Abstract

We numerically demonstrate the feasibility of constructing an all-optical AND gate by using a microresonator structure with Kerr nonlinearity. The gate is much smaller than similar AND gates based on Bragg gratings and has lower power requirements.

© 2003 Optical Society of America

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References

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  1. B. E. Little, S. T. Chu, J. V. Hryniewicz, and P. P. Absil, Opt. Lett. 25, 344 (2000).
    [CrossRef]
  2. A. Melloni, Opt. Lett. 26, 917 (2001).
    [CrossRef]
  3. S. Pereira, J. E. Sipe, J. E. Heebner, and R. W. Boyd, Opt. Lett. 27, 536 (2002).
    [CrossRef]
  4. S. Pereira, P. Chak, and J. E. Sipe, J. Opt. Soc. Am. B 19, 2191 (2002).
    [CrossRef]
  5. S. Lee and S.-T. Ho, Opt. Lett. 18, 962 (1993).
    [CrossRef] [PubMed]
  6. D. Taverner, N. G. R. Broderick, D. J. Richardson, M. Ibsen, and R. I. Laming, Opt. Lett. 23, 259 (1998).
    [CrossRef]
  7. J. E. Heebner, R. W. Boyd, and Q.-H. Park, J. Opt. Soc. Am. B 19, 722 (2002).
    [CrossRef]
  8. Optical bistability comes into play only when the carrier frequency of the pulse is positively detuned from the resonance frequency of the resonator. See P. Chak, J. E. Sipe, and S. Pereira, Opt. Commun. 213, 163 (2002).
    [CrossRef]
  9. A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, and C. N. Ironside, Appl. Phys. Lett. 61, 147 (1992).
    [CrossRef]
  10. V. Van, P. P. Absil, J. V. Hryniewicz, and P.-T. Ho, Opt. Lett. 19, 1734 (2001).

2002 (4)

S. Pereira, J. E. Sipe, J. E. Heebner, and R. W. Boyd, Opt. Lett. 27, 536 (2002).
[CrossRef]

S. Pereira, P. Chak, and J. E. Sipe, J. Opt. Soc. Am. B 19, 2191 (2002).
[CrossRef]

J. E. Heebner, R. W. Boyd, and Q.-H. Park, J. Opt. Soc. Am. B 19, 722 (2002).
[CrossRef]

Optical bistability comes into play only when the carrier frequency of the pulse is positively detuned from the resonance frequency of the resonator. See P. Chak, J. E. Sipe, and S. Pereira, Opt. Commun. 213, 163 (2002).
[CrossRef]

2001 (2)

V. Van, P. P. Absil, J. V. Hryniewicz, and P.-T. Ho, Opt. Lett. 19, 1734 (2001).

A. Melloni, Opt. Lett. 26, 917 (2001).
[CrossRef]

2000 (1)

1998 (1)

1993 (1)

1992 (1)

A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, and C. N. Ironside, Appl. Phys. Lett. 61, 147 (1992).
[CrossRef]

Absil, P. P.

V. Van, P. P. Absil, J. V. Hryniewicz, and P.-T. Ho, Opt. Lett. 19, 1734 (2001).

B. E. Little, S. T. Chu, J. V. Hryniewicz, and P. P. Absil, Opt. Lett. 25, 344 (2000).
[CrossRef]

Aitchison, J. S.

A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, and C. N. Ironside, Appl. Phys. Lett. 61, 147 (1992).
[CrossRef]

Boyd, R. W.

Broderick, N. G. R.

Chak, P.

S. Pereira, P. Chak, and J. E. Sipe, J. Opt. Soc. Am. B 19, 2191 (2002).
[CrossRef]

Optical bistability comes into play only when the carrier frequency of the pulse is positively detuned from the resonance frequency of the resonator. See P. Chak, J. E. Sipe, and S. Pereira, Opt. Commun. 213, 163 (2002).
[CrossRef]

Chu, S. T.

Heebner, J. E.

Ho, P.-T.

V. Van, P. P. Absil, J. V. Hryniewicz, and P.-T. Ho, Opt. Lett. 19, 1734 (2001).

Ho, S.-T.

Hryniewicz, J. V.

V. Van, P. P. Absil, J. V. Hryniewicz, and P.-T. Ho, Opt. Lett. 19, 1734 (2001).

B. E. Little, S. T. Chu, J. V. Hryniewicz, and P. P. Absil, Opt. Lett. 25, 344 (2000).
[CrossRef]

Ibsen, M.

Ironside, C. N.

A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, and C. N. Ironside, Appl. Phys. Lett. 61, 147 (1992).
[CrossRef]

Laming, R. I.

Lee, S.

Little, B. E.

Melloni, A.

Park, Q.-H.

Pereira, S.

S. Pereira, P. Chak, and J. E. Sipe, J. Opt. Soc. Am. B 19, 2191 (2002).
[CrossRef]

S. Pereira, J. E. Sipe, J. E. Heebner, and R. W. Boyd, Opt. Lett. 27, 536 (2002).
[CrossRef]

Optical bistability comes into play only when the carrier frequency of the pulse is positively detuned from the resonance frequency of the resonator. See P. Chak, J. E. Sipe, and S. Pereira, Opt. Commun. 213, 163 (2002).
[CrossRef]

Richardson, D. J.

Sipe, J. E.

S. Pereira, J. E. Sipe, J. E. Heebner, and R. W. Boyd, Opt. Lett. 27, 536 (2002).
[CrossRef]

S. Pereira, P. Chak, and J. E. Sipe, J. Opt. Soc. Am. B 19, 2191 (2002).
[CrossRef]

Optical bistability comes into play only when the carrier frequency of the pulse is positively detuned from the resonance frequency of the resonator. See P. Chak, J. E. Sipe, and S. Pereira, Opt. Commun. 213, 163 (2002).
[CrossRef]

Stegeman, G. I.

A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, and C. N. Ironside, Appl. Phys. Lett. 61, 147 (1992).
[CrossRef]

Taverner, D.

Van, V.

V. Van, P. P. Absil, J. V. Hryniewicz, and P.-T. Ho, Opt. Lett. 19, 1734 (2001).

Villeneuve, A.

A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, and C. N. Ironside, Appl. Phys. Lett. 61, 147 (1992).
[CrossRef]

Wigley, P. G. J.

A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, and C. N. Ironside, Appl. Phys. Lett. 61, 147 (1992).
[CrossRef]

Yang, C. C.

A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, and C. N. Ironside, Appl. Phys. Lett. 61, 147 (1992).
[CrossRef]

Appl. Phys. Lett. (1)

A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, and C. N. Ironside, Appl. Phys. Lett. 61, 147 (1992).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Commun. (1)

Optical bistability comes into play only when the carrier frequency of the pulse is positively detuned from the resonance frequency of the resonator. See P. Chak, J. E. Sipe, and S. Pereira, Opt. Commun. 213, 163 (2002).
[CrossRef]

Opt. Lett. (6)

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Figures (3)

Fig. 1
Fig. 1

(a) Schematic of an AND gate with three cells, (b) schematic of one cell of the system.

Fig. 2
Fig. 2

Continuous-wave transmission spectra for a 1-cell (solid curve) and a 5-cell (dashed curve) structure. The large filled circle indicates the resonant frequency of the microresonators.

Fig. 3
Fig. 3

(a) AND gate contrast ratio, γIp, for a 5- (solid) and a 10- (dashed curve) cell structure. (b) Input (dashed curve) and output (solid curve) pulses along the bottom channel of the five-cell AND gate at Ip=11 MW/cm2, which corresponds to the maximum value of γIp.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

E3E1=σiκiκσE4E2,
ldud=1tt2-r2r-r1l0u0,
Ajζ,t+δt=iω¯cδζneff+n2JjAjζ-δζ,t-12δζα1+α2Jj+α3Kj×Ajζ-δζ,t,
Jj=Ajζ-δζ,t2+2Aj˜ζ-δζ,t2,
Kj=Ajζ-δζ,t4+3Aj˜ζ-δζ,t4,

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