Abstract

Pulse compressors rely on two separate sections. The first section is for bandwidth generation through self-phase modulation and chirp linearization through normal dispersion. In conventional compressors this first section consists of a normal dispersion fiber of appropriate length. The second section is for compensating this linear chirp through anomalous dispersion, typically a prism pair or grating pair. In this way a transform-limited input pulse is compressed into an almost-transform-limited pulse. This scheme is quite different from chirped fiber gratings that are used in reflection to compensate existing chirp: no extra bandwidth is generated and nonlinear effects are not necessary. We propose a scheme for optical pulse compression utilizing an apodized fiber grating in transmission as the nonlinear dispersive element for the first section of the compressor. Near the band edge, on the long-wavelength side of the stop band of the grating, the normal quadratic dispersion is orders of magnitude greater than in a standard optical fiber. Therefore the first section of the compressor may be scaled down in length and the constraints placed on these systems may be relaxed. In this paper we discuss the limitations and the design of such fiber-grating compressors. Analysis and numerical simulation show efficient pulse compression. Further numerical simulation reveals that sufficiently far from the band edge the fiber grating can be modeled as an effective homogeneous medium obeying the nonlinear Schrödinger equation.

© 1998 Optical Society of America

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References

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  1. G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, 1989).
  2. 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]
  3. 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]
  4. 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]
  5. W. J. Tomlinson, R. H. Stolen, and C. V. Shank, “Compression of optical pulses chirped by self phase modulation in fibers,” J. Opt. Soc. Am. B 1, 139–143 (1984).
    [CrossRef]
  6. J. A. R. Williams, I. Bennion, and L. Zhang, “The compression of optical pulses using self-phase-modulation and linearly chirped Bragg-gratings in fibers,” IEEE Photonics Technol. Lett. 7, 491–493 (1995).
    [CrossRef]
  7. R. L. Fork, C. H. Brito Cruz, P. C. Becker, and C. V. Shank, “Compression of optical pulses to six femtoseconds by using cubic phase compensation,” Opt. Lett. 12, 483–485 (1987).
    [CrossRef] [PubMed]
  8. E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, G. I. Onishchukov, A. M. Prokhorov, M. F. Stel’makh, and A. A. Fomichev, “Picosecond structure of the pump pulse in stimulated Raman scattering in a single-mode optical fiber,” JETP Lett. 39, 691–695 (1984).
  9. L. Dong, M. J. Cole, A. D. Ellis, M. Durkin, M. Ibsen, V. Gusmeroli, and R. I. Laming, “40 Gbit/s 1.55 μm transmission over 109 km of non-dispersion shifted fibre with long continuously chirped fibre gratings,” presented at the Optical Fiber Communication Conference of the Optical Society of America, Dallas, Texas, February 16–21, 1997, postdeadline paper PD6.
  10. 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]
  11. 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]
  12. M. Asobe, “Nonlinear optical properties of chalcogenide glass fibers and their application to all-optical switching,” Opt. Fiber Technol. 3, 142–148 (1997).
    [CrossRef]

1997 (2)

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]

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

1996 (1)

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]

1995 (1)

J. A. R. Williams, I. Bennion, and L. Zhang, “The compression of optical pulses using self-phase-modulation and linearly chirped Bragg-gratings in fibers,” IEEE Photonics Technol. Lett. 7, 491–493 (1995).
[CrossRef]

1991 (1)

1987 (1)

1984 (2)

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, G. I. Onishchukov, A. M. Prokhorov, M. F. Stel’makh, and A. A. Fomichev, “Picosecond structure of the pump pulse in stimulated Raman scattering in a single-mode optical fiber,” JETP Lett. 39, 691–695 (1984).

W. J. Tomlinson, R. H. Stolen, and C. V. Shank, “Compression of optical pulses chirped by self phase modulation in fibers,” J. Opt. Soc. Am. B 1, 139–143 (1984).
[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]

Becker, P. C.

Bennion, I.

J. A. R. Williams, I. Bennion, and L. Zhang, “The compression of optical pulses using self-phase-modulation and linearly chirped Bragg-gratings in fibers,” IEEE Photonics Technol. Lett. 7, 491–493 (1995).
[CrossRef]

Brito Cruz, C. H.

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]

de Sterke, C. M.

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]

Dianov, E. M.

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, G. I. Onishchukov, A. M. Prokhorov, M. F. Stel’makh, and A. A. Fomichev, “Picosecond structure of the pump pulse in stimulated Raman scattering in a single-mode optical fiber,” JETP Lett. 39, 691–695 (1984).

Eggleton, B. J.

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]

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]

Fomichev, A. A.

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, G. I. Onishchukov, A. M. Prokhorov, M. F. Stel’makh, and A. A. Fomichev, “Picosecond structure of the pump pulse in stimulated Raman scattering in a single-mode optical fiber,” JETP Lett. 39, 691–695 (1984).

Fork, R. L.

Jackson, K. R.

Karasik, A. Ya.

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, G. I. Onishchukov, A. M. Prokhorov, M. F. Stel’makh, and A. A. Fomichev, “Picosecond structure of the pump pulse in stimulated Raman scattering in a single-mode optical fiber,” JETP Lett. 39, 691–695 (1984).

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]

Litchinitser, N. M.

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]

Mamyshev, P. V.

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, G. I. Onishchukov, A. M. Prokhorov, M. F. Stel’makh, and A. A. Fomichev, “Picosecond structure of the pump pulse in stimulated Raman scattering in a single-mode optical fiber,” JETP Lett. 39, 691–695 (1984).

Onishchukov, G. I.

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, G. I. Onishchukov, A. M. Prokhorov, M. F. Stel’makh, and A. A. Fomichev, “Picosecond structure of the pump pulse in stimulated Raman scattering in a single-mode optical fiber,” JETP Lett. 39, 691–695 (1984).

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]

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]

Prokhorov, A. M.

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, G. I. Onishchukov, A. M. Prokhorov, M. F. Stel’makh, and A. A. Fomichev, “Picosecond structure of the pump pulse in stimulated Raman scattering in a single-mode optical fiber,” JETP Lett. 39, 691–695 (1984).

Robert, B. D.

Shank, C. V.

Stel’makh, M. F.

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, G. I. Onishchukov, A. M. Prokhorov, M. F. Stel’makh, and A. A. Fomichev, “Picosecond structure of the pump pulse in stimulated Raman scattering in a single-mode optical fiber,” JETP Lett. 39, 691–695 (1984).

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]

Stolen, R. H.

Tomlinson, W. J.

Williams, J. A. R.

J. A. R. Williams, I. Bennion, and L. Zhang, “The compression of optical pulses using self-phase-modulation and linearly chirped Bragg-gratings in fibers,” IEEE Photonics Technol. Lett. 7, 491–493 (1995).
[CrossRef]

Zhang, L.

J. A. R. Williams, I. Bennion, and L. Zhang, “The compression of optical pulses using self-phase-modulation and linearly chirped Bragg-gratings in fibers,” IEEE Photonics Technol. Lett. 7, 491–493 (1995).
[CrossRef]

Electron. Lett. (1)

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]

IEEE Photonics Technol. Lett. (1)

J. A. R. Williams, I. Bennion, and L. Zhang, “The compression of optical pulses using self-phase-modulation and linearly chirped Bragg-gratings in fibers,” IEEE Photonics Technol. Lett. 7, 491–493 (1995).
[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 (2)

JETP Lett. (1)

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, G. I. Onishchukov, A. M. Prokhorov, M. F. Stel’makh, and A. A. Fomichev, “Picosecond structure of the pump pulse in stimulated Raman scattering in a single-mode optical fiber,” JETP Lett. 39, 691–695 (1984).

Opt. Fiber Technol. (1)

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. (1)

Other (4)

L. Dong, M. J. Cole, A. D. Ellis, M. Durkin, M. Ibsen, V. Gusmeroli, and R. I. Laming, “40 Gbit/s 1.55 μm transmission over 109 km of non-dispersion shifted fibre with long continuously chirped fibre gratings,” presented at the Optical Fiber Communication Conference of the Optical Society of America, Dallas, Texas, February 16–21, 1997, postdeadline paper PD6.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, 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]

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]

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Figures (4)

Fig. 1
Fig. 1

Schematic drawing of a compressor. The first section generates bandwidth and linear chirp, and the second section compensates this chirp. Ideally the result is an almost-transform-limited compressed pulse.

Fig. 2
Fig. 2

Effect of cubic dispersion on the compressor performance. M is a measure of the relative magnitude of quadratic and cubic dispersion (see text). This simulation assumes a 70-ps Gaussian pulse of 170-GW/cm2 peak intensity propagating in a 10-cm homogeneous medium with β2=50 ps2/cm and β3 =0, β3=175, and β3=350 ps3/cm for M=0, M=0.05, and M=0.1, respectively.

Fig. 3
Fig. 3

(a) Input 60-ps transform-limited Gaussian pulse of 20-GW/cm2 peak intensity and the final compressed pulse. (b) The corresponding spectra; the location and width of the stop band are indicated by the hatched region. (c) The pulse and its chirp after propagating through 63.5 cm of a homogeneous medium with β2=6.3 ps2/cm and β3=13.6 ps3/cm.

Fig. 4
Fig. 4

Comparison of simulation results using the split-step Fourier method (dashed curve) and the full nonlinear coupled-mode equations for gratings (solid curve), for (a) the pulse intensity profile before and (b) after the dispersion-compensating section.

Equations (19)

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LD=τ02s2β,
LNL=λAeff2πn2P,
N=LDLNL,
zopt6LDLNLforN1.
Fc1+0.6(N2L/LD).
βg=-nc2 1δ (κ/δ)2[1-(κ/δ)2]3/2,
βg=3nc3 1δ2 (κ/δ)2[1-(κ/δ)2]5/2.
M=βgβgτ0=3 ncτ0 1|δ| 11-(κ/δ)2.
gRPLeffAeff<16PL<16AeffgR,
LNL>gRλ32πn2 L.
|δ|-κ>2πnc 0.22 Fcτ0=1.39 ncτ0 Fc=1.39l Fc,
|δ|>3n2Mτ0c+3n2Mτ0c2+κ21/2,
β<nc1/2Mτ03δc3/2κ2.
LD>cn1/23δcM3/2 τ0κ2s2.
qzoptL6LDLLNLL1/2.
FcN1.6=q1.66 32πn2λgR=25.65q n2λgR.
δ(I)=π2nλ+2n2Iλ-1Λ=δ0+2πn2Iλ,
β(I)β(0)=1-2πλ n2I 1δ0 31-(κ/δ0)2=1-1LNLδ0 31-(κ/δ0)2,
β(I)β(0)=1-2πλ n2I 1δ0 4+(κ/δ0)21-(κ/δ0)2=1-1LNLδ0 4+(κ/δ0)21-(κ/δ0)2.

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