Abstract

The propagation of ultrashort light pulses in fibers with saturable nonlinearity and positive group-velocity dispersion has been investigated. Using a variational approach, frequency chirp and the other main characteristics of pulse evolution are studied. The minimum duration of the output-pulse of a fiber-grating compressor is calculated.

© 1991 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. 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]
  2. I. G. Fujimoto, A. M. Weiner, and E. P. Ippen, “Generation and measurement of optical pulses as short as 16 fs,” Appl. Phys. Lett. 45, 832–834 (1984).
    [CrossRef]
  3. J. M. Halbout and D. Grischkowsky, “12-fs ultrashort optical pulse compression at high repetition rate,” Appl. Phys. Lett. 45, 1281–1283 (1984).
    [CrossRef]
  4. W. H. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, C. V. Shank, and J. A. Valdmanis, “Optical pulse compression to 8 fs at a 5-kHz repetition rate,” Appl. Phys. Lett. 46, 1120–1121 (1985).
    [CrossRef]
  5. R. L. Fork, C. H. Brito-Cruz, P. C. Becker, and C. V. Shank, “Compression of optical pulses to 6 fsec using cubic phase competition,” Opt. Lett. 12, 483–485 (1987).
    [CrossRef] [PubMed]
  6. A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers,” Appl. Phys. Lett. 23, 142–144 (1973).
    [CrossRef]
  7. L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Lett. 45, 1095–1097 (1987).
    [CrossRef]
  8. A. Hasegawa, “Numerical study of optical soliton transmission amplified periodically by the stimulated Raman process,” Appl. Opt. 23, 3302–3309 (1984).
    [CrossRef] [PubMed]
  9. L. F. Mollenauer and K. Smith, “Demonstration of soliton transmission over more than 4000 km in fiber with loss periodically compensated by Raman gain,” Opt. Lett. 8, 675–677 (1988).
    [CrossRef]
  10. D. Grischkowsky and A. C. Balant, “Optical pulse compression based on enhanced frequency chirping,” Appl. Phys. Lett. 41, 1–3 (1982).
    [CrossRef]
  11. R. Meinel, “Generation of chirped pulses in optical fibers suitable for an effective pulse compression,” Opt. Commun. 47, 343–346 (1983).
    [CrossRef]
  12. W. J. Tomlinson, R. H. Stolen, and C. V. Shank, “Compression of optical pulses in fibers,” J. Opt. Soc. Am. B 1, 139–149 (1984).
    [CrossRef]
  13. D. Anderson, “Variational approach to nonlinear pulse propagation in optical fibers,” Phys. Rev. A 27, 3135–3145 (1983).
    [CrossRef]
  14. E. B. Treacy, “Optical pulse compression with diffraction gratings,” IEEE J. Quantum Electron. QE-5, 454–458 (1969).
    [CrossRef]
  15. J. Herrmann and B. Wilhelmi, Lasers for Ultrashort Pulses (North-Holland, Amsterdam, 1987).

1988 (1)

L. F. Mollenauer and K. Smith, “Demonstration of soliton transmission over more than 4000 km in fiber with loss periodically compensated by Raman gain,” Opt. Lett. 8, 675–677 (1988).
[CrossRef]

1987 (2)

R. L. Fork, C. H. Brito-Cruz, P. C. Becker, and C. V. Shank, “Compression of optical pulses to 6 fsec using cubic phase competition,” Opt. Lett. 12, 483–485 (1987).
[CrossRef] [PubMed]

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Lett. 45, 1095–1097 (1987).
[CrossRef]

1985 (1)

W. H. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, C. V. Shank, and J. A. Valdmanis, “Optical pulse compression to 8 fs at a 5-kHz repetition rate,” Appl. Phys. Lett. 46, 1120–1121 (1985).
[CrossRef]

1984 (4)

I. G. Fujimoto, A. M. Weiner, and E. P. Ippen, “Generation and measurement of optical pulses as short as 16 fs,” Appl. Phys. Lett. 45, 832–834 (1984).
[CrossRef]

J. M. Halbout and D. Grischkowsky, “12-fs ultrashort optical pulse compression at high repetition rate,” Appl. Phys. Lett. 45, 1281–1283 (1984).
[CrossRef]

A. Hasegawa, “Numerical study of optical soliton transmission amplified periodically by the stimulated Raman process,” Appl. Opt. 23, 3302–3309 (1984).
[CrossRef] [PubMed]

W. J. Tomlinson, R. H. Stolen, and C. V. Shank, “Compression of optical pulses in fibers,” J. Opt. Soc. Am. B 1, 139–149 (1984).
[CrossRef]

1983 (2)

D. Anderson, “Variational approach to nonlinear pulse propagation in optical fibers,” Phys. Rev. A 27, 3135–3145 (1983).
[CrossRef]

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

1982 (2)

D. Grischkowsky and A. C. Balant, “Optical pulse compression based on enhanced frequency chirping,” Appl. Phys. Lett. 41, 1–3 (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]

1973 (1)

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

1969 (1)

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

Anderson, D.

D. Anderson, “Variational approach to nonlinear pulse propagation in optical fibers,” Phys. Rev. A 27, 3135–3145 (1983).
[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).
[CrossRef]

Becker, P. C.

Brito-Cruz, C. H.

Downer, M. C.

W. H. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, C. V. Shank, and J. A. Valdmanis, “Optical pulse compression to 8 fs at a 5-kHz repetition rate,” Appl. Phys. Lett. 46, 1120–1121 (1985).
[CrossRef]

Fork, R. L.

R. L. Fork, C. H. Brito-Cruz, P. C. Becker, and C. V. Shank, “Compression of optical pulses to 6 fsec using cubic phase competition,” Opt. Lett. 12, 483–485 (1987).
[CrossRef] [PubMed]

W. H. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, C. V. Shank, and J. A. Valdmanis, “Optical pulse compression to 8 fs at a 5-kHz repetition rate,” Appl. Phys. Lett. 46, 1120–1121 (1985).
[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]

Fujimoto, I. G.

I. G. Fujimoto, A. M. Weiner, and E. P. Ippen, “Generation and measurement of optical pulses as short as 16 fs,” Appl. Phys. Lett. 45, 832–834 (1984).
[CrossRef]

Gordon, J. P.

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Lett. 45, 1095–1097 (1987).
[CrossRef]

Grischkowsky, D.

J. M. Halbout and D. Grischkowsky, “12-fs ultrashort optical pulse compression at high repetition rate,” Appl. Phys. Lett. 45, 1281–1283 (1984).
[CrossRef]

D. Grischkowsky and A. C. Balant, “Optical pulse compression based on enhanced frequency chirping,” Appl. Phys. Lett. 41, 1–3 (1982).
[CrossRef]

Halbout, J. M.

J. M. Halbout and D. Grischkowsky, “12-fs ultrashort optical pulse compression at high repetition rate,” Appl. Phys. Lett. 45, 1281–1283 (1984).
[CrossRef]

Hasegawa, A.

A. Hasegawa, “Numerical study of optical soliton transmission amplified periodically by the stimulated Raman process,” Appl. Opt. 23, 3302–3309 (1984).
[CrossRef] [PubMed]

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

Herrmann, J.

J. Herrmann and B. Wilhelmi, Lasers for Ultrashort Pulses (North-Holland, Amsterdam, 1987).

Ippen, E. P.

I. G. Fujimoto, A. M. Weiner, and E. P. Ippen, “Generation and measurement of optical pulses as short as 16 fs,” Appl. Phys. Lett. 45, 832–834 (1984).
[CrossRef]

Knox, W. H.

W. H. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, C. V. Shank, and J. A. Valdmanis, “Optical pulse compression to 8 fs at a 5-kHz repetition rate,” Appl. Phys. Lett. 46, 1120–1121 (1985).
[CrossRef]

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 and K. Smith, “Demonstration of soliton transmission over more than 4000 km in fiber with loss periodically compensated by Raman gain,” Opt. Lett. 8, 675–677 (1988).
[CrossRef]

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Lett. 45, 1095–1097 (1987).
[CrossRef]

Shank, C. V.

R. L. Fork, C. H. Brito-Cruz, P. C. Becker, and C. V. Shank, “Compression of optical pulses to 6 fsec using cubic phase competition,” Opt. Lett. 12, 483–485 (1987).
[CrossRef] [PubMed]

W. H. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, C. V. Shank, and J. A. Valdmanis, “Optical pulse compression to 8 fs at a 5-kHz repetition rate,” Appl. Phys. Lett. 46, 1120–1121 (1985).
[CrossRef]

W. J. Tomlinson, R. H. Stolen, and C. V. Shank, “Compression of optical pulses in fibers,” J. Opt. Soc. Am. B 1, 139–149 (1984).
[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]

Smith, K.

L. F. Mollenauer and K. Smith, “Demonstration of soliton transmission over more than 4000 km in fiber with loss periodically compensated by Raman gain,” Opt. Lett. 8, 675–677 (1988).
[CrossRef]

Stolen, R. H.

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Lett. 45, 1095–1097 (1987).
[CrossRef]

W. H. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, C. V. Shank, and J. A. Valdmanis, “Optical pulse compression to 8 fs at a 5-kHz repetition rate,” Appl. Phys. Lett. 46, 1120–1121 (1985).
[CrossRef]

W. J. Tomlinson, R. H. Stolen, and C. V. Shank, “Compression of optical pulses in fibers,” J. Opt. Soc. Am. B 1, 139–149 (1984).
[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]

Tappert, F.

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

Tomlinson, W. J.

W. J. Tomlinson, R. H. Stolen, and C. V. Shank, “Compression of optical pulses in fibers,” J. Opt. Soc. Am. B 1, 139–149 (1984).
[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]

Treacy, E. B.

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

Valdmanis, J. A.

W. H. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, C. V. Shank, and J. A. Valdmanis, “Optical pulse compression to 8 fs at a 5-kHz repetition rate,” Appl. Phys. Lett. 46, 1120–1121 (1985).
[CrossRef]

Weiner, A. M.

I. G. Fujimoto, A. M. Weiner, and E. P. Ippen, “Generation and measurement of optical pulses as short as 16 fs,” Appl. Phys. Lett. 45, 832–834 (1984).
[CrossRef]

Wilhelmi, B.

J. Herrmann and B. Wilhelmi, Lasers for Ultrashort Pulses (North-Holland, Amsterdam, 1987).

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. (1)

Appl. Phys. Lett. (6)

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

I. G. Fujimoto, A. M. Weiner, and E. P. Ippen, “Generation and measurement of optical pulses as short as 16 fs,” Appl. Phys. Lett. 45, 832–834 (1984).
[CrossRef]

J. M. Halbout and D. Grischkowsky, “12-fs ultrashort optical pulse compression at high repetition rate,” Appl. Phys. Lett. 45, 1281–1283 (1984).
[CrossRef]

W. H. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, C. V. Shank, and J. A. Valdmanis, “Optical pulse compression to 8 fs at a 5-kHz repetition rate,” Appl. Phys. Lett. 46, 1120–1121 (1985).
[CrossRef]

D. Grischkowsky and A. C. Balant, “Optical pulse compression based on enhanced frequency chirping,” Appl. Phys. Lett. 41, 1–3 (1982).
[CrossRef]

IEEE J. Quantum Electron. (1)

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

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

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)

R. L. Fork, C. H. Brito-Cruz, P. C. Becker, and C. V. Shank, “Compression of optical pulses to 6 fsec using cubic phase competition,” Opt. Lett. 12, 483–485 (1987).
[CrossRef] [PubMed]

L. F. Mollenauer and K. Smith, “Demonstration of soliton transmission over more than 4000 km in fiber with loss periodically compensated by Raman gain,” Opt. Lett. 8, 675–677 (1988).
[CrossRef]

Phys. Lett. (1)

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Lett. 45, 1095–1097 (1987).
[CrossRef]

Phys. Rev. A (1)

D. Anderson, “Variational approach to nonlinear pulse propagation in optical fibers,” Phys. Rev. A 27, 3135–3145 (1983).
[CrossRef]

Other (1)

J. Herrmann and B. Wilhelmi, Lasers for Ultrashort Pulses (North-Holland, Amsterdam, 1987).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (1)

Fig. 1
Fig. 1

Duration of the output pulse of a fiber-grating compressor relative to the input field strength B0 for different saturation parameters x = 6.5 × 10−16 m/V2, kL″ = 6.5 × 10−26 s2/m, and ω = 3 × 1015 s. Curve 1, Δnsat → ∞ (γ → 0). Curves 2, Δnsat = 10−3 (γ = 6.5 × 10−20 m2/V2. Curves 3, Δnsat = 10−4 (γ = 6.5 × 10−19 m2/V2). Curves 4, Δnsat = 10−5 (γ = 6.5 × 10−18 m2/V2). The index a is related to Eq. (23) (rectangular shape); index b to relation (26) (square root of a hyperbolic-secant shape).

Tables (1)

Tables Icon

Table 1 Numerical Factors for Various Pulse-Shape Functions

Equations (31)

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

τ L = ( k L x ) 1 / 2 C 1 A 0 ,
i A z + k L 2 2 A η 2 - x A 2 1 + γ A 2 A = 0 ,
δ d z d η L ( A , A * , A z , A * z , A η , A * η ) = 0.
L = i 2 ( A A * z - A * A z ) + k L 2 | A η | 2 + x γ [ A 2 - 1 γ ln ( 1 + γ A 2 ) ] .
A ( z , η ) = B ( z ) exp [ i ψ ( z ) + i β ( z ) η 2 ] f [ η / τ L ( z ) ] .
f ( η / τ L ) = { 1 for     η / τ L 1 / 2 0 for     η / τ L > 1 , 2 ,
f ( η / τ L ) = [ sech ( 2.64 η / τ L ) ] 1 / 2 .
L = d ψ d z B 2 τ L J 0 + d β d z τ L 3 B 2 J 2 + k L 2 ( S 0 τ L + 4 β 2 τ L 3 J 2 ) + x τ L γ ( B 2 J 0 - Q γ ) .
J 0 = - f 2 ( t ) d t ,             J 2 = - t 2 f 2 ( t ) d t , S 0 = - ( f t ) 2 d t ,             Q = - ln [ 1 + γ B 2 f 2 ( t ) ] d t .
τ L ( z ) B 2 ( z ) = τ L 0 B 0 2 ,
H - k L 2 ( S 0 τ L + 4 β 2 τ L 3 J 2 ) B 2 - x τ L γ ( B 2 J 0 - Q γ ) = H 0 ( z = 0 ) .
β = 1 2 k L 1 y d y d z ,
1 2 ( d y d z ) 2 + U ( y ) = 0 ,
U ( y ) = 12 k L x τ L 0 2 γ 2 B 0 2 [ ln ( 1 + γ B 0 2 ) - y ln ( 1 + γ B 0 2 y ) ] ;
U ( y ) = 1.23 k L 2 τ L 0 4 ( 1 y 2 - 1 ) + 0.9 x k L γ 2 B 0 2 τ L 0 2 { π 2 4 ( 1 - y ) + y [ arccos ( γ B 0 2 y ) 2 ] 2 - [ arccos ( γ B 0 2 ) ] 2 } .
z > τ L 0 ( x k L B 0 2 ) 1 / 2 ,
y = τ L τ L 0 1 ,             γ B 0 2 y 1 ,
τ L F ( z ) = z { 24 k L x γ [ 1 - 1 γ B 0 2 ln ( 1 + γ B 0 2 ) ] } 1 / 2 .
β = 1 2 k L z ,
B ( z ) = B 0 τ L 0 γ 4 z { 24 k L x [ 1 - 1 γ B 0 2 ln ( 1 + γ B 0 2 ) ] } 1 / 4 .
A L g ( η ) = 1 + i 2 π - d η A L F ( η ) exp [ i ( η - η ) 2 ( 2 ψ ) - 1 ] ,
ψ = - λ 2 L g 2 π c 2 d 2 ( cos δ ) 2
ψ = 1 2 β = k L z
τ out = 2.78 β τ L F ( z ) = 1.13 k L γ x [ 1 - 1 γ B 0 2 ln ( 1 + γ B 0 2 ) ] ,
τ out min = C 2 k L γ x = C 2 k L c Δ n sat ω ,
τ L F = z { 2.48 k L 2 τ L 0 2 + 1.8 x k L γ 2 B 0 2 × [ π γ B 0 2 + ( arccos γ B 0 2 ) 2 - π 2 4 ] } 1 / 2 .
τ out 1 β τ L F ( z ) = 0.84 k L γ x { 1 + 1 π γ B 0 2 [ ( arccos γ B 0 2 ) 2 - π 2 4 ] } 1 / 2 .
i A z = - k L 2 2 A η 2 + x A 2 A + x 4 A 4 A .
τ out = r β ( z ) τ L F ( z ) = c 1 k L x B 0 ( 1 + 2 x 4 B 0 2 P 2 3 x P 1 ) 1 / 2 ,
P 1 = - f 4 ( t ) d t ,             P 2 = - f 6 ( t ) d t ,             c 1 = 2 r J 2 P 1 .
C 2 = r 8 P 2 J 2 3 P 1 .

Metrics