Abstract

We present theoretical calculations and experimental measurements of self-phase-modulation spectra generated with picosecond laser pulses at 532 and 1064 nm propagating in optical fibers. The spectral structures of self-phase-modulation spectra are observed with a high-resolution optical spectral analysis system. The experimental observations are in good agreement with the theoretical predictions.

© 1994 Optical Society of America

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  1. R. R. Alfanq and S. L. Shapiro, "Emission in the region 4000-7000 A via four-photon coupling in glass," Phys. Rev. Lett. 24, 584–587 (1970); "Observation of self-phase modulation and small scale filaments in crystals and glasses," 24, 592–594 (1970); "Direct distortion of electronic clouds of rare-gas atoms in intense electric fields," 24, 1217–1220 (1970).
    [CrossRef]
  2. Q. Z. Wang, P. P. Ho, and R. R. Alfano, "Supercontinuum generation in condensed matter," in The Supercontinuum Laser Source, R. R. Alfano, ed. (Springer-Verlag, New York, 1989), Chap. 2.
    [CrossRef]
  3. R. Fork, C. Shank, C. Hirliman, and R. Yen, "Femtosecond white-light continuum pulses," Opt. Lett. 8, 1–3 (1983).
    [CrossRef] [PubMed]
  4. G. Yang and Y. R. Shen, "Spectral broadening of ultrashort pulses in a nonlinear medium," Opt. Lett. 9, 510–512 (1984).
    [CrossRef] [PubMed]
  5. R. H. Stolen and C. Lin, "Self-phase-modulation in silica optical fibers," Phys. Rev. A 17, 1448–1453 (1978).
    [CrossRef]
  6. T. K. Gustafson, J. Taran, P. Kelley, and R. Chiao, "Self-modulation of picosecond pulse in electro-optical crystals," Opt. Commun. 2, 17–21 (1970).
    [CrossRef]
  7. R. R. Alfano and S. L. Shapiro, "Picosecond spectroscopy using the inverse Raman effect," Chem. Phys. Lett. 8, 631–633 (1971).
    [CrossRef]
  8. B. I. Greene, R. M. Hochstrasser, and R. B. Weisman, "Picosecond vibrational and electronic relaxation process in molecules," in Picosecond Phenomena I, C. V. Shank, E. P. Ippen, and S. L. Shapiro, eds. (Springer-Verlag, New York, 1978), p. 12.
    [CrossRef]
  9. A. G. Doukas, V. Stefancic, T. Suzuki, R. H. Callender, and R. R. Alfano, "Squid bathorhodopsin forms within 10 picoseconds," Photobiochem. Photobiophys. 1, 305 (1980).
  10. C. V. Shank, R. L. Fork, R. T. Yen, R. J. Stolen, and W. J. Tomlinson, "Compression of femtosecond optical pulses," Appl. Phys. Lett. 40, 761–773 (1982).
    [CrossRef]
  11. R. Dorsinville, P. P. Ho, and R. R. Alfano, "Applications of supercontinuum," in The Supercontinuum Laser Source, R. R. Alfano, ed. (Springer-Verlag, New York, 1989), Chap. 9.
    [CrossRef]
  12. G. P. Agrawal, Nonlinear Fiber Optics (Academic, Boston, Mass., 1989).
  13. R. R. Alfano, "Interactions of picosecond pulses with matter," Ph.D. dissertation, GTE Tech. Rep. TR72-330.1 (GTE, Bayside, New York, 1972).

1984 (1)

1983 (1)

1982 (1)

C. V. Shank, R. L. Fork, R. T. Yen, R. J. Stolen, and W. J. Tomlinson, "Compression of femtosecond optical pulses," Appl. Phys. Lett. 40, 761–773 (1982).
[CrossRef]

1978 (1)

R. H. Stolen and C. Lin, "Self-phase-modulation in silica optical fibers," Phys. Rev. A 17, 1448–1453 (1978).
[CrossRef]

1971 (1)

R. R. Alfano and S. L. Shapiro, "Picosecond spectroscopy using the inverse Raman effect," Chem. Phys. Lett. 8, 631–633 (1971).
[CrossRef]

1970 (2)

T. K. Gustafson, J. Taran, P. Kelley, and R. Chiao, "Self-modulation of picosecond pulse in electro-optical crystals," Opt. Commun. 2, 17–21 (1970).
[CrossRef]

R. R. Alfanq and S. L. Shapiro, "Emission in the region 4000-7000 A via four-photon coupling in glass," Phys. Rev. Lett. 24, 584–587 (1970); "Observation of self-phase modulation and small scale filaments in crystals and glasses," 24, 592–594 (1970); "Direct distortion of electronic clouds of rare-gas atoms in intense electric fields," 24, 1217–1220 (1970).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, Boston, Mass., 1989).

Alfano, R. R.

R. R. Alfano and S. L. Shapiro, "Picosecond spectroscopy using the inverse Raman effect," Chem. Phys. Lett. 8, 631–633 (1971).
[CrossRef]

A. G. Doukas, V. Stefancic, T. Suzuki, R. H. Callender, and R. R. Alfano, "Squid bathorhodopsin forms within 10 picoseconds," Photobiochem. Photobiophys. 1, 305 (1980).

R. R. Alfano, "Interactions of picosecond pulses with matter," Ph.D. dissertation, GTE Tech. Rep. TR72-330.1 (GTE, Bayside, New York, 1972).

R. Dorsinville, P. P. Ho, and R. R. Alfano, "Applications of supercontinuum," in The Supercontinuum Laser Source, R. R. Alfano, ed. (Springer-Verlag, New York, 1989), Chap. 9.
[CrossRef]

Q. Z. Wang, P. P. Ho, and R. R. Alfano, "Supercontinuum generation in condensed matter," in The Supercontinuum Laser Source, R. R. Alfano, ed. (Springer-Verlag, New York, 1989), Chap. 2.
[CrossRef]

Alfanq, R. R.

R. R. Alfanq and S. L. Shapiro, "Emission in the region 4000-7000 A via four-photon coupling in glass," Phys. Rev. Lett. 24, 584–587 (1970); "Observation of self-phase modulation and small scale filaments in crystals and glasses," 24, 592–594 (1970); "Direct distortion of electronic clouds of rare-gas atoms in intense electric fields," 24, 1217–1220 (1970).
[CrossRef]

Callender, R. H.

A. G. Doukas, V. Stefancic, T. Suzuki, R. H. Callender, and R. R. Alfano, "Squid bathorhodopsin forms within 10 picoseconds," Photobiochem. Photobiophys. 1, 305 (1980).

Chiao, R.

T. K. Gustafson, J. Taran, P. Kelley, and R. Chiao, "Self-modulation of picosecond pulse in electro-optical crystals," Opt. Commun. 2, 17–21 (1970).
[CrossRef]

Dorsinville, R.

R. Dorsinville, P. P. Ho, and R. R. Alfano, "Applications of supercontinuum," in The Supercontinuum Laser Source, R. R. Alfano, ed. (Springer-Verlag, New York, 1989), Chap. 9.
[CrossRef]

Doukas, A. G.

A. G. Doukas, V. Stefancic, T. Suzuki, R. H. Callender, and R. R. Alfano, "Squid bathorhodopsin forms within 10 picoseconds," Photobiochem. Photobiophys. 1, 305 (1980).

Fork, R.

Fork, R. L.

C. V. Shank, R. L. Fork, R. T. Yen, R. J. Stolen, and W. J. Tomlinson, "Compression of femtosecond optical pulses," Appl. Phys. Lett. 40, 761–773 (1982).
[CrossRef]

Greene, B. I.

B. I. Greene, R. M. Hochstrasser, and R. B. Weisman, "Picosecond vibrational and electronic relaxation process in molecules," in Picosecond Phenomena I, C. V. Shank, E. P. Ippen, and S. L. Shapiro, eds. (Springer-Verlag, New York, 1978), p. 12.
[CrossRef]

Gustafson, T. K.

T. K. Gustafson, J. Taran, P. Kelley, and R. Chiao, "Self-modulation of picosecond pulse in electro-optical crystals," Opt. Commun. 2, 17–21 (1970).
[CrossRef]

Hirliman, C.

Ho, P. P.

Q. Z. Wang, P. P. Ho, and R. R. Alfano, "Supercontinuum generation in condensed matter," in The Supercontinuum Laser Source, R. R. Alfano, ed. (Springer-Verlag, New York, 1989), Chap. 2.
[CrossRef]

R. Dorsinville, P. P. Ho, and R. R. Alfano, "Applications of supercontinuum," in The Supercontinuum Laser Source, R. R. Alfano, ed. (Springer-Verlag, New York, 1989), Chap. 9.
[CrossRef]

Hochstrasser, R. M.

B. I. Greene, R. M. Hochstrasser, and R. B. Weisman, "Picosecond vibrational and electronic relaxation process in molecules," in Picosecond Phenomena I, C. V. Shank, E. P. Ippen, and S. L. Shapiro, eds. (Springer-Verlag, New York, 1978), p. 12.
[CrossRef]

Kelley, P.

T. K. Gustafson, J. Taran, P. Kelley, and R. Chiao, "Self-modulation of picosecond pulse in electro-optical crystals," Opt. Commun. 2, 17–21 (1970).
[CrossRef]

Lin, C.

R. H. Stolen and C. Lin, "Self-phase-modulation in silica optical fibers," Phys. Rev. A 17, 1448–1453 (1978).
[CrossRef]

Shank, C.

Shank, C. V.

C. V. Shank, R. L. Fork, R. T. Yen, R. J. Stolen, and W. J. Tomlinson, "Compression of femtosecond optical pulses," Appl. Phys. Lett. 40, 761–773 (1982).
[CrossRef]

Shapiro, S. L.

R. R. Alfano and S. L. Shapiro, "Picosecond spectroscopy using the inverse Raman effect," Chem. Phys. Lett. 8, 631–633 (1971).
[CrossRef]

R. R. Alfanq and S. L. Shapiro, "Emission in the region 4000-7000 A via four-photon coupling in glass," Phys. Rev. Lett. 24, 584–587 (1970); "Observation of self-phase modulation and small scale filaments in crystals and glasses," 24, 592–594 (1970); "Direct distortion of electronic clouds of rare-gas atoms in intense electric fields," 24, 1217–1220 (1970).
[CrossRef]

Shen, Y. R.

Stefancic, V.

A. G. Doukas, V. Stefancic, T. Suzuki, R. H. Callender, and R. R. Alfano, "Squid bathorhodopsin forms within 10 picoseconds," Photobiochem. Photobiophys. 1, 305 (1980).

Stolen, R. H.

R. H. Stolen and C. Lin, "Self-phase-modulation in silica optical fibers," Phys. Rev. A 17, 1448–1453 (1978).
[CrossRef]

Stolen, R. J.

C. V. Shank, R. L. Fork, R. T. Yen, R. J. Stolen, and W. J. Tomlinson, "Compression of femtosecond optical pulses," Appl. Phys. Lett. 40, 761–773 (1982).
[CrossRef]

Suzuki, T.

A. G. Doukas, V. Stefancic, T. Suzuki, R. H. Callender, and R. R. Alfano, "Squid bathorhodopsin forms within 10 picoseconds," Photobiochem. Photobiophys. 1, 305 (1980).

Taran, J.

T. K. Gustafson, J. Taran, P. Kelley, and R. Chiao, "Self-modulation of picosecond pulse in electro-optical crystals," Opt. Commun. 2, 17–21 (1970).
[CrossRef]

Tomlinson, W. J.

C. V. Shank, R. L. Fork, R. T. Yen, R. J. Stolen, and W. J. Tomlinson, "Compression of femtosecond optical pulses," Appl. Phys. Lett. 40, 761–773 (1982).
[CrossRef]

Wang, Q. Z.

Q. Z. Wang, P. P. Ho, and R. R. Alfano, "Supercontinuum generation in condensed matter," in The Supercontinuum Laser Source, R. R. Alfano, ed. (Springer-Verlag, New York, 1989), Chap. 2.
[CrossRef]

Weisman, R. B.

B. I. Greene, R. M. Hochstrasser, and R. B. Weisman, "Picosecond vibrational and electronic relaxation process in molecules," in Picosecond Phenomena I, C. V. Shank, E. P. Ippen, and S. L. Shapiro, eds. (Springer-Verlag, New York, 1978), p. 12.
[CrossRef]

Yang, G.

Yen, R.

Yen, R. T.

C. V. Shank, R. L. Fork, R. T. Yen, R. J. Stolen, and W. J. Tomlinson, "Compression of femtosecond optical pulses," Appl. Phys. Lett. 40, 761–773 (1982).
[CrossRef]

Appl. Phys. Lett. (1)

C. V. Shank, R. L. Fork, R. T. Yen, R. J. Stolen, and W. J. Tomlinson, "Compression of femtosecond optical pulses," Appl. Phys. Lett. 40, 761–773 (1982).
[CrossRef]

Chem. Phys. Lett. (1)

R. R. Alfano and S. L. Shapiro, "Picosecond spectroscopy using the inverse Raman effect," Chem. Phys. Lett. 8, 631–633 (1971).
[CrossRef]

Opt. Commun. (1)

T. K. Gustafson, J. Taran, P. Kelley, and R. Chiao, "Self-modulation of picosecond pulse in electro-optical crystals," Opt. Commun. 2, 17–21 (1970).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (1)

R. H. Stolen and C. Lin, "Self-phase-modulation in silica optical fibers," Phys. Rev. A 17, 1448–1453 (1978).
[CrossRef]

Phys. Rev. Lett. (1)

R. R. Alfanq and S. L. Shapiro, "Emission in the region 4000-7000 A via four-photon coupling in glass," Phys. Rev. Lett. 24, 584–587 (1970); "Observation of self-phase modulation and small scale filaments in crystals and glasses," 24, 592–594 (1970); "Direct distortion of electronic clouds of rare-gas atoms in intense electric fields," 24, 1217–1220 (1970).
[CrossRef]

Other (6)

Q. Z. Wang, P. P. Ho, and R. R. Alfano, "Supercontinuum generation in condensed matter," in The Supercontinuum Laser Source, R. R. Alfano, ed. (Springer-Verlag, New York, 1989), Chap. 2.
[CrossRef]

B. I. Greene, R. M. Hochstrasser, and R. B. Weisman, "Picosecond vibrational and electronic relaxation process in molecules," in Picosecond Phenomena I, C. V. Shank, E. P. Ippen, and S. L. Shapiro, eds. (Springer-Verlag, New York, 1978), p. 12.
[CrossRef]

A. G. Doukas, V. Stefancic, T. Suzuki, R. H. Callender, and R. R. Alfano, "Squid bathorhodopsin forms within 10 picoseconds," Photobiochem. Photobiophys. 1, 305 (1980).

R. Dorsinville, P. P. Ho, and R. R. Alfano, "Applications of supercontinuum," in The Supercontinuum Laser Source, R. R. Alfano, ed. (Springer-Verlag, New York, 1989), Chap. 9.
[CrossRef]

G. P. Agrawal, Nonlinear Fiber Optics (Academic, Boston, Mass., 1989).

R. R. Alfano, "Interactions of picosecond pulses with matter," Ph.D. dissertation, GTE Tech. Rep. TR72-330.1 (GTE, Bayside, New York, 1972).

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Figures (8)

Fig. 1
Fig. 1

Calculated SPM spectra of 532-nm laser pulses propagating in an optical fiber. The core diameter of the optical fiber was 2.5 μm. n2 = 3.2 × 10−16 cm2/W. (a) Input laser, (b) P0 = 110 W, (c) P0 = 225 W, (d) P0 = 460 W, (e) P0 = 630 W, (f) P0 = 790 W.

Fig. 2
Fig. 2

Calculated SPM spectra of 1064-nm laser pulses propagating in an optical fiber. The core diameter of the optical fiber was 4 μm. n2 = 2.28 × 10−16 cm2/W. (a) Input laser, (b) P0 = 1800 W, (c) P0 = 2300 W, (d) P0 = 3900 W, (e) P0 = 4900 W, (f) P0 = 5700 W.

Fig. 3
Fig. 3

Experimental arrangement. F1, a set of color and neutral-density filters; F2, F3, neutral-density filters; L1, L2, 20× microscope objectives; L3, lens.

Fig. 4
Fig. 4

Input laser pulse shape. The laser pulse is slightly asymmetric. The leading edge is shorter than the trailing edge. The dashed curve shows a theoretical fit to the pulse.

Fig. 5
Fig. 5

Video display of the spectra of 532-nm laser pulses propagating in a 1-m 2.5-μm-core optical fiber with different peak powers. (a) Input laser, (b) P0 = 110 W, (c) P0 = 225 W, (d) P0 = 460 W, (e) P0 = 630 W, (f) P0 = 790 W, and (g) P0 = 270 W.

Fig. 6
Fig. 6

Digital-intensity spectral curves of 532-nm laser pulses propagating in a 1-m 2.5-μm-core optical fiber with different peak powers. The left-hand column shows the experimental results, and the right-hand column displays the numerical simulations. (a) Input laser, (b) P0 = 110 W, (c) P0 = 225 W, (d) P0 = 460 W, (e) P0 = 630 W, (f) P0 = 790 W.

Fig. 7
Fig. 7

Video display of the spectra of 1064-nm laser pulses propagating in a 1-m 4-μm-coreoptical fiber with different peak powers. (a) Input laser, (b) P0 = 1800 W, (c) P0 = 2300 W, (d) P0 = 3100 W, (e) P0 = 3920 W, (f) P0 = 4900 W, (g) P0 = 5700 W, (h) P0 = 6900 W, (i) P0 = 7800 W.

Fig. 8
Fig. 8

Digital-intensity spectral curves of 1064-nm laser pulses propagating in a 1-m 2.5-μm-coreoptical fiber with different peak powers. The left-hand column shows the experimental results, and the right-hand column displays the numerical simulations. (a) Input laser, (b) P0 = 1800 W, (c) P0 = 2300 W, (d) P0 = 3900 W, (e) P0 = 4900 W, (f) P0 = 5700 W.

Equations (12)

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A z + 1 v g A t + i 1 2 k ( 2 ) 2 A t 2 = i ω 0 n 2 c A 2 A ,
τ = t - z v g ,
z = z
A ( z , τ ) = a ( z , τ ) exp [ i α ( z , τ ) ] ,
a z = 0 ,
α z = ω 0 n 2 c a 2 .
a ( τ ) = a 0 F ( τ ) ,
α ( z , t ) = ω 0 n 2 c 0 z a 2 ( z , τ ) d z = ω 0 n 2 c a 0 2 F 2 ( τ ) z ,
ω ( τ ) = ω 0 + δ ω ( τ ) ,
δ ω ( τ ) = - α τ = - ω 0 n 2 c a 0 2 F 2 ( τ ) τ .
ɛ ( z , ω - ω 0 ) = 1 2 π A ( τ , z ) exp ( - i ω 0 τ ) exp ( i ω τ ) d τ = 1 2 π a ( τ , z ) exp [ i α ( τ , z ) ] × exp [ i ( ω - ω 0 ) τ ] d τ .
ɛ ( z , ω - ω 0 ) 2 .

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