Abstract

Using computer simulations, we demonstrate an optical cascadable AND gate based on soliton interaction in a fiber Bragg grating. A single soliton that is launched into the device is backreflected. When two solitons are launched, one of the solitons is transmitted while the other is backreflected. The time delay between the solitons may be few times longer than the duration of the solitons. We show that the interaction causes an increase in the frequency of one of the solitons that enables its transmission through the grating bandgap.

© 2007 Optical Society of America

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  1. K. H. Ahn, M. Vaziri, B. C. Barnett, G. R. Williams, X. D. Cao, M. N. Islam, B. Malo, K. O. Hill, and D. Q. Chowdhury, J. Lightwave Technol. 14, 8 (1996).
    [CrossRef]
  2. C. R. Menyuk, Opt. Lett. 12, 614 (1987).
    [CrossRef] [PubMed]
  3. C. R. Menyuk, J. Opt. Soc. Am. B 5, 392 (1988).
    [CrossRef]
  4. C. M. de Sterke and J. E. Sipe, in Progress in Optics XXXIII, E.Wolf ed. (Elsevier, 1994), pp. 203-260.
  5. N. G. R. Broderick, D. J. Richardson, and M. Ibsen, Opt. Lett. 25, 536 (2000).
    [CrossRef]
  6. D. Taverner, N. G. R. Broderick, D. J. Richardson, M. Ibsen, and R. I. Laming, Opt. Lett. 23, 259 (1998).
    [CrossRef]
  7. S. Pereira and J. E. Sipe, Opt. Express 3, 418 (1998).
    [CrossRef] [PubMed]
  8. A. Rosenthal and M. Horowitz, Phys. Rev. E 74, 066611 (2006).
    [CrossRef]
  9. N. G. R. Broderick and C. M. de Sterke, Phys. Rev. E 51, 4978 (1995).
    [CrossRef]
  10. N. G. R. Broderick and C. M. de Sterke, Phys. Rev. E 58, 7941 (1998).
    [CrossRef]
  11. A. Rosenthal and M. Horowitz, Opt. Lett. 31, 1334 (2006).
    [CrossRef] [PubMed]

2006 (2)

A. Rosenthal and M. Horowitz, Phys. Rev. E 74, 066611 (2006).
[CrossRef]

A. Rosenthal and M. Horowitz, Opt. Lett. 31, 1334 (2006).
[CrossRef] [PubMed]

2000 (1)

1998 (3)

1996 (1)

K. H. Ahn, M. Vaziri, B. C. Barnett, G. R. Williams, X. D. Cao, M. N. Islam, B. Malo, K. O. Hill, and D. Q. Chowdhury, J. Lightwave Technol. 14, 8 (1996).
[CrossRef]

1995 (1)

N. G. R. Broderick and C. M. de Sterke, Phys. Rev. E 51, 4978 (1995).
[CrossRef]

1988 (1)

1987 (1)

Ahn, K. H.

K. H. Ahn, M. Vaziri, B. C. Barnett, G. R. Williams, X. D. Cao, M. N. Islam, B. Malo, K. O. Hill, and D. Q. Chowdhury, J. Lightwave Technol. 14, 8 (1996).
[CrossRef]

Barnett, B. C.

K. H. Ahn, M. Vaziri, B. C. Barnett, G. R. Williams, X. D. Cao, M. N. Islam, B. Malo, K. O. Hill, and D. Q. Chowdhury, J. Lightwave Technol. 14, 8 (1996).
[CrossRef]

Broderick, N. G. R.

Cao, X. D.

K. H. Ahn, M. Vaziri, B. C. Barnett, G. R. Williams, X. D. Cao, M. N. Islam, B. Malo, K. O. Hill, and D. Q. Chowdhury, J. Lightwave Technol. 14, 8 (1996).
[CrossRef]

Chowdhury, D. Q.

K. H. Ahn, M. Vaziri, B. C. Barnett, G. R. Williams, X. D. Cao, M. N. Islam, B. Malo, K. O. Hill, and D. Q. Chowdhury, J. Lightwave Technol. 14, 8 (1996).
[CrossRef]

de Sterke, C. M.

N. G. R. Broderick and C. M. de Sterke, Phys. Rev. E 58, 7941 (1998).
[CrossRef]

N. G. R. Broderick and C. M. de Sterke, Phys. Rev. E 51, 4978 (1995).
[CrossRef]

C. M. de Sterke and J. E. Sipe, in Progress in Optics XXXIII, E.Wolf ed. (Elsevier, 1994), pp. 203-260.

Hill, K. O.

K. H. Ahn, M. Vaziri, B. C. Barnett, G. R. Williams, X. D. Cao, M. N. Islam, B. Malo, K. O. Hill, and D. Q. Chowdhury, J. Lightwave Technol. 14, 8 (1996).
[CrossRef]

Horowitz, M.

A. Rosenthal and M. Horowitz, Opt. Lett. 31, 1334 (2006).
[CrossRef] [PubMed]

A. Rosenthal and M. Horowitz, Phys. Rev. E 74, 066611 (2006).
[CrossRef]

Ibsen, M.

Islam, M. N.

K. H. Ahn, M. Vaziri, B. C. Barnett, G. R. Williams, X. D. Cao, M. N. Islam, B. Malo, K. O. Hill, and D. Q. Chowdhury, J. Lightwave Technol. 14, 8 (1996).
[CrossRef]

Laming, R. I.

Malo, B.

K. H. Ahn, M. Vaziri, B. C. Barnett, G. R. Williams, X. D. Cao, M. N. Islam, B. Malo, K. O. Hill, and D. Q. Chowdhury, J. Lightwave Technol. 14, 8 (1996).
[CrossRef]

Menyuk, C. R.

Pereira, S.

Richardson, D. J.

Rosenthal, A.

A. Rosenthal and M. Horowitz, Phys. Rev. E 74, 066611 (2006).
[CrossRef]

A. Rosenthal and M. Horowitz, Opt. Lett. 31, 1334 (2006).
[CrossRef] [PubMed]

Sipe, J. E.

S. Pereira and J. E. Sipe, Opt. Express 3, 418 (1998).
[CrossRef] [PubMed]

C. M. de Sterke and J. E. Sipe, in Progress in Optics XXXIII, E.Wolf ed. (Elsevier, 1994), pp. 203-260.

Taverner, D.

Vaziri, M.

K. H. Ahn, M. Vaziri, B. C. Barnett, G. R. Williams, X. D. Cao, M. N. Islam, B. Malo, K. O. Hill, and D. Q. Chowdhury, J. Lightwave Technol. 14, 8 (1996).
[CrossRef]

Williams, G. R.

K. H. Ahn, M. Vaziri, B. C. Barnett, G. R. Williams, X. D. Cao, M. N. Islam, B. Malo, K. O. Hill, and D. Q. Chowdhury, J. Lightwave Technol. 14, 8 (1996).
[CrossRef]

J. Lightwave Technol. (1)

K. H. Ahn, M. Vaziri, B. C. Barnett, G. R. Williams, X. D. Cao, M. N. Islam, B. Malo, K. O. Hill, and D. Q. Chowdhury, J. Lightwave Technol. 14, 8 (1996).
[CrossRef]

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

Opt. Express (1)

Opt. Lett. (4)

Phys. Rev. E (3)

A. Rosenthal and M. Horowitz, Phys. Rev. E 74, 066611 (2006).
[CrossRef]

N. G. R. Broderick and C. M. de Sterke, Phys. Rev. E 51, 4978 (1995).
[CrossRef]

N. G. R. Broderick and C. M. de Sterke, Phys. Rev. E 58, 7941 (1998).
[CrossRef]

Other (1)

C. M. de Sterke and J. E. Sipe, in Progress in Optics XXXIII, E.Wolf ed. (Elsevier, 1994), pp. 203-260.

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Figures (4)

Fig. 1
Fig. 1

Schematic structure of the chirped FBG. Region I is used to obtain the soliton interaction and to reflect a single soliton. Region II is used to stabilize the transmitted soliton. Region III is used to obtain a soliton at the output of the device with parameters similar to those of the input soliton.

Fig. 2
Fig. 2

Simulation results showing the intensity I of the wave propagating in the device when (a) a single soliton is launched and when (b) two solitons are launched. The relative phase and the delay between the solitons are equal to 5.1 rad and 94 ps , respectively. The 2D plots give an upper view of the solitons’ trajectories. The straight lines mark the different regions of the grating.

Fig. 3
Fig. 3

Central frequency shift of the solitons Δ f as a function of the location when a single soliton is launched (solid curve) and when two solitons are launched (dashed and dashed–dotted curves, corresponding to the trailing and the forward solitons, respectively). The vertical lines mark the different regions of the grating.

Fig. 4
Fig. 4

Simulation results showing the wave propagation in the device when two solitons are launched with a relative phase of π + 5.1 .

Equations (4)

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± i z u ± + i V g 1 t u ± + κ u + Γ ( u ± 2 + 2 u 2 ) u ± + σ ( z ) u ± = 0 ,
Q + ( u + 2 + u 2 ) d z ,
v ̃ Q 1 + ( u + 2 u 2 ) d z .
Q = 2 δ ̃ Γ ( 1 + 1 2 1 + v 2 1 v 2 ) 1 ,

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