Abstract

We present a detailed experimental and theoretical study of nonlinear pulse propagation in an apodized fiber Bragg grating. In particular, we consider the generation and the propagation of Bragg solitons with a frequency content just outside the grating’s photonic bandgap, where, thanks to the apodization, the transmissivity of the grating is high and the strong grating dispersion dominates. We demonstrate the efficient launching of Bragg solitons with velocities as low as 50% of that in untreated fiber. The experimental results agree well with numerical simulations obtained by solving the full nonlinear coupled-mode equations that govern the experimental geometry. We also show that, for most parameters, the experimental results are in very good agreement with a nonlinear-Schrödinger-equation model. Thus many of the results known for the nonlinear Schrödinger equation can be brought to bear on our results.

© 1999 Optical Society of America

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  8. D. Taverner, N. G. R. Broderick, D. J. Richardson, R. I. Laming, and M. Ibsen, “Nonlinear self-switching and multiple-gap soliton formation in a fiber Bragg grating,” Opt. Lett. 23, 328–330 (1998).
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    [CrossRef]
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    [CrossRef]
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  41. M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, and R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tunable group delay with minimal distortion and loss,” Phys. Rev. E 54, 1078–1081 (1996).
    [CrossRef]

1999

C. M. de Sterke and B. J. Eggleton, “Bragg solitons and the nonlinear Schrödinger equation,” Phys. Rev. E 59, 1267–1270 (1999).
[CrossRef]

1998

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

J. E. Sipe, B. J. Eggleton, and T. A. Strasser, “Dispersion characteristics of nonuniform Bragg gratings: implications for WDM systems,” Opt. Commun. 152, 269–274 (1998).
[CrossRef]

N. M. Litchinitser, B. J. Eggleton, C. M. de Sterke, A. B. Aceves, and G. P. Agrawal, “Interaction of Bragg solitons in fiber gratings,” J. Opt. Soc. Am. B 16, 18–23 (1998).
[CrossRef]

D. Taverner, N. G. R. Broderick, D. J. Richardson, M. Ibsen, and R. I. Laming, “All-optical AND gate based on coupled gap–soliton formation in a fiber Bragg grating,” Opt. Lett. 23, 259–261 (1998).
[CrossRef]

D. Taverner, N. G. R. Broderick, D. J. Richardson, R. I. Laming, and M. Ibsen, “Nonlinear self-switching and multiple-gap soliton formation in a fiber Bragg grating,” Opt. Lett. 23, 328–330 (1998).
[CrossRef]

B. J. Eggleton, G. Lenz, R. E. Slusher, and N. M. Litchinitser, “Compression of pulses spectrally broadened by self-phase modulation with a fiber Bragg grating in transmission,” Appl. Opt. 37, 7055–7061 (1998).
[CrossRef]

C. M. de Sterke, “Propagation through nonuniform gratings,” Opt. Express 3, 405–410 (1998).
[CrossRef] [PubMed]

N. M. Litchinitser, G. P. Agrawal, B. J. Eggleton, and G. Lenz, “High repetition-rate soliton-train generation using fiber Bragg gratings,” Opt. Express 3, 411–417 (1998).
[CrossRef] [PubMed]

R. E. Slusher, B. J. Eggleton, T. A. Strasser, and C. M. de Sterke, “Nonlinear pulse reflections from chirped fiber gratings,” Opt. Express 3, 465–475 (1998).
[CrossRef] [PubMed]

G. Lenz and B. J. Eggleton, “Adiabatic compression soliton compression in nonuniform grating structures,” J. Opt. Soc. Am. B 15, 2979–2985 (1998).
[CrossRef]

1997

S. Wang, H. Erlig, H. Fetterman, V. Grubsky, and J. Feinberg, “One-dimensional photonic crystals for CDMA,” Proc. SPIE 3228, 407–416 (1997).

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 recompression,” J. Lightwave Technol. 15, 1303–1313 (1997).
[CrossRef]

C. M. de Sterke, B. J. Eggleton, and P. A. Krug, “High-intensity pulse propagation in uniform gratings and grating superstructures,” J. Lightwave Technol. 15, 2908–2993 (1997).
[CrossRef]

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]

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 (1997).
[CrossRef]

1996

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).
[CrossRef] [PubMed]

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, and R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tunable group delay with minimal distortion and loss,” Phys. Rev. E 54, 1078–1081 (1996).
[CrossRef]

B. J. Eggleton, C. M. de Sterke, and R. E. Slusher, “Nonlinear propagation in superstructure Bragg gratings,” Opt. Lett. 21, 1223–1225 (1996).
[CrossRef] [PubMed]

1995

B. Malo, D. C. Johnson, F. Bilodeau, J. Albert, and K. O. Hill, “Apodized in-fibre Bragg grating reflectors photoimprinted using a phase mask,” Electron. Lett. 31, 223–225 (1995).
[CrossRef]

1994

J. Martin and F. Ouellette, “Novel writing technique of long and highly reflective in-fibre gratings,” Electron. Lett. 30, 812–813 (1994).
[CrossRef]

M. J. Steel and C. Martijn de Sterke, “Schrödinger description for cross-phase modulation in grating structures,” Phys. Rev. A 49, 5048–5055 (1994).
[CrossRef] [PubMed]

1993

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, “Bragg gratings fabricated in monomode photosensitive optical fiber by exposure through a phase mask,” Appl. Phys. Lett. 62, 1035–1037 (1993).
[CrossRef]

1992

1991

C. M. de Sterke, K. R. Jackson, and B. D. Robert, “Nonlinear coupled mode equations on a finite interval: a numerical procedure,” J. Opt. Soc. Am. B 8, 403–412 (1991).
[CrossRef]

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

1990

C. M. de Sterke and J. E. Sipe, “Coupled modes and the nonlinear Schrödinger equation,” Phys. Rev. A 42, 550–555 (1990).
[CrossRef]

1989

D. N. Christodoulides and R. I. Joseph, “Slow Bragg solitons in nonlinear periodic structures,” Phys. Rev. Lett. 62, 1746–1749 (1989).
[CrossRef] [PubMed]

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

1985

H. G. Winful, “Pulse compression in optical fiber filters,” Appl. Phys. Lett. 46, 527–529 (1985).
[CrossRef]

1983

1982

H. G. Winful and G. D. Cooperman, “Self-pulsing and chaos in distributed feedback bistable optical devices,” Appl. Phys. Lett. 40, 298–300 (1982).
[CrossRef]

1980

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 (1980).
[CrossRef]

1978

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
[CrossRef]

1977

1972

D. Von der Linde, “Experimental study of single picosecond light pulses,” IEEE J. Quantum Electron. QE-8, 328–338 (1972).
[CrossRef]

Aceves, A. B.

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

N. M. Litchinitser, B. J. Eggleton, C. M. de Sterke, A. B. Aceves, and G. P. Agrawal, “Interaction of Bragg solitons in fiber gratings,” J. Opt. Soc. Am. B 16, 18–23 (1998).
[CrossRef]

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

Agrawal, G. P.

Albert, J.

B. Malo, D. C. Johnson, F. Bilodeau, J. Albert, and K. O. Hill, “Apodized in-fibre Bragg grating reflectors photoimprinted using a phase mask,” Electron. Lett. 31, 223–225 (1995).
[CrossRef]

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, “Bragg gratings fabricated in monomode photosensitive optical fiber by exposure through a phase mask,” Appl. Phys. Lett. 62, 1035–1037 (1993).
[CrossRef]

Bendickson, J. M.

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, and R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tunable group delay with minimal distortion and loss,” Phys. Rev. E 54, 1078–1081 (1996).
[CrossRef]

Bilodeau, F.

B. Malo, D. C. Johnson, F. Bilodeau, J. Albert, and K. O. Hill, “Apodized in-fibre Bragg grating reflectors photoimprinted using a phase mask,” Electron. Lett. 31, 223–225 (1995).
[CrossRef]

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, “Bragg gratings fabricated in monomode photosensitive optical fiber by exposure through a phase mask,” Appl. Phys. Lett. 62, 1035–1037 (1993).
[CrossRef]

Bloemer, M. J.

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, and R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tunable group delay with minimal distortion and loss,” Phys. Rev. E 54, 1078–1081 (1996).
[CrossRef]

Bowden, C. M.

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, and R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tunable group delay with minimal distortion and loss,” Phys. Rev. E 54, 1078–1081 (1996).
[CrossRef]

Broderick, N. G. R.

Christodoulides, D. N.

D. N. Christodoulides and R. I. Joseph, “Slow Bragg solitons in nonlinear periodic structures,” Phys. Rev. Lett. 62, 1746–1749 (1989).
[CrossRef] [PubMed]

Cooperman, G. D.

H. G. Winful and G. D. Cooperman, “Self-pulsing and chaos in distributed feedback bistable optical devices,” Appl. Phys. Lett. 40, 298–300 (1982).
[CrossRef]

Cross, P. S.

de Sterke, C. M.

C. M. de Sterke and B. J. Eggleton, “Bragg solitons and the nonlinear Schrödinger equation,” Phys. Rev. E 59, 1267–1270 (1999).
[CrossRef]

N. M. Litchinitser, B. J. Eggleton, C. M. de Sterke, A. B. Aceves, and G. P. Agrawal, “Interaction of Bragg solitons in fiber gratings,” J. Opt. Soc. Am. B 16, 18–23 (1998).
[CrossRef]

R. E. Slusher, B. J. Eggleton, T. A. Strasser, and C. M. de Sterke, “Nonlinear pulse reflections from chirped fiber gratings,” Opt. Express 3, 465–475 (1998).
[CrossRef] [PubMed]

C. M. de Sterke, “Propagation through nonuniform gratings,” Opt. Express 3, 405–410 (1998).
[CrossRef] [PubMed]

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

C. M. de Sterke, B. J. Eggleton, and P. A. Krug, “High-intensity pulse propagation in uniform gratings and grating superstructures,” J. Lightwave Technol. 15, 2908–2993 (1997).
[CrossRef]

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]

B. J. Eggleton, C. M. de Sterke, and R. E. Slusher, “Nonlinear propagation in superstructure Bragg gratings,” Opt. Lett. 21, 1223–1225 (1996).
[CrossRef] [PubMed]

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).
[CrossRef] [PubMed]

C. M. de Sterke, K. R. Jackson, and B. D. Robert, “Nonlinear coupled mode equations on a finite interval: a numerical procedure,” J. Opt. Soc. Am. B 8, 403–412 (1991).
[CrossRef]

C. M. de Sterke and J. E. Sipe, “Coupled modes and the nonlinear Schrödinger equation,” Phys. Rev. A 42, 550–555 (1990).
[CrossRef]

Dowling, J. P.

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, and R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tunable group delay with minimal distortion and loss,” Phys. Rev. E 54, 1078–1081 (1996).
[CrossRef]

Eggleton, B. J.

C. M. de Sterke and B. J. Eggleton, “Bragg solitons and the nonlinear Schrödinger equation,” Phys. Rev. E 59, 1267–1270 (1999).
[CrossRef]

N. M. Litchinitser, B. J. Eggleton, C. M. de Sterke, A. B. Aceves, and G. P. Agrawal, “Interaction of Bragg solitons in fiber gratings,” J. Opt. Soc. Am. B 16, 18–23 (1998).
[CrossRef]

R. E. Slusher, B. J. Eggleton, T. A. Strasser, and C. M. de Sterke, “Nonlinear pulse reflections from chirped fiber gratings,” Opt. Express 3, 465–475 (1998).
[CrossRef] [PubMed]

J. E. Sipe, B. J. Eggleton, and T. A. Strasser, “Dispersion characteristics of nonuniform Bragg gratings: implications for WDM systems,” Opt. Commun. 152, 269–274 (1998).
[CrossRef]

G. Lenz and B. J. Eggleton, “Adiabatic compression soliton compression in nonuniform grating structures,” J. Opt. Soc. Am. B 15, 2979–2985 (1998).
[CrossRef]

N. M. Litchinitser, G. P. Agrawal, B. J. Eggleton, and G. Lenz, “High repetition-rate soliton-train generation using fiber Bragg gratings,” Opt. Express 3, 411–417 (1998).
[CrossRef] [PubMed]

B. J. Eggleton, C. M. de Sterke, A. B. Aceves, J. E. Sipe, T. A. Strasser, and R. E. Slusher, “Modulational instability and multiple soliton pulse 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 pulses spectrally broadened by self-phase modulation with a fiber Bragg grating in transmission,” Appl. Opt. 37, 7055–7061 (1998).
[CrossRef]

C. M. de Sterke, B. J. Eggleton, and P. A. Krug, “High-intensity pulse propagation in uniform gratings and grating superstructures,” J. Lightwave Technol. 15, 2908–2993 (1997).
[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 (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 recompression,” J. Lightwave Technol. 15, 1303–1313 (1997).
[CrossRef]

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]

B. J. Eggleton, C. M. de Sterke, and R. E. Slusher, “Nonlinear propagation in superstructure Bragg gratings,” Opt. Lett. 21, 1223–1225 (1996).
[CrossRef] [PubMed]

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).
[CrossRef] [PubMed]

Erlig, H.

S. Wang, H. Erlig, H. Fetterman, V. Grubsky, and J. Feinberg, “One-dimensional photonic crystals for CDMA,” Proc. SPIE 3228, 407–416 (1997).

Feinberg, J.

S. Wang, H. Erlig, H. Fetterman, V. Grubsky, and J. Feinberg, “One-dimensional photonic crystals for CDMA,” Proc. SPIE 3228, 407–416 (1997).

Fetterman, H.

S. Wang, H. Erlig, H. Fetterman, V. Grubsky, and J. Feinberg, “One-dimensional photonic crystals for CDMA,” Proc. SPIE 3228, 407–416 (1997).

Flynn, R. J.

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, and R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tunable group delay with minimal distortion and loss,” Phys. Rev. E 54, 1078–1081 (1996).
[CrossRef]

Fork, R. L.

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, and R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tunable group delay with minimal distortion and loss,” Phys. Rev. E 54, 1078–1081 (1996).
[CrossRef]

Fujii, Y.

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
[CrossRef]

Gordon, J. P.

J. P. Gordon, “Interaction forces among solitons in optical fibers,” Opt. Lett. 8, 596–598 (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 (1980).
[CrossRef]

Grubsky, V.

S. Wang, H. Erlig, H. Fetterman, V. Grubsky, and J. Feinberg, “One-dimensional photonic crystals for CDMA,” Proc. SPIE 3228, 407–416 (1997).

Haus, H.

Hill, K. O.

B. Malo, D. C. Johnson, F. Bilodeau, J. Albert, and K. O. Hill, “Apodized in-fibre Bragg grating reflectors photoimprinted using a phase mask,” Electron. Lett. 31, 223–225 (1995).
[CrossRef]

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, “Bragg gratings fabricated in monomode photosensitive optical fiber by exposure through a phase mask,” Appl. Phys. Lett. 62, 1035–1037 (1993).
[CrossRef]

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
[CrossRef]

Ibsen, M.

Jackson, K. R.

Johnson, D. C.

B. Malo, D. C. Johnson, F. Bilodeau, J. Albert, and K. O. Hill, “Apodized in-fibre Bragg grating reflectors photoimprinted using a phase mask,” Electron. Lett. 31, 223–225 (1995).
[CrossRef]

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, “Bragg gratings fabricated in monomode photosensitive optical fiber by exposure through a phase mask,” Appl. Phys. Lett. 62, 1035–1037 (1993).
[CrossRef]

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
[CrossRef]

Joseph, R. I.

D. N. Christodoulides and R. I. Joseph, “Slow Bragg solitons in nonlinear periodic structures,” Phys. Rev. Lett. 62, 1746–1749 (1989).
[CrossRef] [PubMed]

Kawasaki, B. S.

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
[CrossRef]

Kogelnik, H.

Krug, P. A.

C. M. de Sterke, B. J. Eggleton, and P. A. Krug, “High-intensity pulse propagation in uniform gratings and grating superstructures,” J. Lightwave Technol. 15, 2908–2993 (1997).
[CrossRef]

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).
[CrossRef] [PubMed]

Laming, R. I.

Leavitt, R. P.

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, and R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tunable group delay with minimal distortion and loss,” Phys. Rev. E 54, 1078–1081 (1996).
[CrossRef]

Ledbetter, H. S.

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, and R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tunable group delay with minimal distortion and loss,” Phys. Rev. E 54, 1078–1081 (1996).
[CrossRef]

Lenz, G.

Litchinitser, N.

Litchinitser, N. M.

Malo, B.

B. Malo, D. C. Johnson, F. Bilodeau, J. Albert, and K. O. Hill, “Apodized in-fibre Bragg grating reflectors photoimprinted using a phase mask,” Electron. Lett. 31, 223–225 (1995).
[CrossRef]

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, “Bragg gratings fabricated in monomode photosensitive optical fiber by exposure through a phase mask,” Appl. Phys. Lett. 62, 1035–1037 (1993).
[CrossRef]

Martijn de Sterke, C.

M. J. Steel and C. Martijn de Sterke, “Schrödinger description for cross-phase modulation in grating structures,” Phys. Rev. A 49, 5048–5055 (1994).
[CrossRef] [PubMed]

Martin, J.

J. Martin and F. Ouellette, “Novel writing technique of long and highly reflective in-fibre gratings,” Electron. Lett. 30, 812–813 (1994).
[CrossRef]

Mollenauer, L. F.

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 (1980).
[CrossRef]

Ouellette, F.

J. Martin and F. Ouellette, “Novel writing technique of long and highly reflective in-fibre gratings,” Electron. Lett. 30, 812–813 (1994).
[CrossRef]

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 recompression,” J. Lightwave Technol. 15, 1303–1313 (1997).
[CrossRef]

Reinhardt, S. B.

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, and R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tunable group delay with minimal distortion and loss,” Phys. Rev. E 54, 1078–1081 (1996).
[CrossRef]

Richardson, D. J.

Robert, B. D.

Scalora, M.

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, and R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tunable group delay with minimal distortion and loss,” Phys. Rev. E 54, 1078–1081 (1996).
[CrossRef]

Sipe, J. E.

J. E. Sipe, B. J. Eggleton, and T. A. Strasser, “Dispersion characteristics of nonuniform Bragg gratings: implications for WDM systems,” Opt. Commun. 152, 269–274 (1998).
[CrossRef]

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

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).
[CrossRef] [PubMed]

C. M. de Sterke and J. E. Sipe, “Coupled modes and the nonlinear Schrödinger equation,” Phys. Rev. A 42, 550–555 (1990).
[CrossRef]

Slusher, R. E.

St. J. Russell, P.

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

Steel, M. J.

M. J. Steel and C. Martijn de Sterke, “Schrödinger description for cross-phase modulation in grating structures,” Phys. Rev. A 49, 5048–5055 (1994).
[CrossRef] [PubMed]

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. Rev. Lett. 45, 1095 (1980).
[CrossRef]

Strasser, T. A.

R. E. Slusher, B. J. Eggleton, T. A. Strasser, and C. M. de Sterke, “Nonlinear pulse reflections from chirped fiber gratings,” Opt. Express 3, 465–475 (1998).
[CrossRef] [PubMed]

J. E. Sipe, B. J. Eggleton, and T. A. Strasser, “Dispersion characteristics of nonuniform Bragg gratings: implications for WDM systems,” Opt. Commun. 152, 269–274 (1998).
[CrossRef]

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

Taverner, D.

Tocci, M. D.

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, and R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tunable group delay with minimal distortion and loss,” Phys. Rev. E 54, 1078–1081 (1996).
[CrossRef]

Von der Linde, D.

D. Von der Linde, “Experimental study of single picosecond light pulses,” IEEE J. Quantum Electron. QE-8, 328–338 (1972).
[CrossRef]

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]

Wang, S.

S. Wang, H. Erlig, H. Fetterman, V. Grubsky, and J. Feinberg, “One-dimensional photonic crystals for CDMA,” Proc. SPIE 3228, 407–416 (1997).

Winful, H. G.

H. G. Winful, “Pulse compression in optical fiber filters,” Appl. Phys. Lett. 46, 527–529 (1985).
[CrossRef]

H. G. Winful and G. D. Cooperman, “Self-pulsing and chaos in distributed feedback bistable optical devices,” Appl. Phys. Lett. 40, 298–300 (1982).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

H. G. Winful, “Pulse compression in optical fiber filters,” Appl. Phys. Lett. 46, 527–529 (1985).
[CrossRef]

H. G. Winful and G. D. Cooperman, “Self-pulsing and chaos in distributed feedback bistable optical devices,” Appl. Phys. Lett. 40, 298–300 (1982).
[CrossRef]

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, “Bragg gratings fabricated in monomode photosensitive optical fiber by exposure through a phase mask,” Appl. Phys. Lett. 62, 1035–1037 (1993).
[CrossRef]

K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
[CrossRef]

Electron. Lett.

B. Malo, D. C. Johnson, F. Bilodeau, J. Albert, and K. O. Hill, “Apodized in-fibre Bragg grating reflectors photoimprinted using a phase mask,” Electron. Lett. 31, 223–225 (1995).
[CrossRef]

J. Martin and F. Ouellette, “Novel writing technique of long and highly reflective in-fibre gratings,” Electron. Lett. 30, 812–813 (1994).
[CrossRef]

IEEE J. Quantum Electron.

D. Von der Linde, “Experimental study of single picosecond light pulses,” IEEE J. Quantum Electron. QE-8, 328–338 (1972).
[CrossRef]

J. Lightwave Technol.

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 recompression,” J. Lightwave Technol. 15, 1303–1313 (1997).
[CrossRef]

C. M. de Sterke, B. J. Eggleton, and P. A. Krug, “High-intensity pulse propagation in uniform gratings and grating superstructures,” J. Lightwave Technol. 15, 2908–2993 (1997).
[CrossRef]

J. Mod. Opt.

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

J. Opt. Soc. Am. B

Opt. Commun.

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

J. E. Sipe, B. J. Eggleton, and T. A. Strasser, “Dispersion characteristics of nonuniform Bragg gratings: implications for WDM systems,” Opt. Commun. 152, 269–274 (1998).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Lett. A

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

Phys. Rev. A

C. M. de Sterke and J. E. Sipe, “Coupled modes and the nonlinear Schrödinger equation,” Phys. Rev. A 42, 550–555 (1990).
[CrossRef]

M. J. Steel and C. Martijn de Sterke, “Schrödinger description for cross-phase modulation in grating structures,” Phys. Rev. A 49, 5048–5055 (1994).
[CrossRef] [PubMed]

Phys. Rev. E

C. M. de Sterke and B. J. Eggleton, “Bragg solitons and the nonlinear Schrödinger equation,” Phys. Rev. E 59, 1267–1270 (1999).
[CrossRef]

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, and R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tunable group delay with minimal distortion and loss,” Phys. Rev. E 54, 1078–1081 (1996).
[CrossRef]

Phys. Rev. Lett.

D. N. Christodoulides and R. I. Joseph, “Slow Bragg solitons in nonlinear periodic structures,” Phys. Rev. Lett. 62, 1746–1749 (1989).
[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 (1980).
[CrossRef]

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).
[CrossRef] [PubMed]

Proc. SPIE

S. Wang, H. Erlig, H. Fetterman, V. Grubsky, and J. Feinberg, “One-dimensional photonic crystals for CDMA,” Proc. SPIE 3228, 407–416 (1997).

Other

B. J. Eggleton, R. E. Slusher, N. M. Litchinitser, G. P. Agrawal, A. B. Aceves, and C. M. de Sterke, “Experimental observation of interaction between Bragg solitons,” in International Quantum Electronics Conference, Vol. 7 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), paper QTuJ5.

A. B. Aceves and S. Wabnitz, “Multisoliton-like solutions of wave propagation in periodic nonlinear structures,” in Nonlinear Processes in Physics, A. S. Fokas, D. J. Kaup, A. C. Newell, and V. E. Zakharov, eds. (Springer, New York, 1993), p. 6.

T. A. Strasser, P. J. Chandonnet, J. DeMarko, C. E. Soccolich, J. R. Pedrazzani, D. J. DiGiovanni, M. J. Andrejco, and D. S. Shenk, in Optical Fiber Communication Conference; Vol. 2 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996); postdeadline paper PD8–1.

C. M. de Sterke and J. E. Sipe, “Gap solitons,” in Progress in Optics XXXIII, E. Wolf, ed (Elsevier, Amsterdam, 1994), Chap. III.

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, 1995).

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Figures (16)

Fig. 1
Fig. 1

Schematic of an apodized grating, showing refractive index versus position. The grating has a total length L and consists of a uniform section (length L0) and two tapered sections (each of length Lt). The long-dashed vertical lines indicate the extent of the grating; the short-dashed vertical lines indicate the extent of the central uniform section of the grating.

Fig. 2
Fig. 2

Schematic of our experimental setup. The figure is not drawn to scale.

Fig. 3
Fig. 3

Measured grating reflection spectrum, showing the reflectivity versus wavelength (top scale), where the origin is taken to be at the center of the photonic bandgap. The bottom scale is the detuning from the center of the photonic bandgap. The vertical dashed lines indicate the positions of the edges of the photonic bandgap; these are determined from the measurements described in Subsection 4.A.

Fig. 4
Fig. 4

Intensity versus time after propagation through the grating at low intensity, for seven different values of the detuning (solid curve, 818 m-; dotted curve, 847 m-1; short-dashed curve, 906 m-1; long-dashed curve, 965 m-1; short-dashed–dotted curve, 1023 m-1; long-dashed–dotted curve, 1171 m-1; long–short-dashed curve, 3612 m-1).

Fig. 5
Fig. 5

Full-width at half-maximum (FWHM) of the transmitted pulses versus detuning at low intensity. Experimental results are indicated by dots, numerical results by the solid curve.

Fig. 6
Fig. 6

Delay of the transmitted pulses versus detuning at low intensity. Experimental results are indicated by dots, numerical results by the solid curve.

Fig. 7
Fig. 7

Intensity versus time after propagation through the grating at a peak input intensity of 11 GW/cm2, for seven different values of the detuning (solid curve, 729 m-1; dotted curve, 788 m-1; short-dashed curve, 847 m-1; long-dashed curve, 935 m-1; short-dashed–dotted curve, 1053 m-1; long-dashed–dotted curve, 1406 m-1; long–short-dashed curve, 3612 m-1).

Fig. 8
Fig. 8

Intensity versus time after propagation through the grating at a pulse energy of approximately 0.66 µJ, for a detuning close to the edge of the gap (solid curve) and far from the edge of the gap (dashed curve). The pulse tuned close to the edge of the gap is delayed by approximately 310 ps, corresponding to an average velocity of approximately 0.50V.

Fig. 9
Fig. 9

FWHM of the transmitted pulses versus detuning at an estimated pulse energy of 0.06 µJ. Experimental results are indicated by dots, numerical results obtained by solving Eq. (1) are indicated by the solid curve, and numerical obtained by solving Eq. (10) are indicated by the dashed curve; in both sets of numerical results the peak intensity of the incoming pulse is taken to be 3 GW/cm2.

Fig. 10
Fig. 10

Similar to Fig. 9, except that the measurements were taken at an estimated 0.14 µJ. In both sets of numerical results the peak intensity of the incoming pulse is taken to be 6 GW/cm2.

Fig. 11
Fig. 11

Similar to Fig. 9, except that the measurements were taken at an estimated 0.20 µJ. In both sets of numerical results the peak intensity of the incoming pulse is taken to be 11 GW/cm2. In addition, the long-dashed curve indicates the nonlinear Schrödinger result when enhancement factor (14) is left out.

Fig. 12
Fig. 12

Similar to Fig. 9, except that the measurements were taken at an estimated 0.36 µJ. In both sets of numerical results the peak intensity of the incoming pulse is taken to be 13 GW/cm2.

Fig. 13
Fig. 13

Comparison between the estimated pulse energy in the fiber and the deduced value of the peak intensity. The result, which is consistent with the expected proportionality between the two quantities, leads to a proportionality constant of 47 GW/cm2 µJ-1.

Fig. 14
Fig. 14

Similar to Fig. 9, except that the measurements were taken at an estimated 0.44 µJ. In both sets of numerical results the peak intensity of the incoming pulse is taken to be 23 GW/cm2.

Fig. 15
Fig. 15

Solid curve: Estimated peak power of the fundamental soliton versus detuning with the parameters from the text. Dots: Similar results, but deduced from the experiments, with the criterion that the width does not change upon propagation.

Fig. 16
Fig. 16

Intensity of transmitted pulse versus time for incoming pulse energies of 0.66 µJ at four different detunings. The figures on the left are experimental results; those on the right follow from solving Eq. (1) numerically and convolving the result with the estimated response of the detection system (solid curves) and from the NLSE followed by a convolution (dashed curves). The values of the detuning are 876 m-1 [traces (a) and (b)], 994 m-1 [traces (c) and (d)], 1318 m-1 [traces (e) and (f)], and 1847 m-1 [traces (g) and (h)].

Equations (17)

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

iVE±t±iE±z+κ(z)E+Γ(|E±|2+2|E|2)E±=0,
Egrat(z, t)=E+(z, t)exp[-i(ω0t-k0z)]+E-(z, t)exp[-i(ω0t+k0z)]+c.c.
κ(z)=ηπλ0Δngr.
Einc(z, t)=E+inc(z, t)exp[-i(ω0t-k0z)]+c.c.,
z(|E+|2-|E-|2)=0.
A+(v)1+v2-1-v2exp(-iΩt)+A-(v)×1-v21+v2exp(+iΩt)exp(iQz),
Ω=κ0γV,Q=κ0γv,
γ=1/1-v2.
E(z, t)1+v2-1-v2exp[iκ0γV(vz-t)],
iEz-β222Eτ2+Γ¯|E|2E=0,
Γ¯=3-v22vΓ,β2=-1V21κγ3v3,
E+inc(z, t)=E˜inc(z-Vt)exp(-iΔVt),
κ0γ=Δ,orv=1-κ02/Δ2,
|E+|2+|E-2|=|Einc|2v
E=β2Γ¯1t0sech(t/t0).
I=3.107V2λπw2(3-v2)κγ3vn2.
z0=0.322πwe22|β2|=0.161πwe2V2κγ3v3,

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