Abstract

The use of self-phase modulation in a single-mode fiber to chirp an optical pulse, which is then compressed with a grating-pair compressor, has been shown to be a practical technique for the production of optical pulses at least as short as 30 fsec. We report the results of a theoretical analysis of this process. Numerical results are presented for the achievable compression and compressed pulse quality as functions of fiber length and input pulse intensity. These results are given in normalized units such that they can be scaled to describe a wide variety of experimental situations and can be used to determine the optimum fiber length and compressor parameters for any given input pulse. Specific numerical examples are presented that suggest that the technique will generally be useful for input pulses shorter than about 100 psec. For energies of a few nanojoules per pulse, the compressed pulse widths will typically be in the femtosecond regime.

© 1984 Optical Society of America

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References

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  1. L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, "Experimental observation of picosecond pulse narrowing and solitons in optical fibers," Phys. Rev. Lett. 45, 1095–1098 (1980).
    [CrossRef]
  2. H. Nakatsuka, D. Grischkowsky, and A. C. Balant, "Nonlinear picosecond-pulse propagation through optical fibers with positive group velocity dispersion," Phys. Rev. Lett. 47, 910–913 (1981).
    [CrossRef]
  3. C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, and W. J. Tomlinson, "Compression of femtosecond optical pulses," Appl. Phys. Lett. 40, 761–763 (1982).
    [CrossRef]
  4. B. Nikolaus and D. Grischkowsky, "12Χ pulse compression using optical fibers," Appl. Phys. Lett. 42, 1–2 (1983); "90-fsec tunable optical pulses obtained by two-stage pulse compression," 43, 228–230 (1983).
    [CrossRef]
  5. R. A. Fisher, P. L. Kelley, and T. K. Gustafson, "Subpicosecond pulse generation using the optical Kerr effect," Appl. Phys. Lett. 14, 140–143 (1969).
    [CrossRef]
  6. R. H. Stolen and Chinlon Lin, "Self-phase modulation in silica optical fibers," Phys. Rev. A 17, 1448–1453 (1978).
    [CrossRef]
  7. A. Hasegawa and F. Tappert, "Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers, I. Anomalous dispersion," Appl. Phys. Lett. 23, 142–144 (1973).
    [CrossRef]
  8. L. F. Mollenauer, R. H. Stolen, J. P. Gordon, and W. J. Tomlinson, "Extreme picosecond pulse narrowing by means of soliton effect in single-mode optical fibers," Opt. Lett. 8, 289–291 (1983).
    [CrossRef] [PubMed]
  9. D. Grischkowsky and A. C. Balant, "Optical pulse compression based on enhanced frequency chirping," Appl. Phys. Lett. 41, 1–3 (1982). In this reference the characteristic lengths zL and zS are related to the present z0 and zopt by zL = √3 z0 and zopt ≍ 2zs.
    [CrossRef]
  10. R. H. Stolen and J. E. Bjorkholm, "Parametric amplification and frequency conversion in optical fibers," IEEE J. Quantum Electron. QE-18, 1062–1072 (1982).
    [CrossRef]
  11. W. J. Tomlinson, J. P. Gordon, P. W. Smith, and A. E. Kaplan, "Reflection of a gaussian beam at a nonlinear interface," Appl. Opt. 21, 2041–2051 (1982).
    [CrossRef] [PubMed]
  12. E. B. Treacy, "Optical pulse compression with diffraction gratings," IEEE J. Quantum Electron. QE-5, 454–458 (1969).
    [CrossRef]
  13. R. Meinel, "Generation of chirped pulses in optical fibers suitable for an effective pulse compression," Opt. Commun. 47, 343–346. (1983).
    [CrossRef]
  14. D. Gloge, "Weakly guiding fibers," Appl. Opt. 10, 2252–2258 (1971); D. N. Payne and W. A. Gambling, "Zero material dispersion in optical fibers," Electron. Lett. 11, 176–178 (1975).
    [CrossRef] [PubMed]
  15. J. Desbois, F. Gires, and P. Tournois, "A new approach to picosecond laser pulse analysis shaping and coding," IEEE J. Quantum Electron. QE-9, 213–218 (1973).
    [CrossRef]
  16. R. L. Fork, O. E. Martinez, and J. P. Gordon, "Negative dispersion using pairs of prisms," Opt. Lett, (to be published).
  17. R. G. Smith, "Optical power handling capacity of low-loss optical fibers as determined by stimulated Raman and Brillouin scattering," Appl. Opt. 11, 2489–2494 (1972).
    [CrossRef] [PubMed]
  18. E. H. Turner and R. H. Stolen, "Fiber Faraday circulator or isolator," Opt. Lett. 6, 322–323 (1981).
    [CrossRef] [PubMed]

1983 (3)

B. Nikolaus and D. Grischkowsky, "12Χ pulse compression using optical fibers," Appl. Phys. Lett. 42, 1–2 (1983); "90-fsec tunable optical pulses obtained by two-stage pulse compression," 43, 228–230 (1983).
[CrossRef]

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, and W. J. Tomlinson, "Extreme picosecond pulse narrowing by means of soliton effect in single-mode optical fibers," Opt. Lett. 8, 289–291 (1983).
[CrossRef] [PubMed]

R. Meinel, "Generation of chirped pulses in optical fibers suitable for an effective pulse compression," Opt. Commun. 47, 343–346. (1983).
[CrossRef]

1982 (4)

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, and W. J. Tomlinson, "Compression of femtosecond optical pulses," Appl. Phys. Lett. 40, 761–763 (1982).
[CrossRef]

D. Grischkowsky and A. C. Balant, "Optical pulse compression based on enhanced frequency chirping," Appl. Phys. Lett. 41, 1–3 (1982). In this reference the characteristic lengths zL and zS are related to the present z0 and zopt by zL = √3 z0 and zopt ≍ 2zs.
[CrossRef]

R. H. Stolen and J. E. Bjorkholm, "Parametric amplification and frequency conversion in optical fibers," IEEE J. Quantum Electron. QE-18, 1062–1072 (1982).
[CrossRef]

W. J. Tomlinson, J. P. Gordon, P. W. Smith, and A. E. Kaplan, "Reflection of a gaussian beam at a nonlinear interface," Appl. Opt. 21, 2041–2051 (1982).
[CrossRef] [PubMed]

1981 (2)

H. Nakatsuka, D. Grischkowsky, and A. C. Balant, "Nonlinear picosecond-pulse propagation through optical fibers with positive group velocity dispersion," Phys. Rev. Lett. 47, 910–913 (1981).
[CrossRef]

E. H. Turner and R. H. Stolen, "Fiber Faraday circulator or isolator," Opt. Lett. 6, 322–323 (1981).
[CrossRef] [PubMed]

1980 (1)

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, "Experimental observation of picosecond pulse narrowing and solitons in optical fibers," Phys. Rev. Lett. 45, 1095–1098 (1980).
[CrossRef]

1978 (1)

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

1973 (2)

A. Hasegawa and F. Tappert, "Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers, I. Anomalous dispersion," Appl. Phys. Lett. 23, 142–144 (1973).
[CrossRef]

J. Desbois, F. Gires, and P. Tournois, "A new approach to picosecond laser pulse analysis shaping and coding," IEEE J. Quantum Electron. QE-9, 213–218 (1973).
[CrossRef]

1972 (1)

1971 (1)

1969 (2)

R. A. Fisher, P. L. Kelley, and T. K. Gustafson, "Subpicosecond pulse generation using the optical Kerr effect," Appl. Phys. Lett. 14, 140–143 (1969).
[CrossRef]

E. B. Treacy, "Optical pulse compression with diffraction gratings," IEEE J. Quantum Electron. QE-5, 454–458 (1969).
[CrossRef]

Balant, A. C.

D. Grischkowsky and A. C. Balant, "Optical pulse compression based on enhanced frequency chirping," Appl. Phys. Lett. 41, 1–3 (1982). In this reference the characteristic lengths zL and zS are related to the present z0 and zopt by zL = √3 z0 and zopt ≍ 2zs.
[CrossRef]

H. Nakatsuka, D. Grischkowsky, and A. C. Balant, "Nonlinear picosecond-pulse propagation through optical fibers with positive group velocity dispersion," Phys. Rev. Lett. 47, 910–913 (1981).
[CrossRef]

Bjorkholm, J. E.

R. H. Stolen and J. E. Bjorkholm, "Parametric amplification and frequency conversion in optical fibers," IEEE J. Quantum Electron. QE-18, 1062–1072 (1982).
[CrossRef]

Desbois, J.

J. Desbois, F. Gires, and P. Tournois, "A new approach to picosecond laser pulse analysis shaping and coding," IEEE J. Quantum Electron. QE-9, 213–218 (1973).
[CrossRef]

Fisher, R. A.

R. A. Fisher, P. L. Kelley, and T. K. Gustafson, "Subpicosecond pulse generation using the optical Kerr effect," Appl. Phys. Lett. 14, 140–143 (1969).
[CrossRef]

Fork, R. L.

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, and W. J. Tomlinson, "Compression of femtosecond optical pulses," Appl. Phys. Lett. 40, 761–763 (1982).
[CrossRef]

R. L. Fork, O. E. Martinez, and J. P. Gordon, "Negative dispersion using pairs of prisms," Opt. Lett, (to be published).

Gires, F.

J. Desbois, F. Gires, and P. Tournois, "A new approach to picosecond laser pulse analysis shaping and coding," IEEE J. Quantum Electron. QE-9, 213–218 (1973).
[CrossRef]

Gloge, D.

Gordon, J. P.

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, and W. J. Tomlinson, "Extreme picosecond pulse narrowing by means of soliton effect in single-mode optical fibers," Opt. Lett. 8, 289–291 (1983).
[CrossRef] [PubMed]

W. J. Tomlinson, J. P. Gordon, P. W. Smith, and A. E. Kaplan, "Reflection of a gaussian beam at a nonlinear interface," Appl. Opt. 21, 2041–2051 (1982).
[CrossRef] [PubMed]

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, "Experimental observation of picosecond pulse narrowing and solitons in optical fibers," Phys. Rev. Lett. 45, 1095–1098 (1980).
[CrossRef]

R. L. Fork, O. E. Martinez, and J. P. Gordon, "Negative dispersion using pairs of prisms," Opt. Lett, (to be published).

Grischkowsky, D.

B. Nikolaus and D. Grischkowsky, "12Χ pulse compression using optical fibers," Appl. Phys. Lett. 42, 1–2 (1983); "90-fsec tunable optical pulses obtained by two-stage pulse compression," 43, 228–230 (1983).
[CrossRef]

D. Grischkowsky and A. C. Balant, "Optical pulse compression based on enhanced frequency chirping," Appl. Phys. Lett. 41, 1–3 (1982). In this reference the characteristic lengths zL and zS are related to the present z0 and zopt by zL = √3 z0 and zopt ≍ 2zs.
[CrossRef]

H. Nakatsuka, D. Grischkowsky, and A. C. Balant, "Nonlinear picosecond-pulse propagation through optical fibers with positive group velocity dispersion," Phys. Rev. Lett. 47, 910–913 (1981).
[CrossRef]

Gustafson, T. K.

R. A. Fisher, P. L. Kelley, and T. K. Gustafson, "Subpicosecond pulse generation using the optical Kerr effect," Appl. Phys. Lett. 14, 140–143 (1969).
[CrossRef]

Hasegawa, A.

A. Hasegawa and F. Tappert, "Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers, I. Anomalous dispersion," Appl. Phys. Lett. 23, 142–144 (1973).
[CrossRef]

Kaplan, A. E.

Kelley, P. L.

R. A. Fisher, P. L. Kelley, and T. K. Gustafson, "Subpicosecond pulse generation using the optical Kerr effect," Appl. Phys. Lett. 14, 140–143 (1969).
[CrossRef]

Lin, Chinlon

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

Martinez, O. E.

R. L. Fork, O. E. Martinez, and J. P. Gordon, "Negative dispersion using pairs of prisms," Opt. Lett, (to be published).

Meinel, R.

R. Meinel, "Generation of chirped pulses in optical fibers suitable for an effective pulse compression," Opt. Commun. 47, 343–346. (1983).
[CrossRef]

Mollenauer, L. F.

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, and W. J. Tomlinson, "Extreme picosecond pulse narrowing by means of soliton effect in single-mode optical fibers," Opt. Lett. 8, 289–291 (1983).
[CrossRef] [PubMed]

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, "Experimental observation of picosecond pulse narrowing and solitons in optical fibers," Phys. Rev. Lett. 45, 1095–1098 (1980).
[CrossRef]

Nakatsuka, H.

H. Nakatsuka, D. Grischkowsky, and A. C. Balant, "Nonlinear picosecond-pulse propagation through optical fibers with positive group velocity dispersion," Phys. Rev. Lett. 47, 910–913 (1981).
[CrossRef]

Nikolaus, B.

B. Nikolaus and D. Grischkowsky, "12Χ pulse compression using optical fibers," Appl. Phys. Lett. 42, 1–2 (1983); "90-fsec tunable optical pulses obtained by two-stage pulse compression," 43, 228–230 (1983).
[CrossRef]

Shank, C. V.

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, and W. J. Tomlinson, "Compression of femtosecond optical pulses," Appl. Phys. Lett. 40, 761–763 (1982).
[CrossRef]

Smith, P. W.

Smith, R. G.

Stolen, R. H.

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, and W. J. Tomlinson, "Extreme picosecond pulse narrowing by means of soliton effect in single-mode optical fibers," Opt. Lett. 8, 289–291 (1983).
[CrossRef] [PubMed]

R. H. Stolen and J. E. Bjorkholm, "Parametric amplification and frequency conversion in optical fibers," IEEE J. Quantum Electron. QE-18, 1062–1072 (1982).
[CrossRef]

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, and W. J. Tomlinson, "Compression of femtosecond optical pulses," Appl. Phys. Lett. 40, 761–763 (1982).
[CrossRef]

E. H. Turner and R. H. Stolen, "Fiber Faraday circulator or isolator," Opt. Lett. 6, 322–323 (1981).
[CrossRef] [PubMed]

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, "Experimental observation of picosecond pulse narrowing and solitons in optical fibers," Phys. Rev. Lett. 45, 1095–1098 (1980).
[CrossRef]

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

Tappert, F.

A. Hasegawa and F. Tappert, "Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers, I. Anomalous dispersion," Appl. Phys. Lett. 23, 142–144 (1973).
[CrossRef]

Tomlinson, W. J.

Tournois, P.

J. Desbois, F. Gires, and P. Tournois, "A new approach to picosecond laser pulse analysis shaping and coding," IEEE J. Quantum Electron. QE-9, 213–218 (1973).
[CrossRef]

Treacy, E. B.

E. B. Treacy, "Optical pulse compression with diffraction gratings," IEEE J. Quantum Electron. QE-5, 454–458 (1969).
[CrossRef]

Turner, E. H.

Yen, R.

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, and W. J. Tomlinson, "Compression of femtosecond optical pulses," Appl. Phys. Lett. 40, 761–763 (1982).
[CrossRef]

Appl. Opt. (3)

Appl. Phys. Lett. (5)

D. Grischkowsky and A. C. Balant, "Optical pulse compression based on enhanced frequency chirping," Appl. Phys. Lett. 41, 1–3 (1982). In this reference the characteristic lengths zL and zS are related to the present z0 and zopt by zL = √3 z0 and zopt ≍ 2zs.
[CrossRef]

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, and W. J. Tomlinson, "Compression of femtosecond optical pulses," Appl. Phys. Lett. 40, 761–763 (1982).
[CrossRef]

B. Nikolaus and D. Grischkowsky, "12Χ pulse compression using optical fibers," Appl. Phys. Lett. 42, 1–2 (1983); "90-fsec tunable optical pulses obtained by two-stage pulse compression," 43, 228–230 (1983).
[CrossRef]

R. A. Fisher, P. L. Kelley, and T. K. Gustafson, "Subpicosecond pulse generation using the optical Kerr effect," Appl. Phys. Lett. 14, 140–143 (1969).
[CrossRef]

A. Hasegawa and F. Tappert, "Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers, I. Anomalous dispersion," Appl. Phys. Lett. 23, 142–144 (1973).
[CrossRef]

IEEE J. Quantum Electron. (3)

R. H. Stolen and J. E. Bjorkholm, "Parametric amplification and frequency conversion in optical fibers," IEEE J. Quantum Electron. QE-18, 1062–1072 (1982).
[CrossRef]

E. B. Treacy, "Optical pulse compression with diffraction gratings," IEEE J. Quantum Electron. QE-5, 454–458 (1969).
[CrossRef]

J. Desbois, F. Gires, and P. Tournois, "A new approach to picosecond laser pulse analysis shaping and coding," IEEE J. Quantum Electron. QE-9, 213–218 (1973).
[CrossRef]

Opt. Commun. (1)

R. Meinel, "Generation of chirped pulses in optical fibers suitable for an effective pulse compression," Opt. Commun. 47, 343–346. (1983).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (1)

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

Phys. Rev. Lett. (2)

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, "Experimental observation of picosecond pulse narrowing and solitons in optical fibers," Phys. Rev. Lett. 45, 1095–1098 (1980).
[CrossRef]

H. Nakatsuka, D. Grischkowsky, and A. C. Balant, "Nonlinear picosecond-pulse propagation through optical fibers with positive group velocity dispersion," Phys. Rev. Lett. 47, 910–913 (1981).
[CrossRef]

Other (1)

R. L. Fork, O. E. Martinez, and J. P. Gordon, "Negative dispersion using pairs of prisms," Opt. Lett, (to be published).

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Figures (10)

Fig. 1
Fig. 1

Perspective plots of (a) the temporal and (b) the spectral shapes of a pulse as a function of normalized distance along a fiber for the case of normal (positive) GVD and a normalized peak amplitude A = 5.

Fig. 2
Fig. 2

Various measures of the output pulse for a normalized fiber length z/z0 = 0.5 with A = 5. (a) Intensity as a function of time. (b) Instantaneous frequency as a function of time. (c) Intensity as a function of frequency [Fourier transform of (a)]. (d) Phase of the Fourier transform as a function of frequency.

Fig. 3
Fig. 3

(a) Pulse compression and (b) pulse quality as functions of fiber length for various normalized pulse amplitudes for the case of an ideal compressor.

Fig. 4
Fig. 4

Pulse-compression results from Fig. 3 replotted as functions of the parameter A2z/z0 for comparison with results for the case of zero GVD.

Fig. 5
Fig. 5

Compressed pulse shapes with an ideal compressor. (a) A = 5, z/z0 = 0.5. (b) A2z/z0 = 4.5, zero GVD.

Fig. 6
Fig. 6

Various measures of the output pulse in the absence of GVD for A2z/z0 =4.5. (a) Intensity as a function of time. (b) Instantaneous frequency as a function of time. (c) Intensity as a function of frequency [Fourier transform of (a)]. (d) Phase of the Fourier transform as a function of frequency.

Fig. 7
Fig. 7

Various parameters of the compressed pulse as functions of the quadratic compressor factor for the case A = 10, z/z0 = 0.24. The quantity Ilobe is the peak intensity of the first sidelobe relative to the peak intensity of the input pulse.

Fig. 8
Fig. 8

(a) Pulse compression and (b) pulse quality as functions of fiber length for various normalized pulse amplitudes for the case of an optimum quadratic compressor.

Fig. 9
Fig. 9

Calculated pulse shapes for soliton compression at the point of optimal narrowing (from Ref. 8).

Fig. 10
Fig. 10

Plot of D(λ)λ/(0.322π2c2) as a function of wavelength for fused silica. The normalized length z0 is obtained in meters by dividing the square of the initial pulse length (FWHM) in picoseconds by the value from the graph.

Tables (2)

Tables Icon

Table 1 Optimum Normalized Fiber Lengths, Pulse Compressions, and Required Quadratic Compressor Factors for Various Normalized Pulse Amplitudesa

Tables Icon

Table 2 Estimated Values of Optimum Fiber Length, Grating Separation, and Pulse Compression for Several Initial Pulse Lengths and Powersa

Equations (21)

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

i V ( z / z 0 ) = π 4 [ 2 V ( t / t 0 ) 2 + 2 V 2 V ] ,
V ( z = 0 , t ) = A sech ( t / t 0 ) .
z 0 = 0.322 π 2 c 2 τ 0 2 D ( λ ) λ
A = P / P 1 ,
P 1 = n c λ A eff 16 π z 0 n 2 × 10 - 7 W ,
V ( z , ω ) = A ( ω ) e i Φ ( ω ) ,
V c ( z , ω ) = A ( ω ) exp { i [ Φ ( ω ) + Φ c ( ω ) ] } .
Φ c ( ω ) = Φ 0 - a ω 2 .
τ 0 / τ 0.63 A ,
z opt / z 0 1.6 / A ,
a 0 / t 0 2 τ / τ 0 1.6 / A .
τ 0 / τ 1 + 0.9 ( A 2 z / z 0 ) ,
a 0 / t 0 2 0.25 ( A 2 z / z 0 ) - 1
A 2 = A 1 ( η I peak ( τ 0 / τ 1 ) 2 ) 1 / 2 = A 1 ( η I peak τ 1 / τ 0 τ 0 / τ 1 ) 1 / 2 ,
A 2 1.3 ( η A 1 ) 1 / 2 ,
τ 1 / τ 2 ( η τ 0 / τ 1 ) 1 / 2 .
z 0 = τ 0 2 0.117 ( m - 1 psec 2 ) .
a 0 = b λ 3 4 π c 2 d 2 cos 2 γ .
b 6.4 π c 2 d 2 cos 2 γ λ 3 ( t 0 2 A ) .
b 84 cm psec 2 ( τ 0 2 A ) .
g P L / A eff 16 ,

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