Abstract

We report the results of a series of experiments examining cross-phase modulation effects in apodized fiber Bragg gratings. All-optical switching and the optical pushbroom are observed, depending on the precise wavelength of the probe. The experimental results are then modeled with the coupled-mode equations.

© 2000 Optical Society of America

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References

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  1. D. Taverner, N. G. R. Broderick, D. J. Richardson, R. I. Laming, and M. Isben, “Nonlinear self-switching and multiple gap-soliton formation in a fiber Bragg grating,” Opt. Lett. 23, 328–330 (1998).
    [CrossRef]
  2. B. J. Eggleton, R. E. Slusher, C. Mortijn de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
    [CrossRef] [PubMed]
  3. S. LaRochelle, Y. Hibino, V. Mizrahi, and G. I. Stegeman, “All-optical switching of grating transmission using cross-phase modulation in optical fibres,” Elect. Lett. 26, 1459–1460 (1990).
    [CrossRef]
  4. J. Lauzon, S. LaRochelle, and F. Ouellette, “Numerical analysis of all-optical switching of a fiber Bragg grating induced by a short-detuned pump pulse,” Opt. Commun. 92, 233–239 (1992).
    [CrossRef]
  5. N. G. R. Broderick, D. Taverner, D. J. Richardson, M. Isben, and R. I. Laming, “Optical pulse compression in fibre Bragg gratings,” Phys. Rev. Lett. 79, 4566–4569 (1997).
    [CrossRef]
  6. N. G. R. Broderick, D. Taverner, D. J. Richardson, M. Isben, and R. I. Laming, “Experimental observation of nonlinear pulse compression in nonuniform Bragg gratings,” Opt. Lett. 22, 1837–1839 (1997).
    [CrossRef]
  7. J. E. Rothenberg, “Intrafiber visible pulse-compression by cross-phase modulation in a birefringent optical fiber,” Opt. Lett. 15, 495–497 (1990).
    [CrossRef] [PubMed]
  8. B. Jaskorzynska and D. Schadt, “All-fiber distributed compression of weak pulses in the regime of negative group-velocity dispersion,” IEEE J. Quantum Electron. 24, 2117–2120 (1988).
    [CrossRef]
  9. G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989).
  10. M. J. Steel and C. M. de Sterke, “Schrödinger equation description for cross-phase modulation in grating structures,” Phys. Rev. A 49, 5048–5055 (1994).
    [CrossRef] [PubMed]
  11. 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]
  12. C. M. de Sterke, “Optical push broom,” Opt. Lett. 17, 914–916 (1992).
    [CrossRef] [PubMed]
  13. C. M. de Sterke and J. E. Sipe, “Coupled modes and the nonlinear Schrödinger equation,” Phys. Rev. A 42, 550–555 (1990).
    [CrossRef]
  14. M. J. Steel and C. M. de Sterke, “Continuous-wave parametric amplification in Bragg gratings,” J. Opt. Soc. Am. B 12, 2445–2452 (1995).
    [CrossRef]
  15. M. J. Steel and C. M. de Sterke, “Parametric amplification of short pulses in optical fiber Bragg gratings,” Phys. Rev. E 54, 4271–4284 (1996).
    [CrossRef]
  16. N. G. R. Broderick, “Bistable switching in nonlinear Bragg gratings,” Opt. Commun. 148, 90–94 (1998).
    [CrossRef]
  17. N. Broderick and C. M. de Sterke, “Analysis of nonuniform gratings,” Phys. Rev. E 52, 4458–4464 (1995).
    [CrossRef]
  18. M. J. Steel, D. G. A. Jackson, and C. M. de Sterke, “Approximate model for optical pulse compression by cross-phase modulation in Bragg gratings,” Phys. Rev. A 50, 3447–3452 (1994).
    [CrossRef] [PubMed]

1998 (2)

1997 (2)

N. G. R. Broderick, D. Taverner, D. J. Richardson, M. Isben, and R. I. Laming, “Experimental observation of nonlinear pulse compression in nonuniform Bragg gratings,” Opt. Lett. 22, 1837–1839 (1997).
[CrossRef]

N. G. R. Broderick, D. Taverner, D. J. Richardson, M. Isben, and R. I. Laming, “Optical pulse compression in fibre Bragg gratings,” Phys. Rev. Lett. 79, 4566–4569 (1997).
[CrossRef]

1996 (2)

B. J. Eggleton, R. E. Slusher, C. Mortijn de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
[CrossRef] [PubMed]

M. J. Steel and C. M. de Sterke, “Parametric amplification of short pulses in optical fiber Bragg gratings,” Phys. Rev. E 54, 4271–4284 (1996).
[CrossRef]

1995 (2)

M. J. Steel and C. M. de Sterke, “Continuous-wave parametric amplification in Bragg gratings,” J. Opt. Soc. Am. B 12, 2445–2452 (1995).
[CrossRef]

N. Broderick and C. M. de Sterke, “Analysis of nonuniform gratings,” Phys. Rev. E 52, 4458–4464 (1995).
[CrossRef]

1994 (3)

M. J. Steel, D. G. A. Jackson, and C. M. de Sterke, “Approximate model for optical pulse compression by cross-phase modulation in Bragg gratings,” Phys. Rev. A 50, 3447–3452 (1994).
[CrossRef] [PubMed]

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]

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

1992 (2)

J. Lauzon, S. LaRochelle, and F. Ouellette, “Numerical analysis of all-optical switching of a fiber Bragg grating induced by a short-detuned pump pulse,” Opt. Commun. 92, 233–239 (1992).
[CrossRef]

C. M. de Sterke, “Optical push broom,” Opt. Lett. 17, 914–916 (1992).
[CrossRef] [PubMed]

1990 (3)

J. E. Rothenberg, “Intrafiber visible pulse-compression by cross-phase modulation in a birefringent optical fiber,” Opt. Lett. 15, 495–497 (1990).
[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]

S. LaRochelle, Y. Hibino, V. Mizrahi, and G. I. Stegeman, “All-optical switching of grating transmission using cross-phase modulation in optical fibres,” Elect. Lett. 26, 1459–1460 (1990).
[CrossRef]

1988 (1)

B. Jaskorzynska and D. Schadt, “All-fiber distributed compression of weak pulses in the regime of negative group-velocity dispersion,” IEEE J. Quantum Electron. 24, 2117–2120 (1988).
[CrossRef]

Broderick, N.

N. Broderick and C. M. de Sterke, “Analysis of nonuniform gratings,” Phys. Rev. E 52, 4458–4464 (1995).
[CrossRef]

Broderick, N. G. R.

de Sterke, C. M.

M. J. Steel and C. M. de Sterke, “Parametric amplification of short pulses in optical fiber Bragg gratings,” Phys. Rev. E 54, 4271–4284 (1996).
[CrossRef]

N. Broderick and C. M. de Sterke, “Analysis of nonuniform gratings,” Phys. Rev. E 52, 4458–4464 (1995).
[CrossRef]

M. J. Steel and C. M. de Sterke, “Continuous-wave parametric amplification in Bragg gratings,” J. Opt. Soc. Am. B 12, 2445–2452 (1995).
[CrossRef]

M. J. Steel, D. G. A. Jackson, and C. M. de Sterke, “Approximate model for optical pulse compression by cross-phase modulation in Bragg gratings,” Phys. Rev. A 50, 3447–3452 (1994).
[CrossRef] [PubMed]

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]

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

C. M. de Sterke, “Optical push broom,” Opt. Lett. 17, 914–916 (1992).
[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]

Eggleton, B. J.

B. J. Eggleton, R. E. Slusher, C. Mortijn de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
[CrossRef] [PubMed]

Hibino, Y.

S. LaRochelle, Y. Hibino, V. Mizrahi, and G. I. Stegeman, “All-optical switching of grating transmission using cross-phase modulation in optical fibres,” Elect. Lett. 26, 1459–1460 (1990).
[CrossRef]

Isben, M.

Jackson, D. G. A.

M. J. Steel, D. G. A. Jackson, and C. M. de Sterke, “Approximate model for optical pulse compression by cross-phase modulation in Bragg gratings,” Phys. Rev. A 50, 3447–3452 (1994).
[CrossRef] [PubMed]

Jaskorzynska, B.

B. Jaskorzynska and D. Schadt, “All-fiber distributed compression of weak pulses in the regime of negative group-velocity dispersion,” IEEE J. Quantum Electron. 24, 2117–2120 (1988).
[CrossRef]

Krug, P. A.

B. J. Eggleton, R. E. Slusher, C. Mortijn de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
[CrossRef] [PubMed]

Laming, R. I.

LaRochelle, S.

J. Lauzon, S. LaRochelle, and F. Ouellette, “Numerical analysis of all-optical switching of a fiber Bragg grating induced by a short-detuned pump pulse,” Opt. Commun. 92, 233–239 (1992).
[CrossRef]

S. LaRochelle, Y. Hibino, V. Mizrahi, and G. I. Stegeman, “All-optical switching of grating transmission using cross-phase modulation in optical fibres,” Elect. Lett. 26, 1459–1460 (1990).
[CrossRef]

Lauzon, J.

J. Lauzon, S. LaRochelle, and F. Ouellette, “Numerical analysis of all-optical switching of a fiber Bragg grating induced by a short-detuned pump pulse,” Opt. Commun. 92, 233–239 (1992).
[CrossRef]

Mizrahi, V.

S. LaRochelle, Y. Hibino, V. Mizrahi, and G. I. Stegeman, “All-optical switching of grating transmission using cross-phase modulation in optical fibres,” Elect. Lett. 26, 1459–1460 (1990).
[CrossRef]

Mortijn de Sterke, C.

B. J. Eggleton, R. E. Slusher, C. Mortijn de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
[CrossRef] [PubMed]

Ouellette, F.

J. Lauzon, S. LaRochelle, and F. Ouellette, “Numerical analysis of all-optical switching of a fiber Bragg grating induced by a short-detuned pump pulse,” Opt. Commun. 92, 233–239 (1992).
[CrossRef]

Poladian, L.

Richardson, D. J.

Rothenberg, J. E.

Schadt, D.

B. Jaskorzynska and D. Schadt, “All-fiber distributed compression of weak pulses in the regime of negative group-velocity dispersion,” IEEE J. Quantum Electron. 24, 2117–2120 (1988).
[CrossRef]

Sipe, J. E.

B. J. Eggleton, R. E. Slusher, C. Mortijn de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
[CrossRef] [PubMed]

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]

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.

B. J. Eggleton, R. E. Slusher, C. Mortijn de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
[CrossRef] [PubMed]

Steel, M. J.

M. J. Steel and C. M. de Sterke, “Parametric amplification of short pulses in optical fiber Bragg gratings,” Phys. Rev. E 54, 4271–4284 (1996).
[CrossRef]

M. J. Steel and C. M. de Sterke, “Continuous-wave parametric amplification in Bragg gratings,” J. Opt. Soc. Am. B 12, 2445–2452 (1995).
[CrossRef]

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

M. J. Steel, D. G. A. Jackson, and C. M. de Sterke, “Approximate model for optical pulse compression by cross-phase modulation in Bragg gratings,” Phys. Rev. A 50, 3447–3452 (1994).
[CrossRef] [PubMed]

Stegeman, G. I.

S. LaRochelle, Y. Hibino, V. Mizrahi, and G. I. Stegeman, “All-optical switching of grating transmission using cross-phase modulation in optical fibres,” Elect. Lett. 26, 1459–1460 (1990).
[CrossRef]

Taverner, D.

Elect. Lett. (1)

S. LaRochelle, Y. Hibino, V. Mizrahi, and G. I. Stegeman, “All-optical switching of grating transmission using cross-phase modulation in optical fibres,” Elect. Lett. 26, 1459–1460 (1990).
[CrossRef]

IEEE J. Quantum Electron. (1)

B. Jaskorzynska and D. Schadt, “All-fiber distributed compression of weak pulses in the regime of negative group-velocity dispersion,” IEEE J. Quantum Electron. 24, 2117–2120 (1988).
[CrossRef]

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

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

Opt. Commun. (2)

J. Lauzon, S. LaRochelle, and F. Ouellette, “Numerical analysis of all-optical switching of a fiber Bragg grating induced by a short-detuned pump pulse,” Opt. Commun. 92, 233–239 (1992).
[CrossRef]

N. G. R. Broderick, “Bistable switching in nonlinear Bragg gratings,” Opt. Commun. 148, 90–94 (1998).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. A (3)

M. J. Steel, D. G. A. Jackson, and C. M. de Sterke, “Approximate model for optical pulse compression by cross-phase modulation in Bragg gratings,” Phys. Rev. A 50, 3447–3452 (1994).
[CrossRef] [PubMed]

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

Phys. Rev. E (2)

M. J. Steel and C. M. de Sterke, “Parametric amplification of short pulses in optical fiber Bragg gratings,” Phys. Rev. E 54, 4271–4284 (1996).
[CrossRef]

N. Broderick and C. M. de Sterke, “Analysis of nonuniform gratings,” Phys. Rev. E 52, 4458–4464 (1995).
[CrossRef]

Phys. Rev. Lett. (2)

N. G. R. Broderick, D. Taverner, D. J. Richardson, M. Isben, and R. I. Laming, “Optical pulse compression in fibre Bragg gratings,” Phys. Rev. Lett. 79, 4566–4569 (1997).
[CrossRef]

B. J. Eggleton, R. E. Slusher, C. Mortijn de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
[CrossRef] [PubMed]

Other (1)

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

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Figures (13)

Fig. 1
Fig. 1

Dispersion relationship for a uniform grating with the same parameters as the grating in Fig. 8. Note that no solutions exist in the bandgap. The dashed line indicates the background dispersion relationship.

Fig. 2
Fig. 2

Field profile inside the grating at the first transmission resonance. Solid curves, total intensity |f+|2+|f-|2; short-dashed curve, |f+|2; long-dashed curve, |f-|2. Note that the field structure is single peaked, with the maximum intensity being significantly higher than the input intensity. This illustrates the energy storage capability of a FBG.

Fig. 3
Fig. 3

Theoretical trace of the optical pushbroom. Solid curve, transmitted probe intensity; dashed curve, pump profile. The inset is a blowup of the front spike in the transmission. The parameters chosen match those used in the actual experiment.

Fig. 4
Fig. 4

Theoretical transmitted (dashed curves) and reflected (solid curves) intensity profiles of the probe beam as a function of the time in nanoseconds. The pump is incident on the grating at t=0. The detunings used were 0.662 cm-1, 0.466 cm-1, 0.049 cm-1, and -0.197cm-1 for (a), (b), (c), and (d), respectively.

Fig. 5
Fig. 5

Theoretical transmitted (dashed curves) and reflected (solid curves) intensity profiles of the probe beam as a function of the time in nanoseconds. The pump is incident on the grating at t=0. The detunings used were -0.444cm-1, -0.592cm-1, -0.643cm-1, and -0.891cm-1, for (a), (b), (c), and (d), respectively.

Fig. 6
Fig. 6

Schematic diagram of the experimental setup. PBS, polarization beam splitter; BPF, bandpass filter with a width of <1 nm; LD, laser diode; LA-EDFA, large-mode-area erbium fiber amplifier. The polarizer, POL, is set to minimize the pump. See the text for more details.

Fig. 7
Fig. 7

Measured intensity profile of the pump pulse used in the experiments.

Fig. 8
Fig. 8

Measured reflection spectrum of the grating used in our experiments (solid curve). The dashed curve is a theoretical trace for a grating with the same parameters. The center of the grating is at 1535.9290 nm, and the horizontal scale gives the detuning from the center wavelength. The effect of the apodization can be seen clearly in the lack of sidelobes in the spectrum.

Fig. 9
Fig. 9

Measured transmitted intensity profiles of the probe pulses as a function of the time in nanoseconds. The derived detunings are 0.662 cm-1, 0.466 cm-1, 0.049 cm-1, and -0.197cm-1 for (a), (b), (c), and (d), respectively. The probe’s intensity has been normalized to the peak of the transmission at wavelengths far from the grating.

Fig. 10
Fig. 10

More transmitted intensity profiles for frequencies below the center of the bandgap. The derived detunings are -0.444cm-1, -0.592cm-1, -0.643cm-1, and -0.891cm-1 for (a), (b), (c), and (d), respectively.

Fig. 11
Fig. 11

Experimental traces of the optical pushbroom. (a) Result of optimizing the wavelength for maximum energy storage in the Bragg grating, (b) effect on increasing the pump power.

Fig. 12
Fig. 12

Measured reflected intensity profiles of the probe pulses as a function of the time in nanoseconds. The detuning of the probe is 0.588 cm-1, 0.490 cm-1, 0.246 cm-1, and 0.000 cm-1 for traces (a), (b), (c), and (d), respectively. The probe’s intensity has been normalized so that the peak reflection in the linear regime corresponds to a value of 0.96.

Fig. 13
Fig. 13

More reflected intensity profiles for frequencies below the center of the bandgap. The detuning of the probe is -0.247cm-1,-0.494cm-1,-0.593cm-1, and -0.643 cm-1, for traces (a), (b), (c), and (d), respectively. The graphs are normalized as in Fig. 12.

Equations (15)

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n(x)=n0+n(2)I(x),
n(z)=n0+Δn(z)cos(2k0z),
E(z, t)={f+(z, t)exp[i(k0z-ω0t)]+f-(z, t)exp[-i(k0z+ω0t)]xˆ+P(z, t)exp[i(kpz-ωpt)]yˆ+c.c.,
if+x+ivgf+t+κ f-+δ f++23Γ|P(z, t)|2f+=0,
-if-x+ivgf-t+κ f++δ f-+23Γ|P(z, t)|2f-=0.
δ=ω-ω0vg,κ(z)=πΔn(z)λ,Γ=4πn0λZn(2),
xf+(x)f-(x)=iδiκ(x)-iκ(x)-iδ f+(x)f-(x).
M=1βiδ sin βx+β cos βxiκ sin βx-iκ sin βxβ cos βx-iδ sin βx,
f+(x)f-(x)=Mf+(0)f-(0).
f+f-=κqq2+κ2exp[i(qx-δt)],
q=±δ2-κ2.
V=dδd q=1δδ2-κ2.
|P|232Γκ.
κ(x)=0.45 sin(πx/ll)cm-1,
λ(T)=1538.00-0.149639T-0.00199972T2,

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