Abstract

The spectral distributions of 8-psec ultrashort laser pulses propagating through multimode glass fibers were measured and compared with those of single-mode fibers at comparable intensities. In multimode optical fibers the spectral broadening arising from self-phase modulation was found to be asymmetric to the Stokes side owing to modal dispersion.

© 1989 Optical Society of America

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References

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  1. R. R. Alfano, S. L. Shapiro, Phys. Rev. Lett. 24, 584, 592, 1217 (1970).
    [Crossref]
  2. R. R. Alfano, ed., Supercontinum Laser Sources (Springer-Verlag, New York, 1989).
  3. R. Fork, C. Shank, C. Hirliman, R. Yen, Opt. Lett. 8, 1 (1983).
    [Crossref] [PubMed]
  4. G. Yang, Y. R. Shen, Opt. Lett. 9, 510 (1984).
    [Crossref] [PubMed]
  5. J. Manassah, M. Mustafa, R. Alfano, P. P. Ho, Phys. Lett. 13A, 242 (1985).
  6. R. H. Stolen, Chinlon Lin, Phys. Rev. A 17, 1448 (1978).
    [Crossref]
  7. E. P. Ippen, C. V. Shank, T. K. Gustafson, Appl. Phys. Lett. 33, 1765 (1974).
  8. R. R. Alfano, P. L. Baldeck, F. Raccah, P. P. Ho, Appl. Opt. 26, 3491 (1987).
    [Crossref] [PubMed]
  9. T. Li, AT&T Tech. J. 66, 5 (1987).
  10. P. L. Baldeck, F. Raccah, R. R. Alfano, Opt. Lett. 12, 588 (1987).
    [Crossref] [PubMed]
  11. A. B. Grudinin, E. M. Dianov, D. V. Korbkin, A. M. Prokhorov, D. V. Khaidarov, JETP Lett. 47, 356 (1988).
  12. R. R. Alfano, D. B. Tata, J. Cordero, P. Tomashefsky, R. W. Longo, M. A. Alfano, IEEE J. Quantum Electron. QE-20, 1507 (1984).
    [Crossref]
  13. R. R. Alfano, G. C. Tang, A. Pradhan, W. Lam, D. Choy, E. Opher, IEEE J. Quantum Electron. QE-23, 1806 (1987).
    [Crossref]
  14. A. Sawaki, H. Suzuki, M. Koishi, H. Kume, Y. Mizushima, J. Opt. Soc. Am. A 4, 1283 (1987).
    [Crossref]
  15. P. L. Baldeck, R. R. Alfano, IEEE J. Lightwave Technol. LT-5, 1712 (1987).
    [Crossref]
  16. O. Gloge, Bell Syst. Tech. J. 51, 1767 (1972).
  17. E. Fermi, D. Pasta, S. Ulam, Scientific Work (Nauka, Moscow, 1972), Vol. II.
  18. Z. V. Nesterova, I. V. Aleksandrov, A. A. Polnitskii, D. K. Satlavov, JETP Lett. 34, 371 (1981).
  19. B. Crosignani, A. Cutolo, P. Di Porto, J. Opt. Soc. Am. 72, 1136 (1982).
    [Crossref]

1988 (1)

A. B. Grudinin, E. M. Dianov, D. V. Korbkin, A. M. Prokhorov, D. V. Khaidarov, JETP Lett. 47, 356 (1988).

1987 (6)

R. R. Alfano, P. L. Baldeck, F. Raccah, P. P. Ho, Appl. Opt. 26, 3491 (1987).
[Crossref] [PubMed]

T. Li, AT&T Tech. J. 66, 5 (1987).

P. L. Baldeck, F. Raccah, R. R. Alfano, Opt. Lett. 12, 588 (1987).
[Crossref] [PubMed]

R. R. Alfano, G. C. Tang, A. Pradhan, W. Lam, D. Choy, E. Opher, IEEE J. Quantum Electron. QE-23, 1806 (1987).
[Crossref]

A. Sawaki, H. Suzuki, M. Koishi, H. Kume, Y. Mizushima, J. Opt. Soc. Am. A 4, 1283 (1987).
[Crossref]

P. L. Baldeck, R. R. Alfano, IEEE J. Lightwave Technol. LT-5, 1712 (1987).
[Crossref]

1985 (1)

J. Manassah, M. Mustafa, R. Alfano, P. P. Ho, Phys. Lett. 13A, 242 (1985).

1984 (2)

R. R. Alfano, D. B. Tata, J. Cordero, P. Tomashefsky, R. W. Longo, M. A. Alfano, IEEE J. Quantum Electron. QE-20, 1507 (1984).
[Crossref]

G. Yang, Y. R. Shen, Opt. Lett. 9, 510 (1984).
[Crossref] [PubMed]

1983 (1)

1982 (1)

1981 (1)

Z. V. Nesterova, I. V. Aleksandrov, A. A. Polnitskii, D. K. Satlavov, JETP Lett. 34, 371 (1981).

1978 (1)

R. H. Stolen, Chinlon Lin, Phys. Rev. A 17, 1448 (1978).
[Crossref]

1974 (1)

E. P. Ippen, C. V. Shank, T. K. Gustafson, Appl. Phys. Lett. 33, 1765 (1974).

1972 (1)

O. Gloge, Bell Syst. Tech. J. 51, 1767 (1972).

1970 (1)

R. R. Alfano, S. L. Shapiro, Phys. Rev. Lett. 24, 584, 592, 1217 (1970).
[Crossref]

Aleksandrov, I. V.

Z. V. Nesterova, I. V. Aleksandrov, A. A. Polnitskii, D. K. Satlavov, JETP Lett. 34, 371 (1981).

Alfano, M. A.

R. R. Alfano, D. B. Tata, J. Cordero, P. Tomashefsky, R. W. Longo, M. A. Alfano, IEEE J. Quantum Electron. QE-20, 1507 (1984).
[Crossref]

Alfano, R.

J. Manassah, M. Mustafa, R. Alfano, P. P. Ho, Phys. Lett. 13A, 242 (1985).

Alfano, R. R.

R. R. Alfano, G. C. Tang, A. Pradhan, W. Lam, D. Choy, E. Opher, IEEE J. Quantum Electron. QE-23, 1806 (1987).
[Crossref]

P. L. Baldeck, R. R. Alfano, IEEE J. Lightwave Technol. LT-5, 1712 (1987).
[Crossref]

P. L. Baldeck, F. Raccah, R. R. Alfano, Opt. Lett. 12, 588 (1987).
[Crossref] [PubMed]

R. R. Alfano, P. L. Baldeck, F. Raccah, P. P. Ho, Appl. Opt. 26, 3491 (1987).
[Crossref] [PubMed]

R. R. Alfano, D. B. Tata, J. Cordero, P. Tomashefsky, R. W. Longo, M. A. Alfano, IEEE J. Quantum Electron. QE-20, 1507 (1984).
[Crossref]

R. R. Alfano, S. L. Shapiro, Phys. Rev. Lett. 24, 584, 592, 1217 (1970).
[Crossref]

Baldeck, P. L.

Choy, D.

R. R. Alfano, G. C. Tang, A. Pradhan, W. Lam, D. Choy, E. Opher, IEEE J. Quantum Electron. QE-23, 1806 (1987).
[Crossref]

Cordero, J.

R. R. Alfano, D. B. Tata, J. Cordero, P. Tomashefsky, R. W. Longo, M. A. Alfano, IEEE J. Quantum Electron. QE-20, 1507 (1984).
[Crossref]

Crosignani, B.

Cutolo, A.

Di Porto, P.

Dianov, E. M.

A. B. Grudinin, E. M. Dianov, D. V. Korbkin, A. M. Prokhorov, D. V. Khaidarov, JETP Lett. 47, 356 (1988).

Fermi, E.

E. Fermi, D. Pasta, S. Ulam, Scientific Work (Nauka, Moscow, 1972), Vol. II.

Fork, R.

Gloge, O.

O. Gloge, Bell Syst. Tech. J. 51, 1767 (1972).

Grudinin, A. B.

A. B. Grudinin, E. M. Dianov, D. V. Korbkin, A. M. Prokhorov, D. V. Khaidarov, JETP Lett. 47, 356 (1988).

Gustafson, T. K.

E. P. Ippen, C. V. Shank, T. K. Gustafson, Appl. Phys. Lett. 33, 1765 (1974).

Hirliman, C.

Ho, P. P.

R. R. Alfano, P. L. Baldeck, F. Raccah, P. P. Ho, Appl. Opt. 26, 3491 (1987).
[Crossref] [PubMed]

J. Manassah, M. Mustafa, R. Alfano, P. P. Ho, Phys. Lett. 13A, 242 (1985).

Ippen, E. P.

E. P. Ippen, C. V. Shank, T. K. Gustafson, Appl. Phys. Lett. 33, 1765 (1974).

Khaidarov, D. V.

A. B. Grudinin, E. M. Dianov, D. V. Korbkin, A. M. Prokhorov, D. V. Khaidarov, JETP Lett. 47, 356 (1988).

Koishi, M.

Korbkin, D. V.

A. B. Grudinin, E. M. Dianov, D. V. Korbkin, A. M. Prokhorov, D. V. Khaidarov, JETP Lett. 47, 356 (1988).

Kume, H.

Lam, W.

R. R. Alfano, G. C. Tang, A. Pradhan, W. Lam, D. Choy, E. Opher, IEEE J. Quantum Electron. QE-23, 1806 (1987).
[Crossref]

Li, T.

T. Li, AT&T Tech. J. 66, 5 (1987).

Lin, Chinlon

R. H. Stolen, Chinlon Lin, Phys. Rev. A 17, 1448 (1978).
[Crossref]

Longo, R. W.

R. R. Alfano, D. B. Tata, J. Cordero, P. Tomashefsky, R. W. Longo, M. A. Alfano, IEEE J. Quantum Electron. QE-20, 1507 (1984).
[Crossref]

Manassah, J.

J. Manassah, M. Mustafa, R. Alfano, P. P. Ho, Phys. Lett. 13A, 242 (1985).

Mizushima, Y.

Mustafa, M.

J. Manassah, M. Mustafa, R. Alfano, P. P. Ho, Phys. Lett. 13A, 242 (1985).

Nesterova, Z. V.

Z. V. Nesterova, I. V. Aleksandrov, A. A. Polnitskii, D. K. Satlavov, JETP Lett. 34, 371 (1981).

Opher, E.

R. R. Alfano, G. C. Tang, A. Pradhan, W. Lam, D. Choy, E. Opher, IEEE J. Quantum Electron. QE-23, 1806 (1987).
[Crossref]

Pasta, D.

E. Fermi, D. Pasta, S. Ulam, Scientific Work (Nauka, Moscow, 1972), Vol. II.

Polnitskii, A. A.

Z. V. Nesterova, I. V. Aleksandrov, A. A. Polnitskii, D. K. Satlavov, JETP Lett. 34, 371 (1981).

Pradhan, A.

R. R. Alfano, G. C. Tang, A. Pradhan, W. Lam, D. Choy, E. Opher, IEEE J. Quantum Electron. QE-23, 1806 (1987).
[Crossref]

Prokhorov, A. M.

A. B. Grudinin, E. M. Dianov, D. V. Korbkin, A. M. Prokhorov, D. V. Khaidarov, JETP Lett. 47, 356 (1988).

Raccah, F.

Satlavov, D. K.

Z. V. Nesterova, I. V. Aleksandrov, A. A. Polnitskii, D. K. Satlavov, JETP Lett. 34, 371 (1981).

Sawaki, A.

Shank, C.

Shank, C. V.

E. P. Ippen, C. V. Shank, T. K. Gustafson, Appl. Phys. Lett. 33, 1765 (1974).

Shapiro, S. L.

R. R. Alfano, S. L. Shapiro, Phys. Rev. Lett. 24, 584, 592, 1217 (1970).
[Crossref]

Shen, Y. R.

Stolen, R. H.

R. H. Stolen, Chinlon Lin, Phys. Rev. A 17, 1448 (1978).
[Crossref]

Suzuki, H.

Tang, G. C.

R. R. Alfano, G. C. Tang, A. Pradhan, W. Lam, D. Choy, E. Opher, IEEE J. Quantum Electron. QE-23, 1806 (1987).
[Crossref]

Tata, D. B.

R. R. Alfano, D. B. Tata, J. Cordero, P. Tomashefsky, R. W. Longo, M. A. Alfano, IEEE J. Quantum Electron. QE-20, 1507 (1984).
[Crossref]

Tomashefsky, P.

R. R. Alfano, D. B. Tata, J. Cordero, P. Tomashefsky, R. W. Longo, M. A. Alfano, IEEE J. Quantum Electron. QE-20, 1507 (1984).
[Crossref]

Ulam, S.

E. Fermi, D. Pasta, S. Ulam, Scientific Work (Nauka, Moscow, 1972), Vol. II.

Yang, G.

Yen, R.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

E. P. Ippen, C. V. Shank, T. K. Gustafson, Appl. Phys. Lett. 33, 1765 (1974).

AT&T Tech. J. (1)

T. Li, AT&T Tech. J. 66, 5 (1987).

Bell Syst. Tech. J. (1)

O. Gloge, Bell Syst. Tech. J. 51, 1767 (1972).

IEEE J. Lightwave Technol. (1)

P. L. Baldeck, R. R. Alfano, IEEE J. Lightwave Technol. LT-5, 1712 (1987).
[Crossref]

IEEE J. Quantum Electron. (2)

R. R. Alfano, D. B. Tata, J. Cordero, P. Tomashefsky, R. W. Longo, M. A. Alfano, IEEE J. Quantum Electron. QE-20, 1507 (1984).
[Crossref]

R. R. Alfano, G. C. Tang, A. Pradhan, W. Lam, D. Choy, E. Opher, IEEE J. Quantum Electron. QE-23, 1806 (1987).
[Crossref]

J. Opt. Soc. Am. (1)

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

JETP Lett. (2)

A. B. Grudinin, E. M. Dianov, D. V. Korbkin, A. M. Prokhorov, D. V. Khaidarov, JETP Lett. 47, 356 (1988).

Z. V. Nesterova, I. V. Aleksandrov, A. A. Polnitskii, D. K. Satlavov, JETP Lett. 34, 371 (1981).

Opt. Lett. (3)

Phys. Lett. (1)

J. Manassah, M. Mustafa, R. Alfano, P. P. Ho, Phys. Lett. 13A, 242 (1985).

Phys. Rev. A (1)

R. H. Stolen, Chinlon Lin, Phys. Rev. A 17, 1448 (1978).
[Crossref]

Phys. Rev. Lett. (1)

R. R. Alfano, S. L. Shapiro, Phys. Rev. Lett. 24, 584, 592, 1217 (1970).
[Crossref]

Other (2)

R. R. Alfano, ed., Supercontinum Laser Sources (Springer-Verlag, New York, 1989).

E. Fermi, D. Pasta, S. Ulam, Scientific Work (Nauka, Moscow, 1972), Vol. II.

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Figures (3)

Fig. 1
Fig. 1

Output spectra for 8-psec laser pulses at 527 nm propagating through different lengths of optical fibers. λ, Wavelength. (a) No fiber; (b) multimode fiber, 22 cm; (c) multimode fiber, 42 cm; (d) multimode fiber, 84 cm; (e) single-mode fiber, 20 cm; (f) single-mode fiber, 40 cm; (g) single-mode fiber, 50 cm.

Fig. 2
Fig. 2

Calculated spectral broadening in multimode fibers as a function of length for an 8-psec pulse at 527 nm. λ, Wavelength, (a) No fiber, (b) 20-cm fiber, (c) 40-cm fiber. In the formulation, 16 modes, with effective amplitudes C12 = 1.00, C22 = 0.80, C32 = 0.65, C42 = 0.50, C52 = 0.40, C62 = 0.30, C72 = 0.25, C82 = 0.20, C92 = 0.15, C102 = 0.12, C112 = 0.10, C122 = 0.08, C132 = 0.06, C142 = 0.04, C152 = 0.02, and C162 = 0.01, were chosen for the best data fitting. The unit is 3.78 × 1010 (V/m)2. n2 = 2.3 × 10−22 (m/V)2, υg1 = 3 × 108/1.5 m/sec, υg16 = 1.9600 × 108 m/sec, and υgi = υgi1 – (i – 1)(υg1υg16)/(16 – 1) for i = 2–15. The total pulse energy is 2 μJ.

Fig. 3
Fig. 3

Spectral broading as a function of multimode fiber length (L): ▲, Stokes side; ●, anti-Stokes side. The solid and the dashed curves are the calculated spectral broadening to the Stokes and anti-Stokes sides, respectively, with respect to fiber length.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

E ( t , z ) = C i E i ( t , z ) exp ( i ω 0 t i k i z ) ,
E i ( t , z ) = exp [ ( t z / υ g i ) 2 / τ 2 ] ,
n i = n 0 i + n 2 i | E ( t , z ) | 2 ,
E ( t , z ) = C i E i ( t , z ) exp [ i ω 0 t i n 0 i ω 0 z / c + i Δ ϕ ( t , z ) ] ,
Δ ϕ ( t , z ) = ( n 2 ω 0 z / c ) | E ( t , z ) | 2 .
Δ ϕ ( t , z ) = ( n 2 ω 0 z / c ) C i C j E i ( t , z ) E j ( t , z ) × exp [ i ( n 0 i n 0 j ) ω 0 z / c ] .
Δ ϕ ( t , z ) ( n 2 ω 0 z / c ) C i 2 E i 2 ( t , z ) .

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