Abstract

We show the Cross Phase Modulation (XPM) effect between CW probe that operates in bistability region and strong Gaussian pump in a Fiber Bragg Grating (FBG) by Implicit 4th Order Runge-Kutta Method. The XPM effect results in three unique nonlinear switching behaviors of the probe transmission depending on the pump peak intensity and its Full Width Half Maximum (FWHM) value. From this observation, we offer the FBG three potential nonlinear switching applications in all-optical signal processing domain as: a step-up all-optical switching, an all-optical inverter, and an all-optical limiter. The bistability threshold that determines the nonlinear switching behaviors of probe transmission after Gaussian pump injection is defined numerically and shown to be equivalent to the unstable state inside hysteresis loop.

© 2005 Optical Society of America

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References

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  1. Pochi Yeh, Optical Waves in Layered Media, (Wiley, New York, 1988).
  2. C. M. de Sterke and J. E. Sipe, “Gap Solitons,” Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1994).
  3. B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg Grating Solitons,” Phys. Lett 76, 1627–30 (1996).
    [Crossref]
  4. H. G. Winful, J. H. Marburger, and E. Garmire, “Theory of bistability in nonlinear distributed feedback structures,” Appl. Phys. Lett. 35, 379–381 (1979).
    [Crossref]
  5. Hojoon Lee and Govind P. Agrawal, “Nonlinear Switching of Optical Pulses in Fiber Bragg Gratings,” IEEE J. Quantum Electron.39 (2003).
  6. C. M. de Sterke, “Optical Push Broom,” Opt. Lett. 17, 914–916 (1992).
    [Crossref] [PubMed]
  7. Neil G. R. Broderick, Domino Taverner, David J. Richardson, and Morten Ibsen, “Cross Phase Modulation Effects in nonlinear Fiber Bragg Gratings,” J. Opt. Soc. Am. B 17, 345–353 (2000)
    [Crossref]
  8. 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]
  9. J. H. Lee, T. Tanemura, T. Nagashima, T. Hasegawa, S. Ohara, N. Sugimoto, and K. Kikuchi, “Use of 1-m Bi2O3 nonlinear fiber for 160-Gbit/s optical-time division demultiplexing based on polarization rotation and wavelength shift induced by cross-phase modulation,” Opt. Lett. 30, 3144–3149 (2005).
    [Crossref]
  10. K. Ogusu, “Effect of stimulated Brillouin scattering on nonlinear pulse propagation in fiber Bragg gratings,” J. Opt. Soc. Am. B 17, 769–774 (2000).
    [Crossref]
  11. Hojoon Lee and Govind P. Agrawal, “Suppression of stimulated Brillouin scattering in optical fibers using fiber Bragg gratings,” Opt. Express 11, 3467–3472 (2003).
    [Crossref] [PubMed]

2005 (1)

2003 (1)

2000 (2)

1996 (1)

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg Grating Solitons,” Phys. Lett 76, 1627–30 (1996).
[Crossref]

1992 (1)

1991 (1)

1979 (1)

H. G. Winful, J. H. Marburger, and E. Garmire, “Theory of bistability in nonlinear distributed feedback structures,” Appl. Phys. Lett. 35, 379–381 (1979).
[Crossref]

Agrawal, Govind P.

Hojoon Lee and Govind P. Agrawal, “Suppression of stimulated Brillouin scattering in optical fibers using fiber Bragg gratings,” Opt. Express 11, 3467–3472 (2003).
[Crossref] [PubMed]

Hojoon Lee and Govind P. Agrawal, “Nonlinear Switching of Optical Pulses in Fiber Bragg Gratings,” IEEE J. Quantum Electron.39 (2003).

Broderick, Neil G. R.

de Sterke, C. M.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg Grating Solitons,” Phys. Lett 76, 1627–30 (1996).
[Crossref]

C. M. de Sterke, “Optical Push Broom,” Opt. Lett. 17, 914–916 (1992).
[Crossref] [PubMed]

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

de Sterke, C.M.

Eggleton, B. J.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg Grating Solitons,” Phys. Lett 76, 1627–30 (1996).
[Crossref]

Garmire, E.

H. G. Winful, J. H. Marburger, and E. Garmire, “Theory of bistability in nonlinear distributed feedback structures,” Appl. Phys. Lett. 35, 379–381 (1979).
[Crossref]

Hasegawa, T.

Ibsen, Morten

Jackson, K.R.

Kikuchi, K.

Krug, P. A.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg Grating Solitons,” Phys. Lett 76, 1627–30 (1996).
[Crossref]

Lee, Hojoon

Hojoon Lee and Govind P. Agrawal, “Suppression of stimulated Brillouin scattering in optical fibers using fiber Bragg gratings,” Opt. Express 11, 3467–3472 (2003).
[Crossref] [PubMed]

Hojoon Lee and Govind P. Agrawal, “Nonlinear Switching of Optical Pulses in Fiber Bragg Gratings,” IEEE J. Quantum Electron.39 (2003).

Lee, J. H.

Marburger, J. H.

H. G. Winful, J. H. Marburger, and E. Garmire, “Theory of bistability in nonlinear distributed feedback structures,” Appl. Phys. Lett. 35, 379–381 (1979).
[Crossref]

Nagashima, T.

Ogusu, K.

Ohara, S.

Richardson, David J.

Robert, B. D.

Sipe, J. E.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg Grating Solitons,” Phys. Lett 76, 1627–30 (1996).
[Crossref]

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

Slusher, R. E.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg Grating Solitons,” Phys. Lett 76, 1627–30 (1996).
[Crossref]

Sugimoto, N.

Tanemura, T.

Taverner, Domino

Winful, H. G.

H. G. Winful, J. H. Marburger, and E. Garmire, “Theory of bistability in nonlinear distributed feedback structures,” Appl. Phys. Lett. 35, 379–381 (1979).
[Crossref]

Yeh, Pochi

Pochi Yeh, Optical Waves in Layered Media, (Wiley, New York, 1988).

Appl. Phys. Lett. (1)

H. G. Winful, J. H. Marburger, and E. Garmire, “Theory of bistability in nonlinear distributed feedback structures,” Appl. Phys. Lett. 35, 379–381 (1979).
[Crossref]

J. Opt. Soc. Am. B (3)

Opt. Express (1)

Opt. Lett. (2)

Phys. Lett (1)

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg Grating Solitons,” Phys. Lett 76, 1627–30 (1996).
[Crossref]

Other (3)

Hojoon Lee and Govind P. Agrawal, “Nonlinear Switching of Optical Pulses in Fiber Bragg Gratings,” IEEE J. Quantum Electron.39 (2003).

Pochi Yeh, Optical Waves in Layered Media, (Wiley, New York, 1988).

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

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Figures (5)

Fig. 1.
Fig. 1.

Schematic of the FBG.

Fig. 2.
Fig. 2.

Bistability hysteresis loop in uniform FBG.

Fig. 3.
Fig. 3.

Three unique nonlinear switching behaviors of probe transmission via Gaussian pump injection in FBG.

Fig. 4.
Fig. 4.

Bistability threshold inside the hysteresis loop at 4.6 GW/cm2.

Fig. 5.
Fig. 5.

Bistability threshold inside hysteresis loop of FBG.

Tables (1)

Tables Icon

Table 1. The summary of nonlinear switching behaviors of probe transmission via Gaussian pump injection in the FBG

Equations (6)

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n ( z ) = n ¯ + n 1 ( z ) × cos [ 2 π Λ z + θ ( z ) ] + n 2 × E ( z ) 2
E ( z , t ) = [ A + ( z , t ) . exp ( iK B z ) + A ( z , t ) . exp ( iK B z ) ] . exp ( i ω 0 t )
A + ( z , t ) = P ( z V g t ) exp ( i δ p t ) + ε + ( z , t ) exp ( i δ 0 t )
A ( z , t ) = ε ( z , t ) exp ( i δ 0 t )
+ i ε + z + i 1 V g ε + t + δ ε + + κ ε + Γ [ ε + 2 + 2 ε 2 + 2 P ( z V g t ) 2 ] ε + = 0
+ i ε z + i 1 V g ε t + δ ε + κ * ε + + Γ [ ε 2 + 2 ε + 2 + 2 P ( z V g t ) 2 ] ε = 0

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