Abstract

We propose an all-optical half adder based on two different cross structures in two-dimensional photonic crystals. One cross structure contains nonlinear materials and functions as an “AND” logic gate. The other one only contains linear materials and acts as an “XOR” logic gate. The system is demonstrated numerically by the FDTD method to work as expected. The optimal operating speed without considering the response time of the nonlinear material, the least ON to OFF logic-level contrast ratio, and the minimum power for this half adder obtained were 0.91Tbps, 16dB and 436mW, respectively. The proposed structure has the potential to be used for constructing all-optical integrated digital computing circuits.

© 2008 Optical Society of America

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References

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  1. E. Yablonovitch, "Inhibited Spontaneous Emission in Solid-State Physics and Electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
    [CrossRef] [PubMed]
  2. S. John, "Strong localization of photons in certain disoordered dielectric superlattices," Phys. Rev. Lett. 58,2846-2489 (1987).
    [CrossRef]
  3. J. D. Joannopoulos, "Photonics crystals: putting a new twist on light," Nature (London) 386,143-149 (1997).
    [CrossRef]
  4. H. M. Gibbs, "Optical Bistability," in Controlling Light with Light, (Academic Press, Orlando, 1985).
  5. E. Centeno and D. Felbacq, "Optical bistability in finite-size nonlinear bidimensional photonic crystal doped by a microcavity," Phys. Rev. B 62, 7683-7686 (2000).
    [CrossRef]
  6. K. M. F. Yanik, S. Fan, and M. Soijacic, "High-contrast all-optical bistable switching in photonic crystal microcavities," Appl. Phys. Lett. 83,2739-2741 (2003).
    [CrossRef]
  7. M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, "Optimal bistable switching in nonlinear photonic crystals," Phys. Rev. E 66, 0556011-4 (2002).
    [CrossRef]
  8. M. F. Yanik, S. Fan, M. Soljacic, and J. D. Joannopoulos, "All-optical transistor action with bistable switching in a photonic crystal cross-waveguide geometry," Opt. Lett. 28, 2506-2608 (2003).
    [CrossRef] [PubMed]
  9. Z. -H. Zhu, W. -M. Ye, J. -R. Ji, X. -D. Yuan, and C. Zen, "High-contrast light-by-light swithching and AND gate based on nonlinear photonic crystals," Opt. Express 14, 1783-1788 (2006).
    [CrossRef] [PubMed]
  10. M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, "Optical bistable switching of Si high-Q photonic-crystal nanocavities," Opt. Express 13, 2678 (2005).
    [CrossRef] [PubMed]
  11. Y. -L. Zhang, Y. Zhang, and B. -J. Li, "Optical switches and logic gates based on self-collimated beams in two-dimensional photonic crystals," Opt. Express 15, 9287-9292 (2007).
    [CrossRef] [PubMed]
  12. Yu, X.  and S. Fan, "Bends and splitters for self-collimated beams in photonic crystals," Appl. Phys. Lett. 83, 3251-3253 (2003).
    [CrossRef]
  13. C. -C. Chen, H. -D. Chien, and P. -G. Luan, "Photonic crystal beam splitters," Appl. Opt. 43, 6187-6190 (2004).
    [CrossRef] [PubMed]
  14. K. A. Shinya, T. Tanabe, E. Kuramochi, and M. Notomi, "All-optical Switch and Digital Light Processing Using Photonic Crystals," NTT Tech. Rev. 3, 61-68 (2005).
  15. T. Asai, Y. Amemiya, and M. Kosiba, "A Photonic-Crystal Logic Circuit Based on the Binary Decision Diagram," in Proceeding of International Workshop on Photonic and Electromagnetic Crystal Structures, (Academic, Sendai, Japan, 2000), T4-14.
  16. Y. Kawashita, M. Haraguchi, H, Okamoto, M. Fujii, and M. Fukui, "Optical Amplifier Using Nonlinear Nanodefect Cavity in Photonic Crystal," Jpn. J. Appl. Phys. 45, 7724-7728 (2006).
    [CrossRef]
  17. N. C. Panoiu, M. Bahl, and R. M. Osgood, Jr., "All-optical tunability of a nonlinear photonic crystal channel drop filter," Opt. Express 12, 1605 (2004).
    [CrossRef] [PubMed]
  18. E. P. Kosmidou and T. D. Tsiboukis, "An FDTD analysis of photonic crystal waveguides comprising third-order nonlinear materials," Opt. Quantum Electron. 35, 931-946 (2003).
    [CrossRef]
  19. M. Bahl, N. C. Panoiu, and R. M. Osgood, Jr., "Nonlinear optical effects in a two-dimensional photonic crystal containing one-dimensional Kerr defects," Phys. Rev. E 67, 0566041-9 (2003).
    [CrossRef]
  20. M. L. Povinelli, S. G. Johnson, S. Fan, and J. D. Joannopoulos, "Emulation of two-dimensional photonic crystal defect modes in a photonic crystal with a three-dimensional photonic band gap," Phys. Rev. B 64, 0753131-8 (2001).
    [CrossRef]
  21. H. -H. Lee, K. -M. Chae, S. -Y. Yim, and S. -H. Park, "Finite-difference time-domain analysis of self-focusing in a nonlinear Kerr film," Opt. Express 12, 2603 (2004).
    [CrossRef] [PubMed]
  22. D. Vujic and S. John, "Pulse reshaping in photonic crystal waveguides and microcavities with Kerr nonlinearity: Critical issues for all-optical switching," Phys. Rev. A 72, 0138071-10 (2005).
    [CrossRef]

2007 (1)

2006 (2)

Y. Kawashita, M. Haraguchi, H, Okamoto, M. Fujii, and M. Fukui, "Optical Amplifier Using Nonlinear Nanodefect Cavity in Photonic Crystal," Jpn. J. Appl. Phys. 45, 7724-7728 (2006).
[CrossRef]

Z. -H. Zhu, W. -M. Ye, J. -R. Ji, X. -D. Yuan, and C. Zen, "High-contrast light-by-light swithching and AND gate based on nonlinear photonic crystals," Opt. Express 14, 1783-1788 (2006).
[CrossRef] [PubMed]

2005 (3)

M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, "Optical bistable switching of Si high-Q photonic-crystal nanocavities," Opt. Express 13, 2678 (2005).
[CrossRef] [PubMed]

K. A. Shinya, T. Tanabe, E. Kuramochi, and M. Notomi, "All-optical Switch and Digital Light Processing Using Photonic Crystals," NTT Tech. Rev. 3, 61-68 (2005).

D. Vujic and S. John, "Pulse reshaping in photonic crystal waveguides and microcavities with Kerr nonlinearity: Critical issues for all-optical switching," Phys. Rev. A 72, 0138071-10 (2005).
[CrossRef]

2004 (3)

2003 (5)

M. F. Yanik, S. Fan, M. Soljacic, and J. D. Joannopoulos, "All-optical transistor action with bistable switching in a photonic crystal cross-waveguide geometry," Opt. Lett. 28, 2506-2608 (2003).
[CrossRef] [PubMed]

Yu, X.  and S. Fan, "Bends and splitters for self-collimated beams in photonic crystals," Appl. Phys. Lett. 83, 3251-3253 (2003).
[CrossRef]

E. P. Kosmidou and T. D. Tsiboukis, "An FDTD analysis of photonic crystal waveguides comprising third-order nonlinear materials," Opt. Quantum Electron. 35, 931-946 (2003).
[CrossRef]

M. Bahl, N. C. Panoiu, and R. M. Osgood, Jr., "Nonlinear optical effects in a two-dimensional photonic crystal containing one-dimensional Kerr defects," Phys. Rev. E 67, 0566041-9 (2003).
[CrossRef]

K. M. F. Yanik, S. Fan, and M. Soijacic, "High-contrast all-optical bistable switching in photonic crystal microcavities," Appl. Phys. Lett. 83,2739-2741 (2003).
[CrossRef]

2002 (1)

M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, "Optimal bistable switching in nonlinear photonic crystals," Phys. Rev. E 66, 0556011-4 (2002).
[CrossRef]

2001 (1)

M. L. Povinelli, S. G. Johnson, S. Fan, and J. D. Joannopoulos, "Emulation of two-dimensional photonic crystal defect modes in a photonic crystal with a three-dimensional photonic band gap," Phys. Rev. B 64, 0753131-8 (2001).
[CrossRef]

2000 (1)

E. Centeno and D. Felbacq, "Optical bistability in finite-size nonlinear bidimensional photonic crystal doped by a microcavity," Phys. Rev. B 62, 7683-7686 (2000).
[CrossRef]

1997 (1)

J. D. Joannopoulos, "Photonics crystals: putting a new twist on light," Nature (London) 386,143-149 (1997).
[CrossRef]

1987 (2)

E. Yablonovitch, "Inhibited Spontaneous Emission in Solid-State Physics and Electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

S. John, "Strong localization of photons in certain disoordered dielectric superlattices," Phys. Rev. Lett. 58,2846-2489 (1987).
[CrossRef]

Bahl, M.

N. C. Panoiu, M. Bahl, and R. M. Osgood, Jr., "All-optical tunability of a nonlinear photonic crystal channel drop filter," Opt. Express 12, 1605 (2004).
[CrossRef] [PubMed]

M. Bahl, N. C. Panoiu, and R. M. Osgood, Jr., "Nonlinear optical effects in a two-dimensional photonic crystal containing one-dimensional Kerr defects," Phys. Rev. E 67, 0566041-9 (2003).
[CrossRef]

Centeno, E.

E. Centeno and D. Felbacq, "Optical bistability in finite-size nonlinear bidimensional photonic crystal doped by a microcavity," Phys. Rev. B 62, 7683-7686 (2000).
[CrossRef]

Chae, K. -M.

Chen, C. -C.

Chien, H. -D.

Fan, S.

K. M. F. Yanik, S. Fan, and M. Soijacic, "High-contrast all-optical bistable switching in photonic crystal microcavities," Appl. Phys. Lett. 83,2739-2741 (2003).
[CrossRef]

M. F. Yanik, S. Fan, M. Soljacic, and J. D. Joannopoulos, "All-optical transistor action with bistable switching in a photonic crystal cross-waveguide geometry," Opt. Lett. 28, 2506-2608 (2003).
[CrossRef] [PubMed]

Yu, X.  and S. Fan, "Bends and splitters for self-collimated beams in photonic crystals," Appl. Phys. Lett. 83, 3251-3253 (2003).
[CrossRef]

M. L. Povinelli, S. G. Johnson, S. Fan, and J. D. Joannopoulos, "Emulation of two-dimensional photonic crystal defect modes in a photonic crystal with a three-dimensional photonic band gap," Phys. Rev. B 64, 0753131-8 (2001).
[CrossRef]

Felbacq, D.

E. Centeno and D. Felbacq, "Optical bistability in finite-size nonlinear bidimensional photonic crystal doped by a microcavity," Phys. Rev. B 62, 7683-7686 (2000).
[CrossRef]

Fink, Y.

M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, "Optimal bistable switching in nonlinear photonic crystals," Phys. Rev. E 66, 0556011-4 (2002).
[CrossRef]

Haraguchi, M.

Y. Kawashita, M. Haraguchi, H, Okamoto, M. Fujii, and M. Fukui, "Optical Amplifier Using Nonlinear Nanodefect Cavity in Photonic Crystal," Jpn. J. Appl. Phys. 45, 7724-7728 (2006).
[CrossRef]

Ibanescu, M.

M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, "Optimal bistable switching in nonlinear photonic crystals," Phys. Rev. E 66, 0556011-4 (2002).
[CrossRef]

Ji, J. -R.

Joannopoulos, J. D.

M. F. Yanik, S. Fan, M. Soljacic, and J. D. Joannopoulos, "All-optical transistor action with bistable switching in a photonic crystal cross-waveguide geometry," Opt. Lett. 28, 2506-2608 (2003).
[CrossRef] [PubMed]

M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, "Optimal bistable switching in nonlinear photonic crystals," Phys. Rev. E 66, 0556011-4 (2002).
[CrossRef]

M. L. Povinelli, S. G. Johnson, S. Fan, and J. D. Joannopoulos, "Emulation of two-dimensional photonic crystal defect modes in a photonic crystal with a three-dimensional photonic band gap," Phys. Rev. B 64, 0753131-8 (2001).
[CrossRef]

J. D. Joannopoulos, "Photonics crystals: putting a new twist on light," Nature (London) 386,143-149 (1997).
[CrossRef]

John, S.

D. Vujic and S. John, "Pulse reshaping in photonic crystal waveguides and microcavities with Kerr nonlinearity: Critical issues for all-optical switching," Phys. Rev. A 72, 0138071-10 (2005).
[CrossRef]

S. John, "Strong localization of photons in certain disoordered dielectric superlattices," Phys. Rev. Lett. 58,2846-2489 (1987).
[CrossRef]

Johnson, S. G.

M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, "Optimal bistable switching in nonlinear photonic crystals," Phys. Rev. E 66, 0556011-4 (2002).
[CrossRef]

M. L. Povinelli, S. G. Johnson, S. Fan, and J. D. Joannopoulos, "Emulation of two-dimensional photonic crystal defect modes in a photonic crystal with a three-dimensional photonic band gap," Phys. Rev. B 64, 0753131-8 (2001).
[CrossRef]

Kawashita, Y.

Y. Kawashita, M. Haraguchi, H, Okamoto, M. Fujii, and M. Fukui, "Optical Amplifier Using Nonlinear Nanodefect Cavity in Photonic Crystal," Jpn. J. Appl. Phys. 45, 7724-7728 (2006).
[CrossRef]

Kira, G.

Kosmidou, E. P.

E. P. Kosmidou and T. D. Tsiboukis, "An FDTD analysis of photonic crystal waveguides comprising third-order nonlinear materials," Opt. Quantum Electron. 35, 931-946 (2003).
[CrossRef]

Kuramochi, E.

K. A. Shinya, T. Tanabe, E. Kuramochi, and M. Notomi, "All-optical Switch and Digital Light Processing Using Photonic Crystals," NTT Tech. Rev. 3, 61-68 (2005).

M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, "Optical bistable switching of Si high-Q photonic-crystal nanocavities," Opt. Express 13, 2678 (2005).
[CrossRef] [PubMed]

Lee, H. -H.

Li, B. -J.

Luan, P. -G.

Mitsugi, S.

Notomi, M.

M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, "Optical bistable switching of Si high-Q photonic-crystal nanocavities," Opt. Express 13, 2678 (2005).
[CrossRef] [PubMed]

K. A. Shinya, T. Tanabe, E. Kuramochi, and M. Notomi, "All-optical Switch and Digital Light Processing Using Photonic Crystals," NTT Tech. Rev. 3, 61-68 (2005).

Osgood, R. M.

N. C. Panoiu, M. Bahl, and R. M. Osgood, Jr., "All-optical tunability of a nonlinear photonic crystal channel drop filter," Opt. Express 12, 1605 (2004).
[CrossRef] [PubMed]

M. Bahl, N. C. Panoiu, and R. M. Osgood, Jr., "Nonlinear optical effects in a two-dimensional photonic crystal containing one-dimensional Kerr defects," Phys. Rev. E 67, 0566041-9 (2003).
[CrossRef]

Panoiu, N. C.

N. C. Panoiu, M. Bahl, and R. M. Osgood, Jr., "All-optical tunability of a nonlinear photonic crystal channel drop filter," Opt. Express 12, 1605 (2004).
[CrossRef] [PubMed]

M. Bahl, N. C. Panoiu, and R. M. Osgood, Jr., "Nonlinear optical effects in a two-dimensional photonic crystal containing one-dimensional Kerr defects," Phys. Rev. E 67, 0566041-9 (2003).
[CrossRef]

Park, S. -H.

Povinelli, M. L.

M. L. Povinelli, S. G. Johnson, S. Fan, and J. D. Joannopoulos, "Emulation of two-dimensional photonic crystal defect modes in a photonic crystal with a three-dimensional photonic band gap," Phys. Rev. B 64, 0753131-8 (2001).
[CrossRef]

Shinya, A.

Shinya, K. A.

K. A. Shinya, T. Tanabe, E. Kuramochi, and M. Notomi, "All-optical Switch and Digital Light Processing Using Photonic Crystals," NTT Tech. Rev. 3, 61-68 (2005).

Soijacic, M.

K. M. F. Yanik, S. Fan, and M. Soijacic, "High-contrast all-optical bistable switching in photonic crystal microcavities," Appl. Phys. Lett. 83,2739-2741 (2003).
[CrossRef]

Soljacic, M.

M. F. Yanik, S. Fan, M. Soljacic, and J. D. Joannopoulos, "All-optical transistor action with bistable switching in a photonic crystal cross-waveguide geometry," Opt. Lett. 28, 2506-2608 (2003).
[CrossRef] [PubMed]

M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, "Optimal bistable switching in nonlinear photonic crystals," Phys. Rev. E 66, 0556011-4 (2002).
[CrossRef]

Tanabe, T.

K. A. Shinya, T. Tanabe, E. Kuramochi, and M. Notomi, "All-optical Switch and Digital Light Processing Using Photonic Crystals," NTT Tech. Rev. 3, 61-68 (2005).

M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, "Optical bistable switching of Si high-Q photonic-crystal nanocavities," Opt. Express 13, 2678 (2005).
[CrossRef] [PubMed]

Tsiboukis, T. D.

E. P. Kosmidou and T. D. Tsiboukis, "An FDTD analysis of photonic crystal waveguides comprising third-order nonlinear materials," Opt. Quantum Electron. 35, 931-946 (2003).
[CrossRef]

Vujic, D.

D. Vujic and S. John, "Pulse reshaping in photonic crystal waveguides and microcavities with Kerr nonlinearity: Critical issues for all-optical switching," Phys. Rev. A 72, 0138071-10 (2005).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, "Inhibited Spontaneous Emission in Solid-State Physics and Electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

Yanik, K. M. F.

K. M. F. Yanik, S. Fan, and M. Soijacic, "High-contrast all-optical bistable switching in photonic crystal microcavities," Appl. Phys. Lett. 83,2739-2741 (2003).
[CrossRef]

Yanik, M. F.

Ye, W. -M.

Yim, S. -Y.

Yu,

Yu, X.  and S. Fan, "Bends and splitters for self-collimated beams in photonic crystals," Appl. Phys. Lett. 83, 3251-3253 (2003).
[CrossRef]

Yuan, X. -D.

Zen, C.

Zhang, Y.

Zhang, Y. -L.

Zhu, Z. -H.

Appl. Opt. (1)

Appl. Phys. Lett. (2)

K. M. F. Yanik, S. Fan, and M. Soijacic, "High-contrast all-optical bistable switching in photonic crystal microcavities," Appl. Phys. Lett. 83,2739-2741 (2003).
[CrossRef]

Yu, X.  and S. Fan, "Bends and splitters for self-collimated beams in photonic crystals," Appl. Phys. Lett. 83, 3251-3253 (2003).
[CrossRef]

Jpn. J. Appl. Phys. (1)

Y. Kawashita, M. Haraguchi, H, Okamoto, M. Fujii, and M. Fukui, "Optical Amplifier Using Nonlinear Nanodefect Cavity in Photonic Crystal," Jpn. J. Appl. Phys. 45, 7724-7728 (2006).
[CrossRef]

Nature (London) (1)

J. D. Joannopoulos, "Photonics crystals: putting a new twist on light," Nature (London) 386,143-149 (1997).
[CrossRef]

NTT Tech. Rev. (1)

K. A. Shinya, T. Tanabe, E. Kuramochi, and M. Notomi, "All-optical Switch and Digital Light Processing Using Photonic Crystals," NTT Tech. Rev. 3, 61-68 (2005).

Opt. Express (5)

Opt. Lett. (1)

Opt. Quantum Electron. (1)

E. P. Kosmidou and T. D. Tsiboukis, "An FDTD analysis of photonic crystal waveguides comprising third-order nonlinear materials," Opt. Quantum Electron. 35, 931-946 (2003).
[CrossRef]

Phys. Rev. A (1)

D. Vujic and S. John, "Pulse reshaping in photonic crystal waveguides and microcavities with Kerr nonlinearity: Critical issues for all-optical switching," Phys. Rev. A 72, 0138071-10 (2005).
[CrossRef]

Phys. Rev. B (2)

M. L. Povinelli, S. G. Johnson, S. Fan, and J. D. Joannopoulos, "Emulation of two-dimensional photonic crystal defect modes in a photonic crystal with a three-dimensional photonic band gap," Phys. Rev. B 64, 0753131-8 (2001).
[CrossRef]

E. Centeno and D. Felbacq, "Optical bistability in finite-size nonlinear bidimensional photonic crystal doped by a microcavity," Phys. Rev. B 62, 7683-7686 (2000).
[CrossRef]

Phys. Rev. E (2)

M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, "Optimal bistable switching in nonlinear photonic crystals," Phys. Rev. E 66, 0556011-4 (2002).
[CrossRef]

M. Bahl, N. C. Panoiu, and R. M. Osgood, Jr., "Nonlinear optical effects in a two-dimensional photonic crystal containing one-dimensional Kerr defects," Phys. Rev. E 67, 0566041-9 (2003).
[CrossRef]

Phys. Rev. Lett. (2)

E. Yablonovitch, "Inhibited Spontaneous Emission in Solid-State Physics and Electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

S. John, "Strong localization of photons in certain disoordered dielectric superlattices," Phys. Rev. Lett. 58,2846-2489 (1987).
[CrossRef]

Other (2)

H. M. Gibbs, "Optical Bistability," in Controlling Light with Light, (Academic Press, Orlando, 1985).

T. Asai, Y. Amemiya, and M. Kosiba, "A Photonic-Crystal Logic Circuit Based on the Binary Decision Diagram," in Proceeding of International Workshop on Photonic and Electromagnetic Crystal Structures, (Academic, Sendai, Japan, 2000), T4-14.

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Figures (9)

Fig. 1.
Fig. 1.

Schematic of (a) all-optical “AND” logic gate and (b) “XOR” logic gate.

Fig. 2.
Fig. 2.

Schematic of an all-optical half adder.

Fig. 3.
Fig. 3.

Field distributions at steady state of the “AND” logic gate for (a) one beam with power 0 P being injected into port A, (b) one beam with power 0 P being injected into port B, and (c) two beams each with power 0 P being injected into port A and B simultaneously.

Fig. 4.
Fig. 4.

Plot of T=Pout /PS in versus PS in for the AND logic gate for different radius of the nonlinear rod at the waveguide crosspoint.

Fig. 5.
Fig. 5.

Contrast ratio spectra of the AND logic gate with different powers for rc =0.34a.

Fig. 6.
Fig. 6.

Field distributions of the “XOR” logic gate at steady state for (a) one beam with power P 0 being injected into port A, (b) one beam with power P 0 being injected into port B, and (c) two beams each with power P 0 being injected into port A and B separately.

Fig. 7.
Fig. 7.

Contrast-ratio spectrum of the XOR logic gate.

Fig. 8.
Fig. 8.

The output from port C in Fig. 2 with P 0=2×274mW and rc =0.34a

Fig. 9.
Fig. 9.

The optimal operating speed versus P 0 for the AOHA for different rc without considering Kerr material’s response time.

Tables (2)

Tables Icon

Table 1. Input and output power relations of the AOHA with P 0=2×274mW and rc =0.34a

Tables Icon

Table 2. Input-output logic relations of the AOHA

Equations (9)

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

Δ n = n 2 I ( 1 + I I sat ) ,
Δ n = n ¯ 2 u 2 ( 1 + α u 2 ) ,
β = P in u ( x , 0 ) 2 dx ,
α u max 2 1 .
Δ n = n ¯ 2 u 2 .
ε tot ( E ) = ( n L + Δ n ) 2 n L 2 + 2 n L Δ n .
E = ε 0 1 ( D P L P NL ) ,
P L = ε 0 χ ( 1 ) ( t τ ) E ( r , τ ) d τ
P NL = ε 0 χ ( 3 ) E ( r , t ) 2 E ( r , t )

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