Abstract

The effect of intensity fluctuations and the finite coherence time of the field on the propagation of nonlinear optical pulses is discussed. In particular, the statistical properties of the carrier are shown to affect the power level for soliton propagation.

© 1980 Optical Society of America

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References

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  1. A. Hasegawa, F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973);“Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. II. Normal dispersion,” Appl. Phys. Lett. 23, 171–173 (1973).
    [CrossRef]
  2. M. Jain, N. Tzoar, “Propagation of nonlinear optical pulses in inhomogeneous media,” J. Appl. Phys. 49, 4649–4654 (1978).
    [CrossRef]
  3. M. Jain, N. Tzoar, “Nonlinear pulse propagation in optical fibers,” Opt. Lett. 3, 202–204 (1978).
    [CrossRef] [PubMed]
  4. B. Bendow, P. D. Gianino, “Theory of nonlinear pulse propagation in inhomogeneous waveguides,” Opt. Lett. 4, 164–166 (1979).
    [CrossRef] [PubMed]
  5. M. Bertolotti, B. Crosignani, P. Di Porto, “On the statistics of Gaussian light scattered by a Gaussian medium,” J. Phys. A: Gen. Phys. 3, L37–L38 (1970).
    [CrossRef]
  6. Y. R. Shen, “Quantum theory of nonlinear optics,” in Proceedings of the International School of Physics “Enrico Fermi,”Course XLII, R. J. Glauber, ed. (Academic, New York, 1969), pp. 473–492.

1979 (1)

1978 (2)

M. Jain, N. Tzoar, “Propagation of nonlinear optical pulses in inhomogeneous media,” J. Appl. Phys. 49, 4649–4654 (1978).
[CrossRef]

M. Jain, N. Tzoar, “Nonlinear pulse propagation in optical fibers,” Opt. Lett. 3, 202–204 (1978).
[CrossRef] [PubMed]

1973 (1)

A. Hasegawa, F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973);“Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. II. Normal dispersion,” Appl. Phys. Lett. 23, 171–173 (1973).
[CrossRef]

1970 (1)

M. Bertolotti, B. Crosignani, P. Di Porto, “On the statistics of Gaussian light scattered by a Gaussian medium,” J. Phys. A: Gen. Phys. 3, L37–L38 (1970).
[CrossRef]

Bendow, B.

Bertolotti, M.

M. Bertolotti, B. Crosignani, P. Di Porto, “On the statistics of Gaussian light scattered by a Gaussian medium,” J. Phys. A: Gen. Phys. 3, L37–L38 (1970).
[CrossRef]

Crosignani, B.

M. Bertolotti, B. Crosignani, P. Di Porto, “On the statistics of Gaussian light scattered by a Gaussian medium,” J. Phys. A: Gen. Phys. 3, L37–L38 (1970).
[CrossRef]

Di Porto, P.

M. Bertolotti, B. Crosignani, P. Di Porto, “On the statistics of Gaussian light scattered by a Gaussian medium,” J. Phys. A: Gen. Phys. 3, L37–L38 (1970).
[CrossRef]

Gianino, P. D.

Hasegawa, A.

A. Hasegawa, F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973);“Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. II. Normal dispersion,” Appl. Phys. Lett. 23, 171–173 (1973).
[CrossRef]

Jain, M.

M. Jain, N. Tzoar, “Propagation of nonlinear optical pulses in inhomogeneous media,” J. Appl. Phys. 49, 4649–4654 (1978).
[CrossRef]

M. Jain, N. Tzoar, “Nonlinear pulse propagation in optical fibers,” Opt. Lett. 3, 202–204 (1978).
[CrossRef] [PubMed]

Shen, Y. R.

Y. R. Shen, “Quantum theory of nonlinear optics,” in Proceedings of the International School of Physics “Enrico Fermi,”Course XLII, R. J. Glauber, ed. (Academic, New York, 1969), pp. 473–492.

Tappert, F.

A. Hasegawa, F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973);“Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. II. Normal dispersion,” Appl. Phys. Lett. 23, 171–173 (1973).
[CrossRef]

Tzoar, N.

M. Jain, N. Tzoar, “Propagation of nonlinear optical pulses in inhomogeneous media,” J. Appl. Phys. 49, 4649–4654 (1978).
[CrossRef]

M. Jain, N. Tzoar, “Nonlinear pulse propagation in optical fibers,” Opt. Lett. 3, 202–204 (1978).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

A. Hasegawa, F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973);“Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. II. Normal dispersion,” Appl. Phys. Lett. 23, 171–173 (1973).
[CrossRef]

J. Appl. Phys. (1)

M. Jain, N. Tzoar, “Propagation of nonlinear optical pulses in inhomogeneous media,” J. Appl. Phys. 49, 4649–4654 (1978).
[CrossRef]

J. Phys. A: Gen. Phys. (1)

M. Bertolotti, B. Crosignani, P. Di Porto, “On the statistics of Gaussian light scattered by a Gaussian medium,” J. Phys. A: Gen. Phys. 3, L37–L38 (1970).
[CrossRef]

Opt. Lett. (2)

Other (1)

Y. R. Shen, “Quantum theory of nonlinear optics,” in Proceedings of the International School of Physics “Enrico Fermi,”Course XLII, R. J. Glauber, ed. (Academic, New York, 1969), pp. 473–492.

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Equations (15)

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E ( r , z , t ) = ê U ( r ) Φ ( z , t ) e iqz i ω 0 t ,
Φ ( z , t ) = F ( z , t ) S ( z , t ) ,
| Φ ( z , t ) | 2 = | F ( z , t ) | 2 S 2 ( z , t ) ,
[ p 1 2 q 2 + 2 / z 2 + 2 i q / z + 2 i k 0 k 0 / t ( k 0 2 + k 0 k 0 ) 2 / t 2 + 2 α ( n 2 / n 0 ) k 0 2 | Φ | 2 ] Φ ( z , t ) = 0 ,
( Φ * 2 Φ / z 2 Φ 2 Φ * / z 2 ) + 2 i q ( Φ * Φ / z + Φ Φ * / z ) + 2 i k 0 k 0 ( Φ * Φ / t + Φ Φ * / t ) + ( k 0 2 + k 0 k 0 ) ( Φ 2 Φ * / t 2 Φ * 2 Φ / t 2 ) = 0
2 ( p 1 2 q 2 ) | Φ | 2 + Φ * 2 Φ / z 2 + Φ 2 Φ * / z 2 + 2 i q ( Φ * Φ / z Φ Φ * / z ) + 2 i k 0 k 0 ( Φ * Φ / t Φ Φ * / t ) ( k 0 2 + k 0 k 0 ) ( Φ * 2 Φ / t 2 + Φ 2 Φ * / t 2 ) + 4 α ( n 2 / n 0 ) k 0 2 | Φ | 4 = 0 .
q S / z + k 0 k 0 S / t = 0 ,
υ g = q / ( k 0 k 0 )
[ p 1 2 q 2 + 1 / z c 2 ( k 0 2 + k 0 k 0 ) / t c 2 ] S + 2 S / z 2 ( k 0 2 + k 0 k 0 ) 2 S / t 2 + 2 α ( n 2 / n 0 ) k 0 2 η A 2 S 3 = 0 .
F = A e i γ ,
1 / z c 2 = A 2 A / z 2 / A 2 ( γ / z ) 2 ,
1 / t c 2 = A 2 A / t 2 / A 2 ( γ / t ) 2 ,
η = A 4 / A 2 2 .
q 2 = p 1 2 + α ( n 2 / n 0 ) η k 0 2 A 2 S 0 2 ( 1 + τ 2 / t c 2 ) + 1 / z c 2 1 / ( t c 2 υ g 2 )
A 2 S 0 2 = [ 1 / υ g 2 ( k 0 2 + k 0 k 0 ) ] / [ α ( n 2 / n 0 ) η k 0 2 τ 2 ] .

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