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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Appl. Phys. Lett.

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]

IEEE J. Quantum Electron

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

J. Opt. Soc. Am. B

Opt. Express

Opt. Lett.

Phys. Lett

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]

Progress in Optics

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

Other

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

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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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