapiro, Phys. Rev. Lett. 24, 592 (1970)
[CrossRef]

Borshch, A.

Brodin, M.

De Martini, F.

F. De Martini, C. H. Townes, T. K. Gustafsson, P. L. Kelley, Phys. Rev. 164, 312 (1967); D. Anderson, M. Lisak, Phys. Rev. A 27, 1393 (1983).
[CrossRef]

Gustafsson, T. K.

F. De Martini, C. H. Townes, T. K. Gustafsson, P. L. Kelley, Phys. Rev. 164, 312 (1967); D. Anderson, M. Lisak, Phys. Rev. A 27, 1393 (1983).
[CrossRef]

Ho, P. P.

J. T. Manassah, M. A. Mustafa, R. R. Alfano, P. P. Ho, IEEE J. Quantum Electron. QE-22, 197 (1986).
[CrossRef]

Kelley, P. L.

F. De Martini, C. H. Townes, T. K. Gustafsson, P. L. Kelley, Phys. Rev. 164, 312 (1967); D. Anderson, M. Lisak, Phys. Rev. A 27, 1393 (1983).
[CrossRef]

Kukhtarev, N.

Manassah, J. T.

J. T. Manassah, M. A. Mustafa, Opt. Lett. 13, 752 (1988).
[CrossRef] [PubMed]

J. T. Manassah, M. A. Mustafa, R. R. Alfano, P. P. Ho, IEEE J. Quantum Electron. QE-22, 197 (1986).
[CrossRef]

J. T. Manassah, M. A. Mustafa, “Phase, spectral shape, and frequency shift of a self-phase-modulated pulse,” Phys. Lett. (to be published).

Mustafa, M. A.

J. T. Manassah, M. A. Mustafa, Opt. Lett. 13, 752 (1988).
[CrossRef] [PubMed]

J. T. Manassah, M. A. Mustafa, R. R. Alfano, P. P. Ho, IEEE J. Quantum Electron. QE-22, 197 (1986).
[CrossRef]

J. T. Manassah, M. A. Mustafa, “Phase, spectral shape, and frequency shift of a self-phase-modulated pulse,” Phys. Lett. (to be published).

Nayfeh, A. H.

A. H. Nayfeh, Introduction to Perturbation Techniques (Wiley, New York, 1981).

Shapiro, S. L.

R. R. Alfano, S. L. Shapiro, Phys. Rev. Lett. 24, 592 (1970)
[CrossRef]

Starkov, V.

Townes, C. H.

F. De Martini, C. H. Townes, T. K. Gustafsson, P. L. Kelley, Phys. Rev. 164, 312 (1967); D. Anderson, M. Lisak, Phys. Rev. A 27, 1393 (1983).
[CrossRef]

Volkov, V.

IEEE J. Quantum Electron. (1)

J. T. Manassah, M. A. Mustafa, R. R. Alfano, P. P. Ho, IEEE J. Quantum Electron. QE-22, 197 (1986).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Lett. (1)

Phys. Rev. (1)

F. De Martini, C. H. Townes, T. K. Gustafsson, P. L. Kelley, Phys. Rev. 164, 312 (1967); D. Anderson, M. Lisak, Phys. Rev. A 27, 1393 (1983).
[CrossRef]

Phys. Rev. Lett. (1)

R. R. Alfano, S. L. Shapiro, Phys. Rev. Lett. 24, 592 (1970)
[CrossRef]

Other (2)

A. H. Nayfeh, Introduction to Perturbation Techniques (Wiley, New York, 1981).

J. T. Manassah, M. A. Mustafa, “Phase, spectral shape, and frequency shift of a self-phase-modulated pulse,” Phys. Lett. (to be published).

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Figures (6)

Fig. 1
Fig. 1

Amplitude of the electric field as a function of U. Curve a, V = 0.05; curve b, V = 0.20; curve c, V = 0.34.

Fig. 2
Fig. 2

Slope of the amplitude as a function of U. Curve a, V = 0.05; curve b, V = 0.2; curve c, V = 0.34.

Fig. 3
Fig. 3

Normalized phase of the electric field as a function of U. Curve a, V = 0.05; curve b, V = 0.2; curve c, V = 0.34.

Fig. 4
Fig. 4

Normalized slope of the phase as a function of U. Curve a, V = 0.05; curve b, V = 0.2; curve c, V = 0.34.

Fig. 5
Fig. 5

Values of the maximum (curve a) and minimum (curve b) of the frequency sweep as a function of ′V.

Fig. 6
Fig. 6

Spectral distribution of a pulse (K = ωτ = 300) for different V. The right-hand side of the spectrum corresponds to the Stokes region. (a) (V = 0.05; (b) V = 0.34.

Equations (19)

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2 E - n 0 2 c 2 2 t 2 E = 4 n 0 n 4 c 2 2 t 2 E · E 2 E ,
T = t / τ ,             Z = z / v g τ ,             E = E 0 Φ ,
= n 4 E 0 4 / n 0 ,
( 2 Z 2 - 2 T 2 ) Φ = 2 T 2 Φ 4 Φ .
Φ = a exp [ i ( α + K U ) ] ,
a V - 5 2 a 4 a U = 0 ,
α V - 2 a 4 α U = K 2 a 4 - K 2 8 a 8 ,
a ( U , 0 ) = sech ( U ) ,
α ( U , 0 ) = 0.
a 2 = sec 2 ( U + 5 2 V a 4 ) ,
V crit = 5 5 32 0.349.
a U = - a ( 1 - a 2 ) 1 / 2 10 V a 4 ( 1 - a 2 ) 1 / 2 ± 1 ,
α ¯ α K = - U - 6 - 0 U a 4 ( p , V ) d p - 5 24 2 0 V a 8 ( 0 , q ) d q + tanh - 1 [ sin g ( U , V ) ] + 6 sin g ( U , V ) - 18 sin 3 g ( U , V ) ,
g ( U , V ) = 2 0 V a 5 ( U , q ) d q + sin - 1 ( tanh U ) .
α ¯ U = 1 - 6 a 4 + a cos g + 6 a ( cos g ) + 6 a ( sin 2 g ) ( cos g ) .
U α - 3 V 2 ,             α M K V 2 .
W - W anti - Stokes max ( α U ) , W - W Stokes min ( α U ) ,
a = min ( α ¯ U ) + 1 ,             b = max ( α ¯ U ) + 1.
N α M π K V 2 π .

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