Abstract

An investigation is made of the combined effects of nonlinearity and diffraction on self-phase modulation of optical pulses propagating in dispersionless homogeneous bulk material. It is found that the presence of transverse spatial dynamics leaves the phase characteristics qualitatively the same as for conventional self-phase modulation. In particular, this implies that, contrary to what has recently been claimed, the red always leads the blue in the supercontinuum.

© 1991 Optical Society of America

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References

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  1. J. H. Marburger, Prog. Quantum Electron. 4, 35 (1975).
    [Crossref]
  2. V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).
  3. L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
    [Crossref]
  4. P. L. Kelley, Phys. Rev. Lett. 15, 1005 (1965).
    [Crossref]
  5. Yu. K. Danileiko, L. M. Degtyarerv, A. L. Kopa-Ovdienko, T. P. Lebedeva, Sov. Phys. JETP 60, 417 (1984).
  6. J. T. Manassah, P. L. Baldeck, R. R. Alfano, Opt. Lett. 13, 1090 (1988).
    [Crossref] [PubMed]
  7. Y. Silberberg, Opt. Lett. 15, 1282 (1990).
    [Crossref] [PubMed]
  8. K. Okamoto, E. A. J. Marcatili, IEEE J. Lightwave Technol. 7, 1988 (1989).
    [Crossref]
  9. R. A. Sammut, C. Pask, Opt. Lett. 16, 70 (1991).
    [Crossref] [PubMed]
  10. J. T. Manassah, P. L. Baldeck, R. R. Alfano, Opt. Lett. 13, 589 (1988).
    [Crossref] [PubMed]
  11. D. Anderson, M. Bonnedal, M. Lisak, Phys. Fluids 22, 1838 (1979).
    [Crossref]
  12. M. Desaix, D. Anderson, M. Lisak, “Variational approach to collapse of optical pulses,” submitted to J. Opt. Soc. Am. B.
  13. D. Anderson, Phys. Rev. A 27, 3135 (1983).
    [Crossref]

1991 (1)

1990 (1)

1989 (1)

K. Okamoto, E. A. J. Marcatili, IEEE J. Lightwave Technol. 7, 1988 (1989).
[Crossref]

1988 (2)

1984 (1)

Yu. K. Danileiko, L. M. Degtyarerv, A. L. Kopa-Ovdienko, T. P. Lebedeva, Sov. Phys. JETP 60, 417 (1984).

1983 (1)

D. Anderson, Phys. Rev. A 27, 3135 (1983).
[Crossref]

1980 (1)

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[Crossref]

1979 (1)

D. Anderson, M. Bonnedal, M. Lisak, Phys. Fluids 22, 1838 (1979).
[Crossref]

1975 (1)

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

1972 (1)

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

1965 (1)

P. L. Kelley, Phys. Rev. Lett. 15, 1005 (1965).
[Crossref]

Alfano, R. R.

Anderson, D.

D. Anderson, Phys. Rev. A 27, 3135 (1983).
[Crossref]

D. Anderson, M. Bonnedal, M. Lisak, Phys. Fluids 22, 1838 (1979).
[Crossref]

M. Desaix, D. Anderson, M. Lisak, “Variational approach to collapse of optical pulses,” submitted to J. Opt. Soc. Am. B.

Baldeck, P. L.

Bonnedal, M.

D. Anderson, M. Bonnedal, M. Lisak, Phys. Fluids 22, 1838 (1979).
[Crossref]

Danileiko, Yu. K.

Yu. K. Danileiko, L. M. Degtyarerv, A. L. Kopa-Ovdienko, T. P. Lebedeva, Sov. Phys. JETP 60, 417 (1984).

Degtyarerv, L. M.

Yu. K. Danileiko, L. M. Degtyarerv, A. L. Kopa-Ovdienko, T. P. Lebedeva, Sov. Phys. JETP 60, 417 (1984).

Desaix, M.

M. Desaix, D. Anderson, M. Lisak, “Variational approach to collapse of optical pulses,” submitted to J. Opt. Soc. Am. B.

Gordon, J. P.

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[Crossref]

Kelley, P. L.

P. L. Kelley, Phys. Rev. Lett. 15, 1005 (1965).
[Crossref]

Kopa-Ovdienko, A. L.

Yu. K. Danileiko, L. M. Degtyarerv, A. L. Kopa-Ovdienko, T. P. Lebedeva, Sov. Phys. JETP 60, 417 (1984).

Lebedeva, T. P.

Yu. K. Danileiko, L. M. Degtyarerv, A. L. Kopa-Ovdienko, T. P. Lebedeva, Sov. Phys. JETP 60, 417 (1984).

Lisak, M.

D. Anderson, M. Bonnedal, M. Lisak, Phys. Fluids 22, 1838 (1979).
[Crossref]

M. Desaix, D. Anderson, M. Lisak, “Variational approach to collapse of optical pulses,” submitted to J. Opt. Soc. Am. B.

Manassah, J. T.

Marburger, J. H.

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

Marcatili, E. A. J.

K. Okamoto, E. A. J. Marcatili, IEEE J. Lightwave Technol. 7, 1988 (1989).
[Crossref]

Mollenauer, L. F.

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[Crossref]

Okamoto, K.

K. Okamoto, E. A. J. Marcatili, IEEE J. Lightwave Technol. 7, 1988 (1989).
[Crossref]

Pask, C.

Sammut, R. A.

Shabat, A. B.

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

Silberberg, Y.

Stolen, R. H.

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[Crossref]

Zakharov, V. E.

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

IEEE J. Lightwave Technol. (1)

K. Okamoto, E. A. J. Marcatili, IEEE J. Lightwave Technol. 7, 1988 (1989).
[Crossref]

Opt. Lett. (4)

Phys. Fluids (1)

D. Anderson, M. Bonnedal, M. Lisak, Phys. Fluids 22, 1838 (1979).
[Crossref]

Phys. Rev. A (1)

D. Anderson, Phys. Rev. A 27, 3135 (1983).
[Crossref]

Phys. Rev. Lett. (2)

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[Crossref]

P. L. Kelley, Phys. Rev. Lett. 15, 1005 (1965).
[Crossref]

Prog. Quantum Electron. (1)

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

Sov. Phys. JETP (2)

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

Yu. K. Danileiko, L. M. Degtyarerv, A. L. Kopa-Ovdienko, T. P. Lebedeva, Sov. Phys. JETP 60, 417 (1984).

Other (1)

M. Desaix, D. Anderson, M. Lisak, “Variational approach to collapse of optical pulses,” submitted to J. Opt. Soc. Am. B.

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Figures (4)

Fig. 1
Fig. 1

Variation of the regularized phase ϕreg with a normalized distance of propagation for different values of p from p = 0.6 to p = 3.0 with steps of 0.3.

Fig. 2
Fig. 2

Variation of the regularized phase ϕreg with a normalized time for three different normalized distances of propagation when E0 is equal to the critical self-focusing intensity Ec.

Fig. 3
Fig. 3

Three-dimensional plot of the pulse amplitude versus time and radius for y = 0 and p(u = 0) = 1.

Fig. 4
Fig. 4

Three-dimensional plot of the pulse amplitude versus time and radius for y = 50 and p(u = 0) = 1.

Equations (11)

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1 r r ( r E r ) 2 i k E z + 2 n 2 k 2 n 0 | E | 2 E = 0 ,
E ( z , r ) = A ( z ) exp [ 1 2 r 2 a 2 ( z ) + i b ( z ) r 2 ] .
L = r | E r | 2 ikr ( E E * z E * E z ) n 2 n 0 k 2 r | E | 4 .
δ 0 0 L d r d z = 0 ,
d d z ( | A | 2 a 2 ) = 0 ,
ika 2 ( A * d A d z A d A * d z ) = | A | 2 ( 2 k a 4 d b d z 1 4 b 2 a 4 + n 2 k 2 a 2 n 0 | A | 2 ) ,
b = k 2 a d a d z ,
d 2 a d z 2 + 1 k 2 a 3 ( n 2 A 0 2 a 0 2 k 2 2 n 0 1 ) = 0 ,
k d ϕ d z = 1 a 2 ( 1 3 2 p ) ,
p = n 2 k 2 a 0 2 A 0 2 2 n 0 A 0 2 E c 2 ,
a ( z ) = a 0 1 + ( 1 p ) y 2 , b ( z ) = y ( 1 p ) 2 a 0 2 [ 1 + ( 1 p ) y 2 ] , ϕ ( z ) = { ( 1 3 p 2 ) [ 1 1 p arctan ( y 1 p ) ] 0 < p < 1 , ( 1 3 p 2 ) [ 1 2 p 1 ln ( 1 + y p 1 1 y p 1 ) ] p > 1

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