Abstract

The effects of self-phase modulation on an incoherent field are calculated. I show that the field’s coherence time is shortened, i.e., an incoherent light spectral distribution is broadened, if this field propagates in a nonlinear Kerr medium.

© 1990 Optical Society of America

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References

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  1. F. Shimizu, Phys. Rev. Lett. 19, 1097 (1967).
    [CrossRef]
  2. L. A. Ostrovskii, JETP Lett. 6, 260 (1967).
  3. R. R. Alfano, S. L. Shapiro, Phys. Rev. Lett. 24, 584 (1970). For a recent review, see R. R. Alfano, ed., The Supercontinuum Laser Source (Springer-Verlag, New York, 1989).
    [CrossRef]
  4. D. Grischkowsky, A. C. Balant, Appl. Phys. Lett. 41, 1 (1982).
    [CrossRef]
  5. T. Yajima, Y. Taira, J. Phys. Soc. Jpn. 47, 1620 (1979).
    [CrossRef]
  6. J. G. Fujimoto, E. P. Ippen, Opt. Lett. 8, 446 (1983); A. M. Weiner, E. P. Ippen, Opt. Lett. 9, 53 (1984); A. M. Weiner, S. De Dilvestri, E. P. Ippen, J. Opt. Soc. Am. B 2, 654 (1985).
    [CrossRef] [PubMed]
  7. P. C. Becker, H. L. Fragnito, J. Y. Bigot, C. H. Brito Cruz, C. V. Shank, Phys. Rev. Lett. 63, 505 (1989).
    [CrossRef] [PubMed]
  8. R. Beach, S. R. Hartmann, Phys. Rev. Lett. 53, 663 (1984).
    [CrossRef]
  9. S. Asaka, H. Nakatsuka, M. Fujiwara, M. Matsuoka, Phys. Rev. A 29, 2286 (1984).
    [CrossRef]
  10. N. Morita, T. Yajima, Phys. Rev. A 30, 2525 (1984).
    [CrossRef]
  11. F. De Martini, C. H. Townes, T. K. Gustafson, P. L. Kelley, Phys. Rev. 164, 312 (1967).
    [CrossRef]
  12. P. L. Kelley, Phys. Rev. Lett. 15, 1085 (1965).
    [CrossRef]
  13. T. K. Gustafson, J. P. Taran, H. A. Haus, J. R. Lifsits, P. L. Kelley, Phys. Rev. 177, 306 (1969).
    [CrossRef]
  14. J. H. Marburger, Prog. Quantum Electron. 4, 35 (1975).
    [CrossRef]
  15. For a recent review, see J. T. Manassah, in The Super-continuum Laser Source, R. R. Alfano, ed. (Springer-Verlag, New York, 1989), pp. 184–294.
  16. N. Wax, ed., Noise and Stochastic Processes (New York, Dover, 1954).

1989 (1)

P. C. Becker, H. L. Fragnito, J. Y. Bigot, C. H. Brito Cruz, C. V. Shank, Phys. Rev. Lett. 63, 505 (1989).
[CrossRef] [PubMed]

1984 (3)

R. Beach, S. R. Hartmann, Phys. Rev. Lett. 53, 663 (1984).
[CrossRef]

S. Asaka, H. Nakatsuka, M. Fujiwara, M. Matsuoka, Phys. Rev. A 29, 2286 (1984).
[CrossRef]

N. Morita, T. Yajima, Phys. Rev. A 30, 2525 (1984).
[CrossRef]

1983 (1)

1982 (1)

D. Grischkowsky, A. C. Balant, Appl. Phys. Lett. 41, 1 (1982).
[CrossRef]

1979 (1)

T. Yajima, Y. Taira, J. Phys. Soc. Jpn. 47, 1620 (1979).
[CrossRef]

1975 (1)

J. H. Marburger, Prog. Quantum Electron. 4, 35 (1975).
[CrossRef]

1970 (1)

R. R. Alfano, S. L. Shapiro, Phys. Rev. Lett. 24, 584 (1970). For a recent review, see R. R. Alfano, ed., The Supercontinuum Laser Source (Springer-Verlag, New York, 1989).
[CrossRef]

1969 (1)

T. K. Gustafson, J. P. Taran, H. A. Haus, J. R. Lifsits, P. L. Kelley, Phys. Rev. 177, 306 (1969).
[CrossRef]

1967 (3)

F. Shimizu, Phys. Rev. Lett. 19, 1097 (1967).
[CrossRef]

L. A. Ostrovskii, JETP Lett. 6, 260 (1967).

F. De Martini, C. H. Townes, T. K. Gustafson, P. L. Kelley, Phys. Rev. 164, 312 (1967).
[CrossRef]

1965 (1)

P. L. Kelley, Phys. Rev. Lett. 15, 1085 (1965).
[CrossRef]

Alfano, R. R.

R. R. Alfano, S. L. Shapiro, Phys. Rev. Lett. 24, 584 (1970). For a recent review, see R. R. Alfano, ed., The Supercontinuum Laser Source (Springer-Verlag, New York, 1989).
[CrossRef]

Asaka, S.

S. Asaka, H. Nakatsuka, M. Fujiwara, M. Matsuoka, Phys. Rev. A 29, 2286 (1984).
[CrossRef]

Balant, A. C.

D. Grischkowsky, A. C. Balant, Appl. Phys. Lett. 41, 1 (1982).
[CrossRef]

Beach, R.

R. Beach, S. R. Hartmann, Phys. Rev. Lett. 53, 663 (1984).
[CrossRef]

Becker, P. C.

P. C. Becker, H. L. Fragnito, J. Y. Bigot, C. H. Brito Cruz, C. V. Shank, Phys. Rev. Lett. 63, 505 (1989).
[CrossRef] [PubMed]

Bigot, J. Y.

P. C. Becker, H. L. Fragnito, J. Y. Bigot, C. H. Brito Cruz, C. V. Shank, Phys. Rev. Lett. 63, 505 (1989).
[CrossRef] [PubMed]

Brito Cruz, C. H.

P. C. Becker, H. L. Fragnito, J. Y. Bigot, C. H. Brito Cruz, C. V. Shank, Phys. Rev. Lett. 63, 505 (1989).
[CrossRef] [PubMed]

De Martini, F.

F. De Martini, C. H. Townes, T. K. Gustafson, P. L. Kelley, Phys. Rev. 164, 312 (1967).
[CrossRef]

Fragnito, H. L.

P. C. Becker, H. L. Fragnito, J. Y. Bigot, C. H. Brito Cruz, C. V. Shank, Phys. Rev. Lett. 63, 505 (1989).
[CrossRef] [PubMed]

Fujimoto, J. G.

Fujiwara, M.

S. Asaka, H. Nakatsuka, M. Fujiwara, M. Matsuoka, Phys. Rev. A 29, 2286 (1984).
[CrossRef]

Grischkowsky, D.

D. Grischkowsky, A. C. Balant, Appl. Phys. Lett. 41, 1 (1982).
[CrossRef]

Gustafson, T. K.

T. K. Gustafson, J. P. Taran, H. A. Haus, J. R. Lifsits, P. L. Kelley, Phys. Rev. 177, 306 (1969).
[CrossRef]

F. De Martini, C. H. Townes, T. K. Gustafson, P. L. Kelley, Phys. Rev. 164, 312 (1967).
[CrossRef]

Hartmann, S. R.

R. Beach, S. R. Hartmann, Phys. Rev. Lett. 53, 663 (1984).
[CrossRef]

Haus, H. A.

T. K. Gustafson, J. P. Taran, H. A. Haus, J. R. Lifsits, P. L. Kelley, Phys. Rev. 177, 306 (1969).
[CrossRef]

Ippen, E. P.

Kelley, P. L.

T. K. Gustafson, J. P. Taran, H. A. Haus, J. R. Lifsits, P. L. Kelley, Phys. Rev. 177, 306 (1969).
[CrossRef]

F. De Martini, C. H. Townes, T. K. Gustafson, P. L. Kelley, Phys. Rev. 164, 312 (1967).
[CrossRef]

P. L. Kelley, Phys. Rev. Lett. 15, 1085 (1965).
[CrossRef]

Lifsits, J. R.

T. K. Gustafson, J. P. Taran, H. A. Haus, J. R. Lifsits, P. L. Kelley, Phys. Rev. 177, 306 (1969).
[CrossRef]

Manassah, J. T.

For a recent review, see J. T. Manassah, in The Super-continuum Laser Source, R. R. Alfano, ed. (Springer-Verlag, New York, 1989), pp. 184–294.

Marburger, J. H.

J. H. Marburger, Prog. Quantum Electron. 4, 35 (1975).
[CrossRef]

Matsuoka, M.

S. Asaka, H. Nakatsuka, M. Fujiwara, M. Matsuoka, Phys. Rev. A 29, 2286 (1984).
[CrossRef]

Morita, N.

N. Morita, T. Yajima, Phys. Rev. A 30, 2525 (1984).
[CrossRef]

Nakatsuka, H.

S. Asaka, H. Nakatsuka, M. Fujiwara, M. Matsuoka, Phys. Rev. A 29, 2286 (1984).
[CrossRef]

Ostrovskii, L. A.

L. A. Ostrovskii, JETP Lett. 6, 260 (1967).

Shank, C. V.

P. C. Becker, H. L. Fragnito, J. Y. Bigot, C. H. Brito Cruz, C. V. Shank, Phys. Rev. Lett. 63, 505 (1989).
[CrossRef] [PubMed]

Shapiro, S. L.

R. R. Alfano, S. L. Shapiro, Phys. Rev. Lett. 24, 584 (1970). For a recent review, see R. R. Alfano, ed., The Supercontinuum Laser Source (Springer-Verlag, New York, 1989).
[CrossRef]

Shimizu, F.

F. Shimizu, Phys. Rev. Lett. 19, 1097 (1967).
[CrossRef]

Taira, Y.

T. Yajima, Y. Taira, J. Phys. Soc. Jpn. 47, 1620 (1979).
[CrossRef]

Taran, J. P.

T. K. Gustafson, J. P. Taran, H. A. Haus, J. R. Lifsits, P. L. Kelley, Phys. Rev. 177, 306 (1969).
[CrossRef]

Townes, C. H.

F. De Martini, C. H. Townes, T. K. Gustafson, P. L. Kelley, Phys. Rev. 164, 312 (1967).
[CrossRef]

Yajima, T.

N. Morita, T. Yajima, Phys. Rev. A 30, 2525 (1984).
[CrossRef]

T. Yajima, Y. Taira, J. Phys. Soc. Jpn. 47, 1620 (1979).
[CrossRef]

Appl. Phys. Lett. (1)

D. Grischkowsky, A. C. Balant, Appl. Phys. Lett. 41, 1 (1982).
[CrossRef]

J. Phys. Soc. Jpn. (1)

T. Yajima, Y. Taira, J. Phys. Soc. Jpn. 47, 1620 (1979).
[CrossRef]

JETP Lett. (1)

L. A. Ostrovskii, JETP Lett. 6, 260 (1967).

Opt. Lett. (1)

Phys. Rev. (2)

T. K. Gustafson, J. P. Taran, H. A. Haus, J. R. Lifsits, P. L. Kelley, Phys. Rev. 177, 306 (1969).
[CrossRef]

F. De Martini, C. H. Townes, T. K. Gustafson, P. L. Kelley, Phys. Rev. 164, 312 (1967).
[CrossRef]

Phys. Rev. A (2)

S. Asaka, H. Nakatsuka, M. Fujiwara, M. Matsuoka, Phys. Rev. A 29, 2286 (1984).
[CrossRef]

N. Morita, T. Yajima, Phys. Rev. A 30, 2525 (1984).
[CrossRef]

Phys. Rev. Lett. (5)

R. R. Alfano, S. L. Shapiro, Phys. Rev. Lett. 24, 584 (1970). For a recent review, see R. R. Alfano, ed., The Supercontinuum Laser Source (Springer-Verlag, New York, 1989).
[CrossRef]

P. C. Becker, H. L. Fragnito, J. Y. Bigot, C. H. Brito Cruz, C. V. Shank, Phys. Rev. Lett. 63, 505 (1989).
[CrossRef] [PubMed]

R. Beach, S. R. Hartmann, Phys. Rev. Lett. 53, 663 (1984).
[CrossRef]

P. L. Kelley, Phys. Rev. Lett. 15, 1085 (1965).
[CrossRef]

F. Shimizu, Phys. Rev. Lett. 19, 1097 (1967).
[CrossRef]

Prog. Quantum Electron. (1)

J. H. Marburger, Prog. Quantum Electron. 4, 35 (1975).
[CrossRef]

Other (2)

For a recent review, see J. T. Manassah, in The Super-continuum Laser Source, R. R. Alfano, ed. (Springer-Verlag, New York, 1989), pp. 184–294.

N. Wax, ed., Noise and Stochastic Processes (New York, Dover, 1954).

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Figures (2)

Fig. 1
Fig. 1

Magnitude of the outgoing field autocorrelation function K(T/Tc) as a function of normalized time for different values of the α parameter: curve a, α2 a 0.1; curve b, α2 = 1; curve c, α2 = 10. All curves associated with α2 < 0.1 are essentially indistinguishable.

Fig. 2
Fig. 2

Spectral distribution S(Ω) as a function of the normalized frequency difference for different values of the α parameter: curve a, α2 = 0.1; curve b, α2 = 1; curve c, α2 = 10.

Equations (20)

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A z + 1 ν g A t = i ω 0 n 2 c | A | 2 A ,
A ( u , z ) = A ( u , 0 ) exp [ i ω 0 n 2 c | A ( u , 0 ) | 2 z ] .
K ( T , z ) = E * ( u + T , z ) E ( u , z ) = exp (− i ω 0 T ) A * ( u + T , z ) A ( u , z ) ,
S ( Ω , z ) = 1 2 π K ( T , z ) exp ( i ω T ) d T ,
A * ( u + T , 0 ) A ( u , 0 ) = A 0 2 exp ( T 2 T c 2 ) A 0 2 f ( T ) .
L ( T , z ) = exp [− i α ψ * ( T , 0 ) ψ ( T , 0 ) + i α ψ * ( 0 , 0 ) ψ ( 0 , 0 ) ]
K ( T , z ) = A 0 2 exp (− i ω 0 T ) ψ * ( T , 0 ) ψ ( 0 , 0 ) × exp [− i α ψ * ( T , 0 ) ψ ( T , 0 ) + i α ψ * ( 0 , 0 ) ψ ( 0 , 0 ) ] ,
X ( u ) = 0 , ϕ X ( T ) = X ( u + T ) X ( u ) ,
C ( v 1 , ν 2 ,…, ν n ) = exp { i [ ν 1 ν 2 ν n ] [ X 1 X 2 X n ] }
C ( ν 1 , ν 2 ,…, ν n ) = exp { 1 2 [ ν 1 ν 2 ν n ] × [ ϕ 11 ϕ 12 ϕ 1 n ϕ 21 ϕ 21 ϕ 2 n .. ϕ n 1 ϕ n n ] [ ν 1 ν 2 ν n ] } ,
C ( ν 1 , ν 2 ) = exp [− 1 2 ( ν 1 2 + ν 2 2 ) ϕ X ( 0 ) ν 1 ν 2 ϕ X ( T ) ] .
X = α ψ * ψ α ,
ϕ X ( T ) = α 2 f 2 ;
L ( T , z ) = exp [− α 2 ( 1 f 2 ) ] .
X = α ψ * ψ + λ ( ψ * + ψ ) α ,
ϕ X = α 2 f 2 + 2 λ 2 f ;
Q ( ν 1 , ν 2 , λ ; T , z ) = exp { i [ ν 1 X ( T ) + ν 2 X ( 0 ) ] } ,
K ( T , z ) = A 0 2 exp ( i ω 0 T ) × lim λ 0 lim ν 1 1 lim ν 2 1 { 1 4 ν 1 ν 2 [ 2 Q λ 2 + 2 ν 1 2 i α Q ν 1 + 2 ν 2 2 i α Q ν 2 + ( 2 ν 1 2 + 2 ν 2 2 ) Q ] } = A 0 2 exp (− i ω 0 T ) f exp [− α 2 ( 1 f 2 ) ] .
K ( T , z ) A 0 2 exp (− i ω 0 T ) exp [ T 2 ( 1 + 2 α 2 ) T c 2 ] ,
S ( Ω , z ) d Ω = K ( 0 , z ) = A 0 2 .

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