Abstract

Adiabatic soliton compression is an attractive optical pulse compression scheme that relies on monotonic decreasing of the fiber dispersion along the soliton’s propagation path. This scheme requires kilometers of specialty fiber, and only a few dispersion profiles are practically feasible. We propose adiabatic soliton compression in a nonuniform fiber Bragg grating. The Bragg soliton propagates in the passband of a grating, where one or more of its parameters (e.g., the grating pitch) varies along the propagation direction. The capability of manufacturing almost arbitrary grating profiles and hence engineering practically any dispersion profile makes this all-fiber pulse compressor, which is to our knowledge novel, a very versatile component. Additionally, the large dispersion in the spectral vicinity of the grating stop band leads to very short devices (tens of centimeters as opposed to kilometers).

© 1998 Optical Society of America

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References

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  1. L. F. Mollenauer, J. P. Gordon, and P. V. Mamyshev, “Solitons in high bit-rate, long-distance transmission,” in Optical Fiber Telecommunications IIIA, I. P. Kaminow and T. L. Koch, eds. (Academic, San Diego, Calif., 1997).
  2. See, e.g., N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibres with periodic dispersion management,” Electron. Lett. 32, 54–55 (1996).
    [CrossRef]
  3. S. V. Chernikov and P. V. Mamyshev, “Femtosecond soliton propagation in fibers with slowly decreasing dispersion,” J. Opt. Soc. Am. B 8, 1633–1641 (1991); P. V. Mamyshev, S. V. Chernikov, and E. M. Dianov, “Generation of fundamental soliton trains for high-bit-rate optical fiber communication lines,” IEEE J. Quantum Electron. 27, 2347–2355 (1991).
    [CrossRef]
  4. F. Forghieri, R. W. Tkach, and A. R. Chraplyvy, “Fiber nonlinearities and their impact on transmission systems,” in Optical Fiber Telecommunications IIIA, I. P. Kaminow and T. L. Koch, eds. (Academic, San Diego, Calif., 1997), and references therein.
  5. See, e.g., S. V. Chernikov, J. R. Taylor, and R. Kashyap, “Experimental demonstration of step-like dispersion profiling in optical fibre for soliton pulse generation and compression,” Electron. Lett. 30, 433–435 (1994).
    [CrossRef]
  6. J. D. Moores, “Nonlinear compression of chirped solitary waves with and without phase modulation,” Opt. Lett. 21, 555–557 (1996).
    [CrossRef] [PubMed]
  7. B. J. Eggleton, T. Stephens, P. A. Krug, G. Dhosi, Z. Brodzeli, and F. Ouelette, “Dispersion compensation over 100 km at 10 Gbit/s using a fiber grating in transmission,” Electron. Lett. 32, 1610–1611 (1996).
    [CrossRef]
  8. N. M. Litchinitser, B. J. Eggleton, and D. B. Patterson, “Fiber Bragg gratings for dispersion compensation in transmission: theoretical model and design criteria for nearly ideal pulse compression,” J. Lightwave Technol. 15, 1303–1313 (1997).
    [CrossRef]
  9. B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996); B. J. Eggleton, C. M. de Sterke, and R. E. Slusher, “Nonlinear pulse propagation in Bragg gratings,” J. Opt. Soc. Am. B 14, 2980–2993 (1997).
    [CrossRef] [PubMed]
  10. C. M. de Sterke and J. E. Sipe, “Gap solitons,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1994), Vol. 33.
  11. G. Lenz, B. J. Eggleton, and N. Litchinitser, “Pulse compression using fiber gratings as highly dispersive nonlinear elements,” J. Opt. Soc. Am. B 15, 715–721 (1998).
    [CrossRef]
  12. F. Ouellette, “Dispersion cancellation using linearly chirped Bragg grating filters in optical waveguides,” Opt. Lett. 12, 847–849 (1987); J. E. Sipe, L. Poladian, and C. M. de Sterke, “Propagation through nonuniform grating structures,” J. Opt. Soc. Am. A 11, 1307–1320 (1994).
    [CrossRef] [PubMed]
  13. G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989).
  14. A. B. Aceves and S. Wabnitz, “Self-induced transparency solitons in nonlinear refractive periodic media,” Phys. Lett. A 141, 37–42 (1989).
    [CrossRef]
  15. P. C. Hill and B. J. Eggleton, “Strain gradient chirp of fiber Bragg grating,” Electron. Lett. 30, 1172–1174 (1994).
    [CrossRef]
  16. J. Lauzon, S. Thibault, J. Martin, and F. Ouellette, “Implementation and characterization of fiber Bragg gratings linearly chirped by temperature gradient,” Opt. Lett. 19, 2027–2029 (1994).
    [CrossRef] [PubMed]
  17. P. St. J. Russell, “Bloch wave analysis of dispersion and pulse propagation in pure distributed feedback structures,” J. Mod. Opt. 38, 1599–1619 (1991); erratum, J. Mod. Opt. 41, 163–164 (1994).
    [CrossRef]
  18. C. M. de Sterke, N. G. Broderick, B. J. Eggleton, and M. J. Steel, “Nonlinear optics in fiber gratings,” Opt. Fiber Technol. 2, 253–268 (1996).
    [CrossRef]
  19. B. J. Eggleton, C. M. de Sterke, A. Aceves, J. E. Sipe, T. A. Strasser, and R. E. Slusher, “Modulational instabilities and tunable multiple soliton generation in apodized fiber gratings,” Opt. Commun. 149, 267–271 (1998).
    [CrossRef]
  20. B. J. Eggleton, G. Lenz, R. E. Slusher, and N. M. Litchinitser, “Compression of optical pulses spectrally broadened by self-phase modulation with a fiber Bragg grating in transmission,” Appl. Opt. 30, 7055–7061 (1998).
    [CrossRef]
  21. M. Asobe, “Nonlinear optical properties of chalcogenide glass fibers and their application to all-optical switching,” Opt. Fiber Technol. 3, 142–148 (1997).
    [CrossRef]

1998 (3)

B. J. Eggleton, C. M. de Sterke, A. Aceves, J. E. Sipe, T. A. Strasser, and R. E. Slusher, “Modulational instabilities and tunable multiple soliton generation in apodized fiber gratings,” Opt. Commun. 149, 267–271 (1998).
[CrossRef]

B. J. Eggleton, G. Lenz, R. E. Slusher, and N. M. Litchinitser, “Compression of optical pulses spectrally broadened by self-phase modulation with a fiber Bragg grating in transmission,” Appl. Opt. 30, 7055–7061 (1998).
[CrossRef]

G. Lenz, B. J. Eggleton, and N. Litchinitser, “Pulse compression using fiber gratings as highly dispersive nonlinear elements,” J. Opt. Soc. Am. B 15, 715–721 (1998).
[CrossRef]

1997 (2)

M. Asobe, “Nonlinear optical properties of chalcogenide glass fibers and their application to all-optical switching,” Opt. Fiber Technol. 3, 142–148 (1997).
[CrossRef]

N. M. Litchinitser, B. J. Eggleton, and D. B. Patterson, “Fiber Bragg gratings for dispersion compensation in transmission: theoretical model and design criteria for nearly ideal pulse compression,” J. Lightwave Technol. 15, 1303–1313 (1997).
[CrossRef]

1996 (4)

C. M. de Sterke, N. G. Broderick, B. J. Eggleton, and M. J. Steel, “Nonlinear optics in fiber gratings,” Opt. Fiber Technol. 2, 253–268 (1996).
[CrossRef]

See, e.g., N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibres with periodic dispersion management,” Electron. Lett. 32, 54–55 (1996).
[CrossRef]

J. D. Moores, “Nonlinear compression of chirped solitary waves with and without phase modulation,” Opt. Lett. 21, 555–557 (1996).
[CrossRef] [PubMed]

B. J. Eggleton, T. Stephens, P. A. Krug, G. Dhosi, Z. Brodzeli, and F. Ouelette, “Dispersion compensation over 100 km at 10 Gbit/s using a fiber grating in transmission,” Electron. Lett. 32, 1610–1611 (1996).
[CrossRef]

1994 (3)

P. C. Hill and B. J. Eggleton, “Strain gradient chirp of fiber Bragg grating,” Electron. Lett. 30, 1172–1174 (1994).
[CrossRef]

J. Lauzon, S. Thibault, J. Martin, and F. Ouellette, “Implementation and characterization of fiber Bragg gratings linearly chirped by temperature gradient,” Opt. Lett. 19, 2027–2029 (1994).
[CrossRef] [PubMed]

See, e.g., S. V. Chernikov, J. R. Taylor, and R. Kashyap, “Experimental demonstration of step-like dispersion profiling in optical fibre for soliton pulse generation and compression,” Electron. Lett. 30, 433–435 (1994).
[CrossRef]

1989 (1)

A. B. Aceves and S. Wabnitz, “Self-induced transparency solitons in nonlinear refractive periodic media,” Phys. Lett. A 141, 37–42 (1989).
[CrossRef]

Aceves, A.

B. J. Eggleton, C. M. de Sterke, A. Aceves, J. E. Sipe, T. A. Strasser, and R. E. Slusher, “Modulational instabilities and tunable multiple soliton generation in apodized fiber gratings,” Opt. Commun. 149, 267–271 (1998).
[CrossRef]

Aceves, A. B.

A. B. Aceves and S. Wabnitz, “Self-induced transparency solitons in nonlinear refractive periodic media,” Phys. Lett. A 141, 37–42 (1989).
[CrossRef]

Asobe, M.

M. Asobe, “Nonlinear optical properties of chalcogenide glass fibers and their application to all-optical switching,” Opt. Fiber Technol. 3, 142–148 (1997).
[CrossRef]

Bennion, I.

See, e.g., N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibres with periodic dispersion management,” Electron. Lett. 32, 54–55 (1996).
[CrossRef]

Blow, K. J.

See, e.g., N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibres with periodic dispersion management,” Electron. Lett. 32, 54–55 (1996).
[CrossRef]

Broderick, N. G.

C. M. de Sterke, N. G. Broderick, B. J. Eggleton, and M. J. Steel, “Nonlinear optics in fiber gratings,” Opt. Fiber Technol. 2, 253–268 (1996).
[CrossRef]

Brodzeli, Z.

B. J. Eggleton, T. Stephens, P. A. Krug, G. Dhosi, Z. Brodzeli, and F. Ouelette, “Dispersion compensation over 100 km at 10 Gbit/s using a fiber grating in transmission,” Electron. Lett. 32, 1610–1611 (1996).
[CrossRef]

Chernikov, S. V.

See, e.g., S. V. Chernikov, J. R. Taylor, and R. Kashyap, “Experimental demonstration of step-like dispersion profiling in optical fibre for soliton pulse generation and compression,” Electron. Lett. 30, 433–435 (1994).
[CrossRef]

de Sterke, C. M.

B. J. Eggleton, C. M. de Sterke, A. Aceves, J. E. Sipe, T. A. Strasser, and R. E. Slusher, “Modulational instabilities and tunable multiple soliton generation in apodized fiber gratings,” Opt. Commun. 149, 267–271 (1998).
[CrossRef]

C. M. de Sterke, N. G. Broderick, B. J. Eggleton, and M. J. Steel, “Nonlinear optics in fiber gratings,” Opt. Fiber Technol. 2, 253–268 (1996).
[CrossRef]

Dhosi, G.

B. J. Eggleton, T. Stephens, P. A. Krug, G. Dhosi, Z. Brodzeli, and F. Ouelette, “Dispersion compensation over 100 km at 10 Gbit/s using a fiber grating in transmission,” Electron. Lett. 32, 1610–1611 (1996).
[CrossRef]

Doran, N. J.

See, e.g., N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibres with periodic dispersion management,” Electron. Lett. 32, 54–55 (1996).
[CrossRef]

Eggleton, B. J.

G. Lenz, B. J. Eggleton, and N. Litchinitser, “Pulse compression using fiber gratings as highly dispersive nonlinear elements,” J. Opt. Soc. Am. B 15, 715–721 (1998).
[CrossRef]

B. J. Eggleton, C. M. de Sterke, A. Aceves, J. E. Sipe, T. A. Strasser, and R. E. Slusher, “Modulational instabilities and tunable multiple soliton generation in apodized fiber gratings,” Opt. Commun. 149, 267–271 (1998).
[CrossRef]

B. J. Eggleton, G. Lenz, R. E. Slusher, and N. M. Litchinitser, “Compression of optical pulses spectrally broadened by self-phase modulation with a fiber Bragg grating in transmission,” Appl. Opt. 30, 7055–7061 (1998).
[CrossRef]

N. M. Litchinitser, B. J. Eggleton, and D. B. Patterson, “Fiber Bragg gratings for dispersion compensation in transmission: theoretical model and design criteria for nearly ideal pulse compression,” J. Lightwave Technol. 15, 1303–1313 (1997).
[CrossRef]

C. M. de Sterke, N. G. Broderick, B. J. Eggleton, and M. J. Steel, “Nonlinear optics in fiber gratings,” Opt. Fiber Technol. 2, 253–268 (1996).
[CrossRef]

B. J. Eggleton, T. Stephens, P. A. Krug, G. Dhosi, Z. Brodzeli, and F. Ouelette, “Dispersion compensation over 100 km at 10 Gbit/s using a fiber grating in transmission,” Electron. Lett. 32, 1610–1611 (1996).
[CrossRef]

P. C. Hill and B. J. Eggleton, “Strain gradient chirp of fiber Bragg grating,” Electron. Lett. 30, 1172–1174 (1994).
[CrossRef]

Hill, P. C.

P. C. Hill and B. J. Eggleton, “Strain gradient chirp of fiber Bragg grating,” Electron. Lett. 30, 1172–1174 (1994).
[CrossRef]

Kashyap, R.

See, e.g., S. V. Chernikov, J. R. Taylor, and R. Kashyap, “Experimental demonstration of step-like dispersion profiling in optical fibre for soliton pulse generation and compression,” Electron. Lett. 30, 433–435 (1994).
[CrossRef]

Knox, F. M.

See, e.g., N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibres with periodic dispersion management,” Electron. Lett. 32, 54–55 (1996).
[CrossRef]

Krug, P. A.

B. J. Eggleton, T. Stephens, P. A. Krug, G. Dhosi, Z. Brodzeli, and F. Ouelette, “Dispersion compensation over 100 km at 10 Gbit/s using a fiber grating in transmission,” Electron. Lett. 32, 1610–1611 (1996).
[CrossRef]

Lauzon, J.

Lenz, G.

B. J. Eggleton, G. Lenz, R. E. Slusher, and N. M. Litchinitser, “Compression of optical pulses spectrally broadened by self-phase modulation with a fiber Bragg grating in transmission,” Appl. Opt. 30, 7055–7061 (1998).
[CrossRef]

G. Lenz, B. J. Eggleton, and N. Litchinitser, “Pulse compression using fiber gratings as highly dispersive nonlinear elements,” J. Opt. Soc. Am. B 15, 715–721 (1998).
[CrossRef]

Litchinitser, N.

Litchinitser, N. M.

B. J. Eggleton, G. Lenz, R. E. Slusher, and N. M. Litchinitser, “Compression of optical pulses spectrally broadened by self-phase modulation with a fiber Bragg grating in transmission,” Appl. Opt. 30, 7055–7061 (1998).
[CrossRef]

N. M. Litchinitser, B. J. Eggleton, and D. B. Patterson, “Fiber Bragg gratings for dispersion compensation in transmission: theoretical model and design criteria for nearly ideal pulse compression,” J. Lightwave Technol. 15, 1303–1313 (1997).
[CrossRef]

Martin, J.

Moores, J. D.

Ouelette, F.

B. J. Eggleton, T. Stephens, P. A. Krug, G. Dhosi, Z. Brodzeli, and F. Ouelette, “Dispersion compensation over 100 km at 10 Gbit/s using a fiber grating in transmission,” Electron. Lett. 32, 1610–1611 (1996).
[CrossRef]

Ouellette, F.

Patterson, D. B.

N. M. Litchinitser, B. J. Eggleton, and D. B. Patterson, “Fiber Bragg gratings for dispersion compensation in transmission: theoretical model and design criteria for nearly ideal pulse compression,” J. Lightwave Technol. 15, 1303–1313 (1997).
[CrossRef]

Sipe, J. E.

B. J. Eggleton, C. M. de Sterke, A. Aceves, J. E. Sipe, T. A. Strasser, and R. E. Slusher, “Modulational instabilities and tunable multiple soliton generation in apodized fiber gratings,” Opt. Commun. 149, 267–271 (1998).
[CrossRef]

Slusher, R. E.

B. J. Eggleton, C. M. de Sterke, A. Aceves, J. E. Sipe, T. A. Strasser, and R. E. Slusher, “Modulational instabilities and tunable multiple soliton generation in apodized fiber gratings,” Opt. Commun. 149, 267–271 (1998).
[CrossRef]

B. J. Eggleton, G. Lenz, R. E. Slusher, and N. M. Litchinitser, “Compression of optical pulses spectrally broadened by self-phase modulation with a fiber Bragg grating in transmission,” Appl. Opt. 30, 7055–7061 (1998).
[CrossRef]

Smith, N. J.

See, e.g., N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibres with periodic dispersion management,” Electron. Lett. 32, 54–55 (1996).
[CrossRef]

Steel, M. J.

C. M. de Sterke, N. G. Broderick, B. J. Eggleton, and M. J. Steel, “Nonlinear optics in fiber gratings,” Opt. Fiber Technol. 2, 253–268 (1996).
[CrossRef]

Stephens, T.

B. J. Eggleton, T. Stephens, P. A. Krug, G. Dhosi, Z. Brodzeli, and F. Ouelette, “Dispersion compensation over 100 km at 10 Gbit/s using a fiber grating in transmission,” Electron. Lett. 32, 1610–1611 (1996).
[CrossRef]

Strasser, T. A.

B. J. Eggleton, C. M. de Sterke, A. Aceves, J. E. Sipe, T. A. Strasser, and R. E. Slusher, “Modulational instabilities and tunable multiple soliton generation in apodized fiber gratings,” Opt. Commun. 149, 267–271 (1998).
[CrossRef]

Taylor, J. R.

See, e.g., S. V. Chernikov, J. R. Taylor, and R. Kashyap, “Experimental demonstration of step-like dispersion profiling in optical fibre for soliton pulse generation and compression,” Electron. Lett. 30, 433–435 (1994).
[CrossRef]

Thibault, S.

Wabnitz, S.

A. B. Aceves and S. Wabnitz, “Self-induced transparency solitons in nonlinear refractive periodic media,” Phys. Lett. A 141, 37–42 (1989).
[CrossRef]

Appl. Opt. (1)

B. J. Eggleton, G. Lenz, R. E. Slusher, and N. M. Litchinitser, “Compression of optical pulses spectrally broadened by self-phase modulation with a fiber Bragg grating in transmission,” Appl. Opt. 30, 7055–7061 (1998).
[CrossRef]

Electron. Lett. (4)

P. C. Hill and B. J. Eggleton, “Strain gradient chirp of fiber Bragg grating,” Electron. Lett. 30, 1172–1174 (1994).
[CrossRef]

See, e.g., S. V. Chernikov, J. R. Taylor, and R. Kashyap, “Experimental demonstration of step-like dispersion profiling in optical fibre for soliton pulse generation and compression,” Electron. Lett. 30, 433–435 (1994).
[CrossRef]

B. J. Eggleton, T. Stephens, P. A. Krug, G. Dhosi, Z. Brodzeli, and F. Ouelette, “Dispersion compensation over 100 km at 10 Gbit/s using a fiber grating in transmission,” Electron. Lett. 32, 1610–1611 (1996).
[CrossRef]

See, e.g., N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibres with periodic dispersion management,” Electron. Lett. 32, 54–55 (1996).
[CrossRef]

J. Lightwave Technol. (1)

N. M. Litchinitser, B. J. Eggleton, and D. B. Patterson, “Fiber Bragg gratings for dispersion compensation in transmission: theoretical model and design criteria for nearly ideal pulse compression,” J. Lightwave Technol. 15, 1303–1313 (1997).
[CrossRef]

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

Opt. Commun. (1)

B. J. Eggleton, C. M. de Sterke, A. Aceves, J. E. Sipe, T. A. Strasser, and R. E. Slusher, “Modulational instabilities and tunable multiple soliton generation in apodized fiber gratings,” Opt. Commun. 149, 267–271 (1998).
[CrossRef]

Opt. Fiber Technol. (2)

C. M. de Sterke, N. G. Broderick, B. J. Eggleton, and M. J. Steel, “Nonlinear optics in fiber gratings,” Opt. Fiber Technol. 2, 253–268 (1996).
[CrossRef]

M. Asobe, “Nonlinear optical properties of chalcogenide glass fibers and their application to all-optical switching,” Opt. Fiber Technol. 3, 142–148 (1997).
[CrossRef]

Opt. Lett. (2)

Phys. Lett. A (1)

A. B. Aceves and S. Wabnitz, “Self-induced transparency solitons in nonlinear refractive periodic media,” Phys. Lett. A 141, 37–42 (1989).
[CrossRef]

Other (8)

L. F. Mollenauer, J. P. Gordon, and P. V. Mamyshev, “Solitons in high bit-rate, long-distance transmission,” in Optical Fiber Telecommunications IIIA, I. P. Kaminow and T. L. Koch, eds. (Academic, San Diego, Calif., 1997).

S. V. Chernikov and P. V. Mamyshev, “Femtosecond soliton propagation in fibers with slowly decreasing dispersion,” J. Opt. Soc. Am. B 8, 1633–1641 (1991); P. V. Mamyshev, S. V. Chernikov, and E. M. Dianov, “Generation of fundamental soliton trains for high-bit-rate optical fiber communication lines,” IEEE J. Quantum Electron. 27, 2347–2355 (1991).
[CrossRef]

F. Forghieri, R. W. Tkach, and A. R. Chraplyvy, “Fiber nonlinearities and their impact on transmission systems,” in Optical Fiber Telecommunications IIIA, I. P. Kaminow and T. L. Koch, eds. (Academic, San Diego, Calif., 1997), and references therein.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996); B. J. Eggleton, C. M. de Sterke, and R. E. Slusher, “Nonlinear pulse propagation in Bragg gratings,” J. Opt. Soc. Am. B 14, 2980–2993 (1997).
[CrossRef] [PubMed]

C. M. de Sterke and J. E. Sipe, “Gap solitons,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1994), Vol. 33.

F. Ouellette, “Dispersion cancellation using linearly chirped Bragg grating filters in optical waveguides,” Opt. Lett. 12, 847–849 (1987); J. E. Sipe, L. Poladian, and C. M. de Sterke, “Propagation through nonuniform grating structures,” J. Opt. Soc. Am. A 11, 1307–1320 (1994).
[CrossRef] [PubMed]

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989).

P. St. J. Russell, “Bloch wave analysis of dispersion and pulse propagation in pure distributed feedback structures,” J. Mod. Opt. 38, 1599–1619 (1991); erratum, J. Mod. Opt. 41, 163–164 (1994).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Schematic illustration of an adiabatic soliton compressor based on an apodized FBG with an index modulation that decreases linearly along the grating. The shading shows the stop-band region as a function of position along the fiber. The detuning of the pulse center frequency relative to the Bragg frequency is constant in this example.

Fig. 2
Fig. 2

Contour plot of (a) the compression factor and (b) the prefactor of Eq. (14), both as a function of the input and the output x parameters (see text). The desired large compression factor requires large xi, but the desired small prefactor requires small xi.

Fig. 3
Fig. 3

Example of adiabatic soliton compression in a linearly tapered grating, with cubic dispersion set to zero. Input pulse, dashed curve; compressed output pulse, solid curve.

Fig. 4
Fig. 4

Simulation of adiabatic soliton compression in a 100-cm-long grating with cubic dispersion (solid curve) and without cubic dispersion (dashed–dotted curve). The input pulse (dashed curve) is a fundamental soliton with a pulse width of 17.6 ps (FWHM). See text for other parameters. The inset shows the soliton evolution along the grating.

Fig. 5
Fig. 5

Comparison of the analytic result (solid curve) with the results obtained by numerical simulation by the split-step method (dashed curve) and with the numerical solution of the nonlinear coupled-mode equations (dotted curve). In all cases the launched intensity profile was sech2(t/10), with t being given in picoseconds. The peak intensity was 5.93 GW/cm2 for the first two cases and 5.5 GW/cm2 for the last case.

Equations (16)

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

N2=LDLNL=τ02/β21 /γP=γ Eτ0β2=1,
β2=-nc21δx2(1-x2)3/2
β3=3nc31δ 2x2(1-x2)5/2.
M=β3β2τ0=3τ0nc1|δ |11-x2=1|ω-ωB|τ031-x2.
i Φζ-12 β(ζ) 2Φτ 2+σ(ζ)|Φ|2Φ+iγ(ζ)Φ=0.
ξ=0ζβ(ζ)dζ=1τ020zβ2(z)dz,
Ψ=Φ1/β(ζ),
i Ψ(ξ,τ)ξ+122Ψ(ξ,τ)τ2
+|Ψ(ξ,τ)|2Ψ(ξ,τ)-iα(ξ)Ψ(ξ,τ)=0,
α(ξ)=-β/ξ2β.
Weff (ξ)=exp20ξα(ξ)dξ,
Weff (z)=β2(0)β2(z).
2|β2(0)|Lτ02ln[β2(0)/β2(L)]>1.
x(z)=xi+(xf-xi) zL,
Weff (L)=xixf21-xf21-xi23/2.
ξ=nc21δsin-1 xi-sin-1 xf+xf/1-xf2-xi/1-xi2xf-xi×Lτ02.

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