Abstract

The feasibility of and, or, and ex-or functions based on the interaction of optical solitons is proved by use of a five-layer dielectric structure with a nonlinear core. With the exception of the or logic gate, the design of these devices is rather flexible, offering a wide variety of choices with respect to both the geometrical parameters and the input power levels.

© 1995 Optical Society of America

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  1. G. I. Stegeman and E. M. Wright, "All-optical waveguide switching, "Opt. Quantum Electron. 22, 95–122 (1990).
    [CrossRef]
  2. K. Inoue, "High-speed all-optical gate switching experiment in a Fabry–Perot semiconductor laser amplifier," Electron. Lett. 23, 921–922 (1987).
    [CrossRef]
  3. P. Pottier, R. Auffret, H. Dupont, and G. Claveau, "Reconfigurable (NOR, XOR, AND) optical logic gate based on frequency shift induced by optical injection in a two-electrode DFB laser," J. Opt. Commun. 15, 141–143 (1994).
  4. F. Prati, M. Travagnin, and L. A. Lugiato, "Optical switching and logic gates with vertical cavity surface-emitting lasers," Opt. Lett. 19, 1991–1993 (1994).
    [CrossRef] [PubMed]
  5. R. W. Eason and A. Miller, eds., Nonlinear Optics in Signal Processing (Chapman and Hall, London, 1993).
    [CrossRef]
  6. M. M. Mirsalehi, "Optical information processing," in Encyclopedia of Lasers and Optical Technology, R. A. Meyers, ed. (Academic, San Diego, Calif., 1991), pp. 469–504.
  7. C. T. Seaton, J. D. Valera, R. L. Shoemaker, G. I. Stegeman, J. T. Chilwell, and S. D. Smith, "Calculations of nonlinear TE waves guided by thin dielectric films bounded by nonlinear media," IEEE J. Quantum Electron. QE-21, 774–783 (1985).
    [CrossRef]
  8. R. A. Sammut, Q. Y. Li, and C. Pask, "Variational approximations and mode stability in planar nonlinear waveguides," J. Opt. Soc. Am. B 9, 884–890 (1992).
    [CrossRef]
  9. F. Dios, X. Nogues, and F. Canal, "Critical power in a symmetric nonlinear directional coupler," Opt. Quantum Electron. 24, 1191–1202 (1992).
    [CrossRef]
  10. J. P. Torres and L. Torner, "Diagrammatic analysis of nonlinear planar waveguides," J. Opt. Soc. Am. B 11, 45–52 (1994).
    [CrossRef]
  11. X. J. Meng and N. Okamoto, "Improved coupled-mode theory for nonlinear directional couplers," IEEE J. Quantum Electron. 27, 1175–1181 (1991).
    [CrossRef]
  12. Y. Silberberg, "Self-induced waveguides: spatial optical solitons," in Anisotropic and Nonlinear Optical Waveguides, C. G. Someda and G. Stegeman, eds. (Elsevier, Amsterdam, 1992), pp. 143–157.
  13. Q. Y. Li, R. A. Sammut, and C. Pask, "Variational and finite element analyses of nonlinear strip optical waveguides," Opt. Commun. 94, 37–43 (1992).
    [CrossRef]
  14. K. Hayata and M. Koshiba, "Self-localization and spontaneous symmetry breaking of optical fields propagating in strongly nonlinear channel waveguides: limitations of the scalar field approximation," J. Opt. Soc. Am. B 9, 1362–1368 (1992).
    [CrossRef]
  15. X. H. Wang and G. K. Cambrell, "Full vectorial simulation of bistability phenomena in nonlinear-optical channel waveguides," J. Opt. Soc. Am. B 10, 1090–1095 (1993).
    [CrossRef]

1994 (3)

P. Pottier, R. Auffret, H. Dupont, and G. Claveau, "Reconfigurable (NOR, XOR, AND) optical logic gate based on frequency shift induced by optical injection in a two-electrode DFB laser," J. Opt. Commun. 15, 141–143 (1994).

F. Prati, M. Travagnin, and L. A. Lugiato, "Optical switching and logic gates with vertical cavity surface-emitting lasers," Opt. Lett. 19, 1991–1993 (1994).
[CrossRef] [PubMed]

J. P. Torres and L. Torner, "Diagrammatic analysis of nonlinear planar waveguides," J. Opt. Soc. Am. B 11, 45–52 (1994).
[CrossRef]

1993 (1)

1992 (4)

Q. Y. Li, R. A. Sammut, and C. Pask, "Variational and finite element analyses of nonlinear strip optical waveguides," Opt. Commun. 94, 37–43 (1992).
[CrossRef]

K. Hayata and M. Koshiba, "Self-localization and spontaneous symmetry breaking of optical fields propagating in strongly nonlinear channel waveguides: limitations of the scalar field approximation," J. Opt. Soc. Am. B 9, 1362–1368 (1992).
[CrossRef]

R. A. Sammut, Q. Y. Li, and C. Pask, "Variational approximations and mode stability in planar nonlinear waveguides," J. Opt. Soc. Am. B 9, 884–890 (1992).
[CrossRef]

F. Dios, X. Nogues, and F. Canal, "Critical power in a symmetric nonlinear directional coupler," Opt. Quantum Electron. 24, 1191–1202 (1992).
[CrossRef]

1991 (1)

X. J. Meng and N. Okamoto, "Improved coupled-mode theory for nonlinear directional couplers," IEEE J. Quantum Electron. 27, 1175–1181 (1991).
[CrossRef]

1990 (1)

G. I. Stegeman and E. M. Wright, "All-optical waveguide switching, "Opt. Quantum Electron. 22, 95–122 (1990).
[CrossRef]

1987 (1)

K. Inoue, "High-speed all-optical gate switching experiment in a Fabry–Perot semiconductor laser amplifier," Electron. Lett. 23, 921–922 (1987).
[CrossRef]

1985 (1)

C. T. Seaton, J. D. Valera, R. L. Shoemaker, G. I. Stegeman, J. T. Chilwell, and S. D. Smith, "Calculations of nonlinear TE waves guided by thin dielectric films bounded by nonlinear media," IEEE J. Quantum Electron. QE-21, 774–783 (1985).
[CrossRef]

Auffret, R.

P. Pottier, R. Auffret, H. Dupont, and G. Claveau, "Reconfigurable (NOR, XOR, AND) optical logic gate based on frequency shift induced by optical injection in a two-electrode DFB laser," J. Opt. Commun. 15, 141–143 (1994).

Cambrell, G. K.

Canal, F.

F. Dios, X. Nogues, and F. Canal, "Critical power in a symmetric nonlinear directional coupler," Opt. Quantum Electron. 24, 1191–1202 (1992).
[CrossRef]

Chilwell, J. T.

C. T. Seaton, J. D. Valera, R. L. Shoemaker, G. I. Stegeman, J. T. Chilwell, and S. D. Smith, "Calculations of nonlinear TE waves guided by thin dielectric films bounded by nonlinear media," IEEE J. Quantum Electron. QE-21, 774–783 (1985).
[CrossRef]

Claveau, G.

P. Pottier, R. Auffret, H. Dupont, and G. Claveau, "Reconfigurable (NOR, XOR, AND) optical logic gate based on frequency shift induced by optical injection in a two-electrode DFB laser," J. Opt. Commun. 15, 141–143 (1994).

Dios, F.

F. Dios, X. Nogues, and F. Canal, "Critical power in a symmetric nonlinear directional coupler," Opt. Quantum Electron. 24, 1191–1202 (1992).
[CrossRef]

Dupont, H.

P. Pottier, R. Auffret, H. Dupont, and G. Claveau, "Reconfigurable (NOR, XOR, AND) optical logic gate based on frequency shift induced by optical injection in a two-electrode DFB laser," J. Opt. Commun. 15, 141–143 (1994).

Hayata, K.

Inoue, K.

K. Inoue, "High-speed all-optical gate switching experiment in a Fabry–Perot semiconductor laser amplifier," Electron. Lett. 23, 921–922 (1987).
[CrossRef]

Koshiba, M.

Li, Q. Y.

Q. Y. Li, R. A. Sammut, and C. Pask, "Variational and finite element analyses of nonlinear strip optical waveguides," Opt. Commun. 94, 37–43 (1992).
[CrossRef]

R. A. Sammut, Q. Y. Li, and C. Pask, "Variational approximations and mode stability in planar nonlinear waveguides," J. Opt. Soc. Am. B 9, 884–890 (1992).
[CrossRef]

Lugiato, L. A.

Meng, X. J.

X. J. Meng and N. Okamoto, "Improved coupled-mode theory for nonlinear directional couplers," IEEE J. Quantum Electron. 27, 1175–1181 (1991).
[CrossRef]

Mirsalehi, M. M.

M. M. Mirsalehi, "Optical information processing," in Encyclopedia of Lasers and Optical Technology, R. A. Meyers, ed. (Academic, San Diego, Calif., 1991), pp. 469–504.

Nogues, X.

F. Dios, X. Nogues, and F. Canal, "Critical power in a symmetric nonlinear directional coupler," Opt. Quantum Electron. 24, 1191–1202 (1992).
[CrossRef]

Okamoto, N.

X. J. Meng and N. Okamoto, "Improved coupled-mode theory for nonlinear directional couplers," IEEE J. Quantum Electron. 27, 1175–1181 (1991).
[CrossRef]

Pask, C.

Q. Y. Li, R. A. Sammut, and C. Pask, "Variational and finite element analyses of nonlinear strip optical waveguides," Opt. Commun. 94, 37–43 (1992).
[CrossRef]

R. A. Sammut, Q. Y. Li, and C. Pask, "Variational approximations and mode stability in planar nonlinear waveguides," J. Opt. Soc. Am. B 9, 884–890 (1992).
[CrossRef]

Pottier, P.

P. Pottier, R. Auffret, H. Dupont, and G. Claveau, "Reconfigurable (NOR, XOR, AND) optical logic gate based on frequency shift induced by optical injection in a two-electrode DFB laser," J. Opt. Commun. 15, 141–143 (1994).

Prati, F.

Sammut, R. A.

R. A. Sammut, Q. Y. Li, and C. Pask, "Variational approximations and mode stability in planar nonlinear waveguides," J. Opt. Soc. Am. B 9, 884–890 (1992).
[CrossRef]

Q. Y. Li, R. A. Sammut, and C. Pask, "Variational and finite element analyses of nonlinear strip optical waveguides," Opt. Commun. 94, 37–43 (1992).
[CrossRef]

Seaton, C. T.

C. T. Seaton, J. D. Valera, R. L. Shoemaker, G. I. Stegeman, J. T. Chilwell, and S. D. Smith, "Calculations of nonlinear TE waves guided by thin dielectric films bounded by nonlinear media," IEEE J. Quantum Electron. QE-21, 774–783 (1985).
[CrossRef]

Shoemaker, R. L.

C. T. Seaton, J. D. Valera, R. L. Shoemaker, G. I. Stegeman, J. T. Chilwell, and S. D. Smith, "Calculations of nonlinear TE waves guided by thin dielectric films bounded by nonlinear media," IEEE J. Quantum Electron. QE-21, 774–783 (1985).
[CrossRef]

Silberberg, Y.

Y. Silberberg, "Self-induced waveguides: spatial optical solitons," in Anisotropic and Nonlinear Optical Waveguides, C. G. Someda and G. Stegeman, eds. (Elsevier, Amsterdam, 1992), pp. 143–157.

Smith, S. D.

C. T. Seaton, J. D. Valera, R. L. Shoemaker, G. I. Stegeman, J. T. Chilwell, and S. D. Smith, "Calculations of nonlinear TE waves guided by thin dielectric films bounded by nonlinear media," IEEE J. Quantum Electron. QE-21, 774–783 (1985).
[CrossRef]

Stegeman, G. I.

G. I. Stegeman and E. M. Wright, "All-optical waveguide switching, "Opt. Quantum Electron. 22, 95–122 (1990).
[CrossRef]

C. T. Seaton, J. D. Valera, R. L. Shoemaker, G. I. Stegeman, J. T. Chilwell, and S. D. Smith, "Calculations of nonlinear TE waves guided by thin dielectric films bounded by nonlinear media," IEEE J. Quantum Electron. QE-21, 774–783 (1985).
[CrossRef]

Torner, L.

Torres, J. P.

Travagnin, M.

Valera, J. D.

C. T. Seaton, J. D. Valera, R. L. Shoemaker, G. I. Stegeman, J. T. Chilwell, and S. D. Smith, "Calculations of nonlinear TE waves guided by thin dielectric films bounded by nonlinear media," IEEE J. Quantum Electron. QE-21, 774–783 (1985).
[CrossRef]

Wang, X. H.

Wright, E. M.

G. I. Stegeman and E. M. Wright, "All-optical waveguide switching, "Opt. Quantum Electron. 22, 95–122 (1990).
[CrossRef]

Electron. Lett. (1)

K. Inoue, "High-speed all-optical gate switching experiment in a Fabry–Perot semiconductor laser amplifier," Electron. Lett. 23, 921–922 (1987).
[CrossRef]

IEEE J. Quantum Electron. (2)

C. T. Seaton, J. D. Valera, R. L. Shoemaker, G. I. Stegeman, J. T. Chilwell, and S. D. Smith, "Calculations of nonlinear TE waves guided by thin dielectric films bounded by nonlinear media," IEEE J. Quantum Electron. QE-21, 774–783 (1985).
[CrossRef]

X. J. Meng and N. Okamoto, "Improved coupled-mode theory for nonlinear directional couplers," IEEE J. Quantum Electron. 27, 1175–1181 (1991).
[CrossRef]

J. Opt. Commun. (1)

P. Pottier, R. Auffret, H. Dupont, and G. Claveau, "Reconfigurable (NOR, XOR, AND) optical logic gate based on frequency shift induced by optical injection in a two-electrode DFB laser," J. Opt. Commun. 15, 141–143 (1994).

J. Opt. Soc. Am. B (4)

Opt. Commun. (1)

Q. Y. Li, R. A. Sammut, and C. Pask, "Variational and finite element analyses of nonlinear strip optical waveguides," Opt. Commun. 94, 37–43 (1992).
[CrossRef]

Opt. Lett. (1)

Opt. Quantum Electron. (1)

F. Dios, X. Nogues, and F. Canal, "Critical power in a symmetric nonlinear directional coupler," Opt. Quantum Electron. 24, 1191–1202 (1992).
[CrossRef]

pt. Quantum Electron. (1)

G. I. Stegeman and E. M. Wright, "All-optical waveguide switching, "Opt. Quantum Electron. 22, 95–122 (1990).
[CrossRef]

Other (3)

R. W. Eason and A. Miller, eds., Nonlinear Optics in Signal Processing (Chapman and Hall, London, 1993).
[CrossRef]

M. M. Mirsalehi, "Optical information processing," in Encyclopedia of Lasers and Optical Technology, R. A. Meyers, ed. (Academic, San Diego, Calif., 1991), pp. 469–504.

Y. Silberberg, "Self-induced waveguides: spatial optical solitons," in Anisotropic and Nonlinear Optical Waveguides, C. G. Someda and G. Stegeman, eds. (Elsevier, Amsterdam, 1992), pp. 143–157.

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Figures (12)

Fig. 1
Fig. 1

Five-layer dielectric waveguide with nonlinearity in the central layer.

Fig. 2
Fig. 2

Amplitude distribution of the excitation at the input ports.

Fig. 3
Fig. 3

Amplitude evolution when d = 2 μm, w = 3.4 μm, a1 = a2 = 1, θ = 0, and Ps(0) = 65 W/m.

Fig. 4
Fig. 4

Amplitude evolution when d = 2 μm, w = 3.4 μm, a1 = a2 = 1, θ = π, and Ps(0) = 65 W/m.

Fig. 5
Fig. 5

Amplitude evolution when d = 2 μm, w = 3.4 μm, a1 = a2 = 1, θ = π, and Ps(0) = 180 W/m.

Fig. 6
Fig. 6

Amplitude evolution when d = 2 μm, w = 2 μm, a1 = a2 = 1, θ = 0, and Ps(0) = 40 W/m.

Fig. 7
Fig. 7

Example of an and gate when (a) a1 = a2 = 1 and (b) a1 = 1, a2 = 0.

Fig. 8
Fig. 8

Example of an ex-or gate when (a) a1 = a2 = 1 and (b) a1 = 1, a2 = 0.

Fig. 9
Fig. 9

Example of an or gate when (a) a1 = a2 = 1 and (b) a1 = 1, a2 = 0.

Fig. 10
Fig. 10

Regions of acceptable LPs(0) pairs for an and gate with d = 2 μm: (1) w = 3.7 μm, (2) w = 3.4 μm, (3) w = 2.7 μm, (4) w = 2 μm, (5) w = 1.5 μm.

Fig. 11
Fig. 11

Regions of acceptable LPs(0) pairs for an and gate with w = 3.4 μm: (1) d = 2 μm, (2) d = 1.5 μm, (3) d = 1 μm.

Fig. 12
Fig. 12

Regions of acceptable LPs(0) pairs for an ex-or gate with d = 2 μm: (1) w = 3.4 μm, (2) w = 2.7 μm, (3) w = 2 μm.

Equations (4)

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n 2 ( x ) = { n 1 2 x > w 2 + d n 2 2 w 2 < x w 2 + d n 3 2 + α E 2 - w 2 x w 2 n 2 2 - w 2 - d x < - w 2 n 1 2 x < - w 2 - d ,
2 A x 2 - 2 j n e k 0 A z - k 0 2 [ n e 2 - n 2 ( x ) ] A = 0 ,
A ( x , z ) = E ( x , z ) exp ( j ω 0 t - j n e k 0 z ) ,
P ( 0 ) = n e 2 Z 0 - + A ( x , 0 ) 2 d x ,

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