Abstract

Reliable optical switching at a nonlinear interface is obtained from the symmetry of a two-beam information lossless interaction. The device configuration, which is noise insensitive and cascadable, performs bit-conserving inverse and product functions reversibly. Numerical computations of the optical field redistribution at a dual-beam interface with opposing diffusive Kerr nonlinearities show the first reported evidence of Gaussianlike switching with high contrast.

© 1988 Optical Society of America

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References

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  1. R. Landauer, “Computation and Physics: Wheeler’s Meaning Circuit,” Found. Phys. 16, 551 (1986).
    [CrossRef]
  2. R. Landauer, “Fundamental Physical Limitations of the Computational Process,” Ann. N.Y. Acad. Sci. 426, 161 (1985).
    [CrossRef]
  3. E. Fredkin, T. Toffoli, “Conservative Logic,” Int. J. Theor. Phys. 21, 219 (1982).
    [CrossRef]
  4. R. P. Feynman, “Quantum Mechanical Computers,” Found. Phys. 16, 507 (1986).
    [CrossRef]
  5. J. Shamir, H. J. Caulfield, W. J. Micelli, R. J. Seymour, “Optical Computing and the Fredkin Gates,” Appl. Opt. 25, 1604 (1986); K. M. Johnson, M. A. Handschy, L. A. Pagano-Stauffer, “Optical Computing and Image Processing with Ferroelectric Liquid Crystals,” Opt. Engr. 26, 385 (1987).
    [CrossRef] [PubMed]
  6. R. Cuykendall, D. McMillin, “Limitations to Optical Fredkin Circuits,” OSA Tech. Digest Ser. 11, 70 (1987).
  7. R. Cuykendall, D. McMillin, “Control-Specific Optical Fredkin Circuits,” Appl. Opt. 26, 1959 (1987).
    [CrossRef] [PubMed]
  8. L. Priese, “On a Simple Combinatorial Structure Sufficient for Sublying Nontrivial Self-Reproduction,” J. Cybern. 6, 101 (1976).
    [CrossRef]
  9. R. Cuykendall, “Optical Reversible Computing,” Technical Memo, Applied Physics Group, ECE Dept., U. Iowa, (Aug.1986).
  10. A. E. Kaplan, “Theory of Hysteresis Reflection and Refraction of Light by a Boundary of a Nonlinear Medium,” Sov. Phys. JETP 45, 896 (1977).
  11. R. Cuykendall, D. R. Andersen, “Reversible Computing: All-Optical Implementation of Interaction and Priese Gates,” Opt. Commun. 62, 232 (1987).
    [CrossRef]
  12. R. Cuykendall, D. R. Andersen, “Reversible Optical Computing Circuits,” Opt. Lett. 12, 542 (1987).
    [CrossRef] [PubMed]
  13. A. Korpel, A. W. Lohmann, “Polarization and Optical Bistability,” Appl. Opt. 25, 1528 (1986).
    [CrossRef] [PubMed]
  14. D. S. Chemla, D. A. B. Miller, P. W. Smith, A. C. Gossard, W. Wiegmann, “Room Temperature Excitonic Nonlinear Absorption and Refraction in GaAs/AlGaAs Multiple Quantum Well Structures,” IEEE J. Quantum Electron. QE-20, 265 (1984).
    [CrossRef]
  15. W. J. Tomlinson, J. P. Gordon, P. W. Smith, A. E. Kaplan, “Reflection of a Gaussian Beam at a Nonlinear Interface,” Appl. Opt. 21, 2041 (1982).
    [CrossRef] [PubMed]
  16. P. W. Smith, J. P. Hermann, W. J. Tomlinson, P. J. Maloney, “Optical Bistability at a Nonlinear Interface,” Appl. Phys. Lett. 35, 846 (1979).
    [CrossRef]
  17. P. W. Smith, W. J. Tomlinson, P. J. Maloney, J. P. Hermann, “Experimental Studies of a Nonlinear Interface,” IEEE J. Quantum Electron. QE-17, 340 (1981).
    [CrossRef]
  18. P. W. Smith, W. J. Tomlinson, “Nonlinear Optical Interfaces: Switching Behavior,” IEEE J. Quantum Electron. QE-20, 30 (1984).
    [CrossRef]
  19. D. Marcuse, “Reflection of a Gaussian Beam from a Nonlinear Interface,” Appl. Opt. 19, 3130 (1980).
    [CrossRef] [PubMed]
  20. E. M. Wright, W. J. Firth, I. Galbraith, “Beam Propagation in a Medium with a Diffusive Kerr-Type Nonlinearity,” J. Opt. Soc. Am. B 2, 383 (1985).
    [CrossRef]
  21. J. Moloney, “Beam Reflection, Transmission, and Trapping at Nonlinear Dielectric Interfaces,” Proc. International Conference on Soliton and Chaotic Behaviour in Optical Systems, San Jose, CA, Jan. 1988, to be published by Plenum Press, 1989.

1987 (4)

R. Cuykendall, D. R. Andersen, “Reversible Computing: All-Optical Implementation of Interaction and Priese Gates,” Opt. Commun. 62, 232 (1987).
[CrossRef]

R. Cuykendall, D. McMillin, “Limitations to Optical Fredkin Circuits,” OSA Tech. Digest Ser. 11, 70 (1987).

R. Cuykendall, D. R. Andersen, “Reversible Optical Computing Circuits,” Opt. Lett. 12, 542 (1987).
[CrossRef] [PubMed]

R. Cuykendall, D. McMillin, “Control-Specific Optical Fredkin Circuits,” Appl. Opt. 26, 1959 (1987).
[CrossRef] [PubMed]

1986 (4)

1985 (2)

R. Landauer, “Fundamental Physical Limitations of the Computational Process,” Ann. N.Y. Acad. Sci. 426, 161 (1985).
[CrossRef]

E. M. Wright, W. J. Firth, I. Galbraith, “Beam Propagation in a Medium with a Diffusive Kerr-Type Nonlinearity,” J. Opt. Soc. Am. B 2, 383 (1985).
[CrossRef]

1984 (2)

P. W. Smith, W. J. Tomlinson, “Nonlinear Optical Interfaces: Switching Behavior,” IEEE J. Quantum Electron. QE-20, 30 (1984).
[CrossRef]

D. S. Chemla, D. A. B. Miller, P. W. Smith, A. C. Gossard, W. Wiegmann, “Room Temperature Excitonic Nonlinear Absorption and Refraction in GaAs/AlGaAs Multiple Quantum Well Structures,” IEEE J. Quantum Electron. QE-20, 265 (1984).
[CrossRef]

1982 (2)

1981 (1)

P. W. Smith, W. J. Tomlinson, P. J. Maloney, J. P. Hermann, “Experimental Studies of a Nonlinear Interface,” IEEE J. Quantum Electron. QE-17, 340 (1981).
[CrossRef]

1980 (1)

1979 (1)

P. W. Smith, J. P. Hermann, W. J. Tomlinson, P. J. Maloney, “Optical Bistability at a Nonlinear Interface,” Appl. Phys. Lett. 35, 846 (1979).
[CrossRef]

1977 (1)

A. E. Kaplan, “Theory of Hysteresis Reflection and Refraction of Light by a Boundary of a Nonlinear Medium,” Sov. Phys. JETP 45, 896 (1977).

1976 (1)

L. Priese, “On a Simple Combinatorial Structure Sufficient for Sublying Nontrivial Self-Reproduction,” J. Cybern. 6, 101 (1976).
[CrossRef]

Andersen, D. R.

R. Cuykendall, D. R. Andersen, “Reversible Computing: All-Optical Implementation of Interaction and Priese Gates,” Opt. Commun. 62, 232 (1987).
[CrossRef]

R. Cuykendall, D. R. Andersen, “Reversible Optical Computing Circuits,” Opt. Lett. 12, 542 (1987).
[CrossRef] [PubMed]

Caulfield, H. J.

Chemla, D. S.

D. S. Chemla, D. A. B. Miller, P. W. Smith, A. C. Gossard, W. Wiegmann, “Room Temperature Excitonic Nonlinear Absorption and Refraction in GaAs/AlGaAs Multiple Quantum Well Structures,” IEEE J. Quantum Electron. QE-20, 265 (1984).
[CrossRef]

Cuykendall, R.

R. Cuykendall, D. McMillin, “Control-Specific Optical Fredkin Circuits,” Appl. Opt. 26, 1959 (1987).
[CrossRef] [PubMed]

R. Cuykendall, D. R. Andersen, “Reversible Computing: All-Optical Implementation of Interaction and Priese Gates,” Opt. Commun. 62, 232 (1987).
[CrossRef]

R. Cuykendall, D. R. Andersen, “Reversible Optical Computing Circuits,” Opt. Lett. 12, 542 (1987).
[CrossRef] [PubMed]

R. Cuykendall, D. McMillin, “Limitations to Optical Fredkin Circuits,” OSA Tech. Digest Ser. 11, 70 (1987).

R. Cuykendall, “Optical Reversible Computing,” Technical Memo, Applied Physics Group, ECE Dept., U. Iowa, (Aug.1986).

Feynman, R. P.

R. P. Feynman, “Quantum Mechanical Computers,” Found. Phys. 16, 507 (1986).
[CrossRef]

Firth, W. J.

Fredkin, E.

E. Fredkin, T. Toffoli, “Conservative Logic,” Int. J. Theor. Phys. 21, 219 (1982).
[CrossRef]

Galbraith, I.

Gordon, J. P.

Gossard, A. C.

D. S. Chemla, D. A. B. Miller, P. W. Smith, A. C. Gossard, W. Wiegmann, “Room Temperature Excitonic Nonlinear Absorption and Refraction in GaAs/AlGaAs Multiple Quantum Well Structures,” IEEE J. Quantum Electron. QE-20, 265 (1984).
[CrossRef]

Hermann, J. P.

P. W. Smith, W. J. Tomlinson, P. J. Maloney, J. P. Hermann, “Experimental Studies of a Nonlinear Interface,” IEEE J. Quantum Electron. QE-17, 340 (1981).
[CrossRef]

P. W. Smith, J. P. Hermann, W. J. Tomlinson, P. J. Maloney, “Optical Bistability at a Nonlinear Interface,” Appl. Phys. Lett. 35, 846 (1979).
[CrossRef]

Kaplan, A. E.

W. J. Tomlinson, J. P. Gordon, P. W. Smith, A. E. Kaplan, “Reflection of a Gaussian Beam at a Nonlinear Interface,” Appl. Opt. 21, 2041 (1982).
[CrossRef] [PubMed]

A. E. Kaplan, “Theory of Hysteresis Reflection and Refraction of Light by a Boundary of a Nonlinear Medium,” Sov. Phys. JETP 45, 896 (1977).

Korpel, A.

Landauer, R.

R. Landauer, “Computation and Physics: Wheeler’s Meaning Circuit,” Found. Phys. 16, 551 (1986).
[CrossRef]

R. Landauer, “Fundamental Physical Limitations of the Computational Process,” Ann. N.Y. Acad. Sci. 426, 161 (1985).
[CrossRef]

Lohmann, A. W.

Maloney, P. J.

P. W. Smith, W. J. Tomlinson, P. J. Maloney, J. P. Hermann, “Experimental Studies of a Nonlinear Interface,” IEEE J. Quantum Electron. QE-17, 340 (1981).
[CrossRef]

P. W. Smith, J. P. Hermann, W. J. Tomlinson, P. J. Maloney, “Optical Bistability at a Nonlinear Interface,” Appl. Phys. Lett. 35, 846 (1979).
[CrossRef]

Marcuse, D.

McMillin, D.

R. Cuykendall, D. McMillin, “Limitations to Optical Fredkin Circuits,” OSA Tech. Digest Ser. 11, 70 (1987).

R. Cuykendall, D. McMillin, “Control-Specific Optical Fredkin Circuits,” Appl. Opt. 26, 1959 (1987).
[CrossRef] [PubMed]

Micelli, W. J.

Miller, D. A. B.

D. S. Chemla, D. A. B. Miller, P. W. Smith, A. C. Gossard, W. Wiegmann, “Room Temperature Excitonic Nonlinear Absorption and Refraction in GaAs/AlGaAs Multiple Quantum Well Structures,” IEEE J. Quantum Electron. QE-20, 265 (1984).
[CrossRef]

Moloney, J.

J. Moloney, “Beam Reflection, Transmission, and Trapping at Nonlinear Dielectric Interfaces,” Proc. International Conference on Soliton and Chaotic Behaviour in Optical Systems, San Jose, CA, Jan. 1988, to be published by Plenum Press, 1989.

Priese, L.

L. Priese, “On a Simple Combinatorial Structure Sufficient for Sublying Nontrivial Self-Reproduction,” J. Cybern. 6, 101 (1976).
[CrossRef]

Seymour, R. J.

Shamir, J.

Smith, P. W.

D. S. Chemla, D. A. B. Miller, P. W. Smith, A. C. Gossard, W. Wiegmann, “Room Temperature Excitonic Nonlinear Absorption and Refraction in GaAs/AlGaAs Multiple Quantum Well Structures,” IEEE J. Quantum Electron. QE-20, 265 (1984).
[CrossRef]

P. W. Smith, W. J. Tomlinson, “Nonlinear Optical Interfaces: Switching Behavior,” IEEE J. Quantum Electron. QE-20, 30 (1984).
[CrossRef]

W. J. Tomlinson, J. P. Gordon, P. W. Smith, A. E. Kaplan, “Reflection of a Gaussian Beam at a Nonlinear Interface,” Appl. Opt. 21, 2041 (1982).
[CrossRef] [PubMed]

P. W. Smith, W. J. Tomlinson, P. J. Maloney, J. P. Hermann, “Experimental Studies of a Nonlinear Interface,” IEEE J. Quantum Electron. QE-17, 340 (1981).
[CrossRef]

P. W. Smith, J. P. Hermann, W. J. Tomlinson, P. J. Maloney, “Optical Bistability at a Nonlinear Interface,” Appl. Phys. Lett. 35, 846 (1979).
[CrossRef]

Toffoli, T.

E. Fredkin, T. Toffoli, “Conservative Logic,” Int. J. Theor. Phys. 21, 219 (1982).
[CrossRef]

Tomlinson, W. J.

P. W. Smith, W. J. Tomlinson, “Nonlinear Optical Interfaces: Switching Behavior,” IEEE J. Quantum Electron. QE-20, 30 (1984).
[CrossRef]

W. J. Tomlinson, J. P. Gordon, P. W. Smith, A. E. Kaplan, “Reflection of a Gaussian Beam at a Nonlinear Interface,” Appl. Opt. 21, 2041 (1982).
[CrossRef] [PubMed]

P. W. Smith, W. J. Tomlinson, P. J. Maloney, J. P. Hermann, “Experimental Studies of a Nonlinear Interface,” IEEE J. Quantum Electron. QE-17, 340 (1981).
[CrossRef]

P. W. Smith, J. P. Hermann, W. J. Tomlinson, P. J. Maloney, “Optical Bistability at a Nonlinear Interface,” Appl. Phys. Lett. 35, 846 (1979).
[CrossRef]

Wiegmann, W.

D. S. Chemla, D. A. B. Miller, P. W. Smith, A. C. Gossard, W. Wiegmann, “Room Temperature Excitonic Nonlinear Absorption and Refraction in GaAs/AlGaAs Multiple Quantum Well Structures,” IEEE J. Quantum Electron. QE-20, 265 (1984).
[CrossRef]

Wright, E. M.

Ann. N.Y. Acad. Sci. (1)

R. Landauer, “Fundamental Physical Limitations of the Computational Process,” Ann. N.Y. Acad. Sci. 426, 161 (1985).
[CrossRef]

Appl. Opt. (5)

Appl. Phys. Lett. (1)

P. W. Smith, J. P. Hermann, W. J. Tomlinson, P. J. Maloney, “Optical Bistability at a Nonlinear Interface,” Appl. Phys. Lett. 35, 846 (1979).
[CrossRef]

Found. Phys. (2)

R. P. Feynman, “Quantum Mechanical Computers,” Found. Phys. 16, 507 (1986).
[CrossRef]

R. Landauer, “Computation and Physics: Wheeler’s Meaning Circuit,” Found. Phys. 16, 551 (1986).
[CrossRef]

IEEE J. Quantum Electron. (3)

P. W. Smith, W. J. Tomlinson, P. J. Maloney, J. P. Hermann, “Experimental Studies of a Nonlinear Interface,” IEEE J. Quantum Electron. QE-17, 340 (1981).
[CrossRef]

P. W. Smith, W. J. Tomlinson, “Nonlinear Optical Interfaces: Switching Behavior,” IEEE J. Quantum Electron. QE-20, 30 (1984).
[CrossRef]

D. S. Chemla, D. A. B. Miller, P. W. Smith, A. C. Gossard, W. Wiegmann, “Room Temperature Excitonic Nonlinear Absorption and Refraction in GaAs/AlGaAs Multiple Quantum Well Structures,” IEEE J. Quantum Electron. QE-20, 265 (1984).
[CrossRef]

Int. J. Theor. Phys. (1)

E. Fredkin, T. Toffoli, “Conservative Logic,” Int. J. Theor. Phys. 21, 219 (1982).
[CrossRef]

J. Cybern. (1)

L. Priese, “On a Simple Combinatorial Structure Sufficient for Sublying Nontrivial Self-Reproduction,” J. Cybern. 6, 101 (1976).
[CrossRef]

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

Opt. Commun. (1)

R. Cuykendall, D. R. Andersen, “Reversible Computing: All-Optical Implementation of Interaction and Priese Gates,” Opt. Commun. 62, 232 (1987).
[CrossRef]

Opt. Lett. (1)

OSA Tech. Digest Ser. (1)

R. Cuykendall, D. McMillin, “Limitations to Optical Fredkin Circuits,” OSA Tech. Digest Ser. 11, 70 (1987).

Sov. Phys. JETP (1)

A. E. Kaplan, “Theory of Hysteresis Reflection and Refraction of Light by a Boundary of a Nonlinear Medium,” Sov. Phys. JETP 45, 896 (1977).

Other (2)

R. Cuykendall, “Optical Reversible Computing,” Technical Memo, Applied Physics Group, ECE Dept., U. Iowa, (Aug.1986).

J. Moloney, “Beam Reflection, Transmission, and Trapping at Nonlinear Dielectric Interfaces,” Proc. International Conference on Soliton and Chaotic Behaviour in Optical Systems, San Jose, CA, Jan. 1988, to be published by Plenum Press, 1989.

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Figures (9)

Fig. 1
Fig. 1

(a) Interaction gate (input signals p,q routed to one of two output ports depending on the values of q,p) and its inverse; (b) Priese switch gate (input signal p routed to one of two output ports depending on the value of control signal c) and its inverse; and (c) Fredkin gate (input signals p,q routed to the same or exchanged output ports depending on the value of control signal c) and its inverse.

Fig. 2
Fig. 2

Nonlinear interface with polarized signal beams of intensity I0 incident at glancing angle ψ.

Fig. 3
Fig. 3

Signal replication circuits consisting of an RNI and a half-wave plate. Note that P ˜ or Q ˜ is the degraded signal and P or Q is the restored signal.

Fig. 4
Fig. 4

Results of numerical computations of intensity profiles for a 2-D Gaussian beam incident at a nonlinear interface: (a) nondiffusive case which corresponds exactly to Fig. 9 of Ref. 15; (b) diffusive case at ψ = 5° with diffusion length LD = 20 μm, beam waist ω0 = 10 μm, wavelength λ = 1.0 μm, ΔnL = 0.02, n10 = 1.5, n2p = ±0.75 × 10−9 (both mediums nonlinear in opposite directions); (c) n2p = ±1.5 × 10−9.

Fig. 5
Fig. 5

Interaction gate implemented with a Fabry-Perot cavity.

Fig. 6
Fig. 6

Minimal full adder circuits using (a) interaction, (b) Priese, and (c) Fredkin gates.

Fig. 7
Fig. 7

RNI half-adder.

Fig. 8
Fig. 8

Sequential n-bit adder.

Fig. 9
Fig. 9

Parallel adder.

Equations (6)

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n 1 = n 10 , n 2 = n 10 Δ n L + n 2 N L ( I 0 ) , 90 ° θ inc sin 1 n 10 Δ n L + n 2 N L ( I 0 ) n 10 ,
n 2 I Δ = 1 ( 1 + r 2 ) [ 1 4 r ( 1 + r ) ( ψ ψ c ) 2 ] .
n 2 ( I c ) Δ = 1 2 [ 1 ( ψ ψ c ) 2 ] 1 2 ψ ψ c < 1 , 1 8 ( ψ c ψ ) 2 0 < ψ ψ c 1 2 ,
D 0 2 p ( x ) x 2 + G 0 I ( x ) p ( x ) τ = 0 .
n 2 N L [ I ( x ) ] = n 2 p p ( x ) .
[ 2 p ( x ) z 2 ] ,

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