Abstract

Optical signal processing and computing was triggered by the invention of the laser. Starting practically in 1960, it really took off with the introduction of the spatial-matched filter in 1964. Almost half a century later, research and engineering activity in the field continues unabated but in directions that could not have been anticipated in those early days. This paper presents an overview of the developments in the field, discussing the advantages, disadvantages, and limitations of optics in computing paradigms to indicate where and how optics can be exploited in this area. Initially, optical methods were introduced for processing analog signals. Early attempts to extend optical methods toward digital processing failed because the differences between photons and electrons were not properly appreciated. In the last part of the paper we show that some novel concepts and advanced technology may revitalize also optical processes within the digital computing world. This latter development is demonstrated by digital logic functions implemented on simple electro-optic networks. (My personal perspective on the role of optics in computing is deeply rooted in many years of collaboration with my late friend, H. John Caulfield, and I dedicate this paper to his memory.)

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. W. Strutt (Lord Rayleigh), “Investigations in optics, with special reference to the spectroscope,” Philos. Mag. 8, 40–55 (1880). Reprinted in The Collection of Optics Papers of Lord Rayleigh, J. W. Strutt, ed. (Optical Society of America, 1994), pp. 117–130.
  2. P. Elias, D. S. Gray, and D. Z. Robinson, “Fourier treatment of optical processes,” J. Opt. Soc. Am. 42, 127–134 (1952).
    [CrossRef]
  3. P. Elias, “Optics in communication theory,” J. Opt. Soc. Am. 43, 229–232 (1953).
    [CrossRef]
  4. L. J. Cutrona, E. N. Leith, C. J. Palermo, and L. J. Porcello, “Optical data processing and filtering systems,” IRE Trans. Inf. Theory IT-6, 386–400 (1960).
  5. A. B. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory 10, 139–145 (1964).
    [CrossRef]
  6. H. J. Caulfield and J. Shamir, “Wave-particle duality considerations in optical computing,” Appl. Opt. 28, 2184–2186 (1989).
    [CrossRef]
  7. H. J. Caulfield and J. Shamir, “Wave-particle duality processors—characteristics, requirements and applications,” J. Opt. Soc. Am. A 7, 1314–1323 (1990).
    [CrossRef]
  8. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).
  9. J. Shamir, Optical Systems and Processes (SPIE, 1999). Reprinted by Prentice-Hall India, 2004.
  10. J. Shamir, H. J. Caulfield, and R. B. Johnson, “Massive holographic interconnection networks and their limitations,” Appl. Opt. 28, 311–324 (1989).
    [CrossRef]
  11. H. J. Caulfield, “Parallel N4 weighted optical interconnections,” Appl. Opt. 26, 4039–4040 (1987).
    [CrossRef]
  12. J. Shamir and H. J. Caulfield, “Parallel optical processors—some basic considerations,” Int. J. Opt. Comp. 2, 73–78 (1991).
  13. H.-I. Jeon, J. Shamir, R. B. Johnson, H. J. Caulfield, J. Kinser, C. Hester, and M. Temmen, “The use of fixed holograms for massively-interconnected, low-power neural networks,” in Neural Networks for Perception, H. Wechsler, ed. (Academic, 1992), Vol. 2, pp. 282–309.
  14. H. J. Caulfield and J. Shamir, “Fixed hologram neural networks,” in Real-Time Optical Information Processing, B. Javidi and J. L. Horner, eds. (Academic, 1994), pp. 255–305.
  15. J. W. Goodman, F. I. Leonberger, S. Kung, and R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
    [CrossRef]
  16. J. Shamir, “Paradigms for bit-oriented holographic information storage,” Appl. Opt. 45, 5212–5222 (2006).
    [CrossRef]
  17. H. J. Caulfield and W. T. Maloney, “Improved discrimination in optical character recognition,” Appl. Opt. 8, 2354–2356 (1969).
    [CrossRef]
  18. B. Braunecker, R. Hauch, and A. W. Lohmann, “Optical character recognition based on nonredundant correlation measurements,” Appl. Opt. 18, 2746–2753 (1979).
    [CrossRef]
  19. C. F. Hester and D. Casasent, “Multivariant technique for multiclass pattern recognition,” Appl. Opt. 19, 1758–1761 (1980).
    [CrossRef]
  20. Y. Hsu and H. Arsenault, “Optical pattern recognition using circular harmonic expansion,” Appl. Opt. 21, 4016–4019 (1982).
    [CrossRef]
  21. J. Rosen and J. Shamir, “Circular harmonic phase filters for efficient rotation-invariant pattern recognition,” Appl. Opt. 27, 2895–2899 (1988).
    [CrossRef]
  22. D. Casasent and D. Psaltis, “New optical transforms for pattern recognition,” Proc. IEEE 65, 77–84 (1977).
    [CrossRef]
  23. J. Rosen and J. Shamir, “Scale invariant pattern recognition with logarithmic radial harmonic filters,” Appl. Opt. 28, 240–244 (1989).
    [CrossRef]
  24. D. Casasent, “Unified synthetic discriminant function computational formulation,” Appl. Opt. 23, 1620–1627 (1984).
    [CrossRef]
  25. U. Mahlab and J. Shamir, “Phase-only entropy-optimized filter by simulated annealing,” Opt. Lett. 14, 1168–1170 (1989).
    [CrossRef]
  26. U. Mahlab and J. Shamir, “Optical pattern recognition based on convex functions,” J. Opt. Soc. Am. A 8, 1233–1239 (1991).
    [CrossRef]
  27. B. V. K. Vijaya Kumar, “Tutorial survey of composite filter designs for optical correlators,” Appl. Opt. 31, 4773–4801 (1992).
    [CrossRef]
  28. D. Gabor, “Light and information,” in Progress in Optics, E. Wolf, ed. (Elsevier, 1964), Vol. 1, pp. 109–153.
  29. R. Piestun and J. Shamir, “Synthesis of three-dimensional light-fields and applications,” Proc. IEEE 90, 222–244 (2002).
    [CrossRef]
  30. J. Shamir, “Fundamental speed limitations on parallel processing,” Appl. Opt. 26, 1567–1593 (1987).
    [CrossRef]
  31. A. W. Lohmann and A. S. Marathay, “Globality and speed of optical parallel processors,” Appl. Opt. 28, 3838–3842 (1989).
    [CrossRef]
  32. J. Rosen, U. Mahlab, and J. Shamir, “Adaptive learning with joint transform correlators,” Opt. Eng. 29, 1101–1106 (1990).
    [CrossRef]
  33. J. Shamir, “Adaptive pattern recognition correlators,” Opt. Eng. 36, 2675–2689 (1997).
    [CrossRef]
  34. J. Shamir, “Iterative procedures in electro-optical pattern recognition,” in Optical Pattern Recognition, F. T. S. Yu, ed. (Cambridge University, 1998), pp. 221–261.
  35. A. Korpel, Acousto-Optics (Marcel Dekker, 1997).
  36. L. J. Cutrona, “On the application of coherent optical processing techniques to synthetic-aperture radar,” Proc. IEEE 54, 1026–1032 (1966).
    [CrossRef]
  37. D. Meshulach, D. Yelin, and Y. Silberberg, “Adaptive real-time femtosecond pulse shaping,” J. Opt. Soc. Am. B 15, 1615–1619 (1998).
    [CrossRef]
  38. C.-S. Pang, K. Oba, Y. T. Mazurenko, and S. Y. Fainman, “Space-time processing with photorefractive volume holography,” Proc. IEEE 87, 2086–2097 (1999).
    [CrossRef]
  39. T. R. Clark, J. U. Kang, and R. D. Esman, “Performance of a time- and wavelength-interleaved photonic sampler for analog-digital conversion,” IEEE Photonics Technol. Lett. 11, 1168–1170 (1999).
    [CrossRef]
  40. P. Daukantas, “Photography in the American Civil War,” Opt. Photonics News 23(6), 24–29 (2012).
    [CrossRef]
  41. G. Indebetouw, “Scanning holographic microscopy with spatially incoherent sources: reconciling the holographic advantage with the sectioning advantage,” J. Opt. Soc. Am. A 26, 252–258 (2009).
    [CrossRef]
  42. J. Shamir, “Moire gauging by projected interference fringes,” Opt. Laser Technol. 5, 78–86 (1973).
    [CrossRef]
  43. D. Caspi, N. Kiryati, and J. Shamir, “Range imaging with adaptive color structured sight,” IEEE Trans. Pattern Anal. Mach. Intell. 20, 470–480 (1998).
    [CrossRef]
  44. H. P. Herzig, Micro-Optics (Taylor & Francis, 1997).
  45. R. Piestun, B. Spektor, and J. Shamir, “Wave fields in three dimensions: analysis and synthesis,” J. Opt. Soc. Am. A 13, 1837–1848 (1996).
    [CrossRef]
  46. R. K. Tyson, Principles of Adaptive Optics (Academic, 1991).
  47. J. Shamir, D. G. Crowe, and J. W. Beletic, “Improved compensation of atmospheric turbulence effects by multiple adaptive mirror systems,” Appl. Opt. 32, 4618–4628 (1993).
    [CrossRef]
  48. P. L. Wizinowich, M. Lloyd-Hart, B. A. McLeod, D. Colucci, R. G. Dekany, D. M. Wittman, J. R. P. Angel, D. W. McCarthy, W. G. Hulburd, and D. G. Sandler, “Neural network adaptive optics for the multimirror telescope,” Proc. SPIE 1542, 148–158 (1991).
    [CrossRef]
  49. N. H. Farhat, “Optoelectronic analogs of self programming neural nets: architecture and methodologies for implementing fast stochastic learning by simulated annealing,” Appl. Opt. 26, 5093–5103 (1987).
    [CrossRef]
  50. H. J. Caulfield, “Fuzzy optical metrology,” IEEE Trans. Fuzzy Syst. 4, 206–207 (1996).
    [CrossRef]
  51. D. Lyszyk and J. Shamir, “Signal processing under uncertain conditions by parallel projections onto fuzzy sets,” J. Opt. Soc. Am A 16, 1602–1611 (1999).
    [CrossRef]
  52. R. Landauer, “Irreversibility and heat generation in the computing process,” IBM J. Res. Dev. 5, 183–191(1961).
    [CrossRef]
  53. C. H. Bennett, “Logical reversibility of computation,” IBM J. Res. Dev. 17, 525–532 (1973).
    [CrossRef]
  54. E. Fredkin and T. Toffoli, “Conservative logic,” Int. J. Theor. Phys. 21, 219–253 (1982).
    [CrossRef]
  55. R. P. Feynman, “Quantum mechanical computing,” Opt. News 11, 11–20 (1985).
    [CrossRef]
  56. J. Shamir, H. J. Caulfield, W. Miceli, and R. J. Seymour, “Optical computing and the Fredkin gate,” Appl. Opt. 25, 1604–1607 (1986).
    [CrossRef]
  57. J. Hardy and J. Shamir, “Optics inspired logic architecture,” Opt. Express 15, 150–165 (2007).
    [CrossRef]
  58. Q. Xu and R. Soref, “Reconfigurable optical directed-logic circuits using microresonator-based optical switches,” Opt. Express 19, 5244–5259 (2011).
    [CrossRef]
  59. L. Zhang, R. Q. Ji, L. X. Jia, L. Yang, P. Zhou, Y. H. Tian, P. Chen, Y. Y. Lu, Z. Y. Jiang, Y. L. Liu, Q. Fang, and M. B. Yu, “Demonstration of directed XOR/XNOR logic gates using two cascaded microring resonators,” Opt. Lett. 35, 1620–1622(2010).
    [CrossRef]
  60. Y. H. Tian, L. Zhang, R. Q. Ji, L. Yang, P. Zhou, H. T. Chen, J. F. Ding, W. W. Zhu, Y. Y. Lu, L. X. Jia, Q. Fang, and M. B. Yu, “Proof of concept of directed OR/NOR and AND/NAND logic circuit consisting of two parallel microring resonators,” Opt. Lett. 36, 1650–1652 (2011).
    [CrossRef]
  61. L. Zhang, R. Q. Ji, Y. H. Tian, L. Yang, P. Zhou, Y. Y. Lu, W. W. Zhu, Y. L. Liu, X. L. Jia, Q. Fang, and M. B. Yu, “Simultaneous implementation of XOR and XNOR operations using a directed logic circuit based on two microring resonators,” Opt. Express 19, 6524–6540 (2011).
    [CrossRef]
  62. S. Papaioannou, K. Vyrsokinos, O. Tsilipakos, A. Pitilakis, K. Hassan, J.-C. Weeber, L. Markey, A. Dereux, S. I. Bozhevolnyi, A. Miliou, E. E. Kriezis, and N. Pleros, “A 320  Gb/s-throughput capable 2×2 silicon-plasmonic router architecture for optical interconnects,” J. Lightwave Technol. 29, 3185–3195 (2011).
    [CrossRef]
  63. J. Shamir and H. J. Caulfield, “High-efficiency rapidly programmable optical interconnections,” Appl. Opt. 26, 1032–1037 (1987).
    [CrossRef]
  64. J. Shamir, “Three-dimensional optical interconnection gate array,” Appl. Opt. 26, 3455–3457 (1987).
    [CrossRef]
  65. M. M. Mirsalehi, J. Shamir, and H. J. Caulfield, “Residue arithmetic processing utilizing optical Fredkin gate arrays,” Appl. Opt. 26, 3940–3946 (1987).
    [CrossRef]
  66. J. Shamir, “Parallel optical logic operations on reversible networks,” Opt. Commun. (to be published).

2012

P. Daukantas, “Photography in the American Civil War,” Opt. Photonics News 23(6), 24–29 (2012).
[CrossRef]

2011

Y. H. Tian, L. Zhang, R. Q. Ji, L. Yang, P. Zhou, H. T. Chen, J. F. Ding, W. W. Zhu, Y. Y. Lu, L. X. Jia, Q. Fang, and M. B. Yu, “Proof of concept of directed OR/NOR and AND/NAND logic circuit consisting of two parallel microring resonators,” Opt. Lett. 36, 1650–1652 (2011).
[CrossRef]

L. Zhang, R. Q. Ji, Y. H. Tian, L. Yang, P. Zhou, Y. Y. Lu, W. W. Zhu, Y. L. Liu, X. L. Jia, Q. Fang, and M. B. Yu, “Simultaneous implementation of XOR and XNOR operations using a directed logic circuit based on two microring resonators,” Opt. Express 19, 6524–6540 (2011).
[CrossRef]

S. Papaioannou, K. Vyrsokinos, O. Tsilipakos, A. Pitilakis, K. Hassan, J.-C. Weeber, L. Markey, A. Dereux, S. I. Bozhevolnyi, A. Miliou, E. E. Kriezis, and N. Pleros, “A 320  Gb/s-throughput capable 2×2 silicon-plasmonic router architecture for optical interconnects,” J. Lightwave Technol. 29, 3185–3195 (2011).
[CrossRef]

Q. Xu and R. Soref, “Reconfigurable optical directed-logic circuits using microresonator-based optical switches,” Opt. Express 19, 5244–5259 (2011).
[CrossRef]

2010

L. Zhang, R. Q. Ji, L. X. Jia, L. Yang, P. Zhou, Y. H. Tian, P. Chen, Y. Y. Lu, Z. Y. Jiang, Y. L. Liu, Q. Fang, and M. B. Yu, “Demonstration of directed XOR/XNOR logic gates using two cascaded microring resonators,” Opt. Lett. 35, 1620–1622(2010).
[CrossRef]

2009

G. Indebetouw, “Scanning holographic microscopy with spatially incoherent sources: reconciling the holographic advantage with the sectioning advantage,” J. Opt. Soc. Am. A 26, 252–258 (2009).
[CrossRef]

2007

J. Hardy and J. Shamir, “Optics inspired logic architecture,” Opt. Express 15, 150–165 (2007).
[CrossRef]

2006

J. Shamir, “Paradigms for bit-oriented holographic information storage,” Appl. Opt. 45, 5212–5222 (2006).
[CrossRef]

2002

R. Piestun and J. Shamir, “Synthesis of three-dimensional light-fields and applications,” Proc. IEEE 90, 222–244 (2002).
[CrossRef]

1999

C.-S. Pang, K. Oba, Y. T. Mazurenko, and S. Y. Fainman, “Space-time processing with photorefractive volume holography,” Proc. IEEE 87, 2086–2097 (1999).
[CrossRef]

T. R. Clark, J. U. Kang, and R. D. Esman, “Performance of a time- and wavelength-interleaved photonic sampler for analog-digital conversion,” IEEE Photonics Technol. Lett. 11, 1168–1170 (1999).
[CrossRef]

D. Lyszyk and J. Shamir, “Signal processing under uncertain conditions by parallel projections onto fuzzy sets,” J. Opt. Soc. Am A 16, 1602–1611 (1999).
[CrossRef]

1998

D. Meshulach, D. Yelin, and Y. Silberberg, “Adaptive real-time femtosecond pulse shaping,” J. Opt. Soc. Am. B 15, 1615–1619 (1998).
[CrossRef]

D. Caspi, N. Kiryati, and J. Shamir, “Range imaging with adaptive color structured sight,” IEEE Trans. Pattern Anal. Mach. Intell. 20, 470–480 (1998).
[CrossRef]

1997

J. Shamir, “Adaptive pattern recognition correlators,” Opt. Eng. 36, 2675–2689 (1997).
[CrossRef]

1996

R. Piestun, B. Spektor, and J. Shamir, “Wave fields in three dimensions: analysis and synthesis,” J. Opt. Soc. Am. A 13, 1837–1848 (1996).
[CrossRef]

H. J. Caulfield, “Fuzzy optical metrology,” IEEE Trans. Fuzzy Syst. 4, 206–207 (1996).
[CrossRef]

1993

J. Shamir, D. G. Crowe, and J. W. Beletic, “Improved compensation of atmospheric turbulence effects by multiple adaptive mirror systems,” Appl. Opt. 32, 4618–4628 (1993).
[CrossRef]

1992

B. V. K. Vijaya Kumar, “Tutorial survey of composite filter designs for optical correlators,” Appl. Opt. 31, 4773–4801 (1992).
[CrossRef]

1991

U. Mahlab and J. Shamir, “Optical pattern recognition based on convex functions,” J. Opt. Soc. Am. A 8, 1233–1239 (1991).
[CrossRef]

J. Shamir and H. J. Caulfield, “Parallel optical processors—some basic considerations,” Int. J. Opt. Comp. 2, 73–78 (1991).

P. L. Wizinowich, M. Lloyd-Hart, B. A. McLeod, D. Colucci, R. G. Dekany, D. M. Wittman, J. R. P. Angel, D. W. McCarthy, W. G. Hulburd, and D. G. Sandler, “Neural network adaptive optics for the multimirror telescope,” Proc. SPIE 1542, 148–158 (1991).
[CrossRef]

1990

H. J. Caulfield and J. Shamir, “Wave-particle duality processors—characteristics, requirements and applications,” J. Opt. Soc. Am. A 7, 1314–1323 (1990).
[CrossRef]

J. Rosen, U. Mahlab, and J. Shamir, “Adaptive learning with joint transform correlators,” Opt. Eng. 29, 1101–1106 (1990).
[CrossRef]

1989

A. W. Lohmann and A. S. Marathay, “Globality and speed of optical parallel processors,” Appl. Opt. 28, 3838–3842 (1989).
[CrossRef]

J. Rosen and J. Shamir, “Scale invariant pattern recognition with logarithmic radial harmonic filters,” Appl. Opt. 28, 240–244 (1989).
[CrossRef]

U. Mahlab and J. Shamir, “Phase-only entropy-optimized filter by simulated annealing,” Opt. Lett. 14, 1168–1170 (1989).
[CrossRef]

J. Shamir, H. J. Caulfield, and R. B. Johnson, “Massive holographic interconnection networks and their limitations,” Appl. Opt. 28, 311–324 (1989).
[CrossRef]

H. J. Caulfield and J. Shamir, “Wave-particle duality considerations in optical computing,” Appl. Opt. 28, 2184–2186 (1989).
[CrossRef]

1988

J. Rosen and J. Shamir, “Circular harmonic phase filters for efficient rotation-invariant pattern recognition,” Appl. Opt. 27, 2895–2899 (1988).
[CrossRef]

1987

H. J. Caulfield, “Parallel N4 weighted optical interconnections,” Appl. Opt. 26, 4039–4040 (1987).
[CrossRef]

J. Shamir, “Fundamental speed limitations on parallel processing,” Appl. Opt. 26, 1567–1593 (1987).
[CrossRef]

N. H. Farhat, “Optoelectronic analogs of self programming neural nets: architecture and methodologies for implementing fast stochastic learning by simulated annealing,” Appl. Opt. 26, 5093–5103 (1987).
[CrossRef]

J. Shamir and H. J. Caulfield, “High-efficiency rapidly programmable optical interconnections,” Appl. Opt. 26, 1032–1037 (1987).
[CrossRef]

J. Shamir, “Three-dimensional optical interconnection gate array,” Appl. Opt. 26, 3455–3457 (1987).
[CrossRef]

M. M. Mirsalehi, J. Shamir, and H. J. Caulfield, “Residue arithmetic processing utilizing optical Fredkin gate arrays,” Appl. Opt. 26, 3940–3946 (1987).
[CrossRef]

1986

J. Shamir, H. J. Caulfield, W. Miceli, and R. J. Seymour, “Optical computing and the Fredkin gate,” Appl. Opt. 25, 1604–1607 (1986).
[CrossRef]

1985

R. P. Feynman, “Quantum mechanical computing,” Opt. News 11, 11–20 (1985).
[CrossRef]

1984

D. Casasent, “Unified synthetic discriminant function computational formulation,” Appl. Opt. 23, 1620–1627 (1984).
[CrossRef]

J. W. Goodman, F. I. Leonberger, S. Kung, and R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

1982

Y. Hsu and H. Arsenault, “Optical pattern recognition using circular harmonic expansion,” Appl. Opt. 21, 4016–4019 (1982).
[CrossRef]

E. Fredkin and T. Toffoli, “Conservative logic,” Int. J. Theor. Phys. 21, 219–253 (1982).
[CrossRef]

1980

C. F. Hester and D. Casasent, “Multivariant technique for multiclass pattern recognition,” Appl. Opt. 19, 1758–1761 (1980).
[CrossRef]

1979

B. Braunecker, R. Hauch, and A. W. Lohmann, “Optical character recognition based on nonredundant correlation measurements,” Appl. Opt. 18, 2746–2753 (1979).
[CrossRef]

1977

D. Casasent and D. Psaltis, “New optical transforms for pattern recognition,” Proc. IEEE 65, 77–84 (1977).
[CrossRef]

1973

J. Shamir, “Moire gauging by projected interference fringes,” Opt. Laser Technol. 5, 78–86 (1973).
[CrossRef]

C. H. Bennett, “Logical reversibility of computation,” IBM J. Res. Dev. 17, 525–532 (1973).
[CrossRef]

1969

H. J. Caulfield and W. T. Maloney, “Improved discrimination in optical character recognition,” Appl. Opt. 8, 2354–2356 (1969).
[CrossRef]

1966

L. J. Cutrona, “On the application of coherent optical processing techniques to synthetic-aperture radar,” Proc. IEEE 54, 1026–1032 (1966).
[CrossRef]

1964

A. B. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory 10, 139–145 (1964).
[CrossRef]

1961

R. Landauer, “Irreversibility and heat generation in the computing process,” IBM J. Res. Dev. 5, 183–191(1961).
[CrossRef]

1960

L. J. Cutrona, E. N. Leith, C. J. Palermo, and L. J. Porcello, “Optical data processing and filtering systems,” IRE Trans. Inf. Theory IT-6, 386–400 (1960).

1953

P. Elias, “Optics in communication theory,” J. Opt. Soc. Am. 43, 229–232 (1953).
[CrossRef]

1952

P. Elias, D. S. Gray, and D. Z. Robinson, “Fourier treatment of optical processes,” J. Opt. Soc. Am. 42, 127–134 (1952).
[CrossRef]

1880

J. W. Strutt (Lord Rayleigh), “Investigations in optics, with special reference to the spectroscope,” Philos. Mag. 8, 40–55 (1880). Reprinted in The Collection of Optics Papers of Lord Rayleigh, J. W. Strutt, ed. (Optical Society of America, 1994), pp. 117–130.

Angel, J. R. P.

P. L. Wizinowich, M. Lloyd-Hart, B. A. McLeod, D. Colucci, R. G. Dekany, D. M. Wittman, J. R. P. Angel, D. W. McCarthy, W. G. Hulburd, and D. G. Sandler, “Neural network adaptive optics for the multimirror telescope,” Proc. SPIE 1542, 148–158 (1991).
[CrossRef]

Arsenault, H.

Y. Hsu and H. Arsenault, “Optical pattern recognition using circular harmonic expansion,” Appl. Opt. 21, 4016–4019 (1982).
[CrossRef]

Athale, R. A.

J. W. Goodman, F. I. Leonberger, S. Kung, and R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

Beletic, J. W.

J. Shamir, D. G. Crowe, and J. W. Beletic, “Improved compensation of atmospheric turbulence effects by multiple adaptive mirror systems,” Appl. Opt. 32, 4618–4628 (1993).
[CrossRef]

Bennett, C. H.

C. H. Bennett, “Logical reversibility of computation,” IBM J. Res. Dev. 17, 525–532 (1973).
[CrossRef]

Bozhevolnyi, S. I.

S. Papaioannou, K. Vyrsokinos, O. Tsilipakos, A. Pitilakis, K. Hassan, J.-C. Weeber, L. Markey, A. Dereux, S. I. Bozhevolnyi, A. Miliou, E. E. Kriezis, and N. Pleros, “A 320  Gb/s-throughput capable 2×2 silicon-plasmonic router architecture for optical interconnects,” J. Lightwave Technol. 29, 3185–3195 (2011).
[CrossRef]

Braunecker, B.

B. Braunecker, R. Hauch, and A. W. Lohmann, “Optical character recognition based on nonredundant correlation measurements,” Appl. Opt. 18, 2746–2753 (1979).
[CrossRef]

Casasent, D.

D. Casasent, “Unified synthetic discriminant function computational formulation,” Appl. Opt. 23, 1620–1627 (1984).
[CrossRef]

C. F. Hester and D. Casasent, “Multivariant technique for multiclass pattern recognition,” Appl. Opt. 19, 1758–1761 (1980).
[CrossRef]

D. Casasent and D. Psaltis, “New optical transforms for pattern recognition,” Proc. IEEE 65, 77–84 (1977).
[CrossRef]

Caspi, D.

D. Caspi, N. Kiryati, and J. Shamir, “Range imaging with adaptive color structured sight,” IEEE Trans. Pattern Anal. Mach. Intell. 20, 470–480 (1998).
[CrossRef]

Caulfield, H. J.

H. J. Caulfield, “Fuzzy optical metrology,” IEEE Trans. Fuzzy Syst. 4, 206–207 (1996).
[CrossRef]

J. Shamir and H. J. Caulfield, “Parallel optical processors—some basic considerations,” Int. J. Opt. Comp. 2, 73–78 (1991).

H. J. Caulfield and J. Shamir, “Wave-particle duality processors—characteristics, requirements and applications,” J. Opt. Soc. Am. A 7, 1314–1323 (1990).
[CrossRef]

H. J. Caulfield and J. Shamir, “Wave-particle duality considerations in optical computing,” Appl. Opt. 28, 2184–2186 (1989).
[CrossRef]

J. Shamir, H. J. Caulfield, and R. B. Johnson, “Massive holographic interconnection networks and their limitations,” Appl. Opt. 28, 311–324 (1989).
[CrossRef]

H. J. Caulfield, “Parallel N4 weighted optical interconnections,” Appl. Opt. 26, 4039–4040 (1987).
[CrossRef]

J. Shamir and H. J. Caulfield, “High-efficiency rapidly programmable optical interconnections,” Appl. Opt. 26, 1032–1037 (1987).
[CrossRef]

M. M. Mirsalehi, J. Shamir, and H. J. Caulfield, “Residue arithmetic processing utilizing optical Fredkin gate arrays,” Appl. Opt. 26, 3940–3946 (1987).
[CrossRef]

J. Shamir, H. J. Caulfield, W. Miceli, and R. J. Seymour, “Optical computing and the Fredkin gate,” Appl. Opt. 25, 1604–1607 (1986).
[CrossRef]

H. J. Caulfield and W. T. Maloney, “Improved discrimination in optical character recognition,” Appl. Opt. 8, 2354–2356 (1969).
[CrossRef]

H.-I. Jeon, J. Shamir, R. B. Johnson, H. J. Caulfield, J. Kinser, C. Hester, and M. Temmen, “The use of fixed holograms for massively-interconnected, low-power neural networks,” in Neural Networks for Perception, H. Wechsler, ed. (Academic, 1992), Vol. 2, pp. 282–309.

H. J. Caulfield and J. Shamir, “Fixed hologram neural networks,” in Real-Time Optical Information Processing, B. Javidi and J. L. Horner, eds. (Academic, 1994), pp. 255–305.

Chen, H. T.

Y. H. Tian, L. Zhang, R. Q. Ji, L. Yang, P. Zhou, H. T. Chen, J. F. Ding, W. W. Zhu, Y. Y. Lu, L. X. Jia, Q. Fang, and M. B. Yu, “Proof of concept of directed OR/NOR and AND/NAND logic circuit consisting of two parallel microring resonators,” Opt. Lett. 36, 1650–1652 (2011).
[CrossRef]

Chen, P.

L. Zhang, R. Q. Ji, L. X. Jia, L. Yang, P. Zhou, Y. H. Tian, P. Chen, Y. Y. Lu, Z. Y. Jiang, Y. L. Liu, Q. Fang, and M. B. Yu, “Demonstration of directed XOR/XNOR logic gates using two cascaded microring resonators,” Opt. Lett. 35, 1620–1622(2010).
[CrossRef]

Clark, T. R.

T. R. Clark, J. U. Kang, and R. D. Esman, “Performance of a time- and wavelength-interleaved photonic sampler for analog-digital conversion,” IEEE Photonics Technol. Lett. 11, 1168–1170 (1999).
[CrossRef]

Colucci, D.

P. L. Wizinowich, M. Lloyd-Hart, B. A. McLeod, D. Colucci, R. G. Dekany, D. M. Wittman, J. R. P. Angel, D. W. McCarthy, W. G. Hulburd, and D. G. Sandler, “Neural network adaptive optics for the multimirror telescope,” Proc. SPIE 1542, 148–158 (1991).
[CrossRef]

Crowe, D. G.

J. Shamir, D. G. Crowe, and J. W. Beletic, “Improved compensation of atmospheric turbulence effects by multiple adaptive mirror systems,” Appl. Opt. 32, 4618–4628 (1993).
[CrossRef]

Cutrona, L. J.

L. J. Cutrona, “On the application of coherent optical processing techniques to synthetic-aperture radar,” Proc. IEEE 54, 1026–1032 (1966).
[CrossRef]

L. J. Cutrona, E. N. Leith, C. J. Palermo, and L. J. Porcello, “Optical data processing and filtering systems,” IRE Trans. Inf. Theory IT-6, 386–400 (1960).

Daukantas, P.

P. Daukantas, “Photography in the American Civil War,” Opt. Photonics News 23(6), 24–29 (2012).
[CrossRef]

Dekany, R. G.

P. L. Wizinowich, M. Lloyd-Hart, B. A. McLeod, D. Colucci, R. G. Dekany, D. M. Wittman, J. R. P. Angel, D. W. McCarthy, W. G. Hulburd, and D. G. Sandler, “Neural network adaptive optics for the multimirror telescope,” Proc. SPIE 1542, 148–158 (1991).
[CrossRef]

Dereux, A.

S. Papaioannou, K. Vyrsokinos, O. Tsilipakos, A. Pitilakis, K. Hassan, J.-C. Weeber, L. Markey, A. Dereux, S. I. Bozhevolnyi, A. Miliou, E. E. Kriezis, and N. Pleros, “A 320  Gb/s-throughput capable 2×2 silicon-plasmonic router architecture for optical interconnects,” J. Lightwave Technol. 29, 3185–3195 (2011).
[CrossRef]

Ding, J. F.

Y. H. Tian, L. Zhang, R. Q. Ji, L. Yang, P. Zhou, H. T. Chen, J. F. Ding, W. W. Zhu, Y. Y. Lu, L. X. Jia, Q. Fang, and M. B. Yu, “Proof of concept of directed OR/NOR and AND/NAND logic circuit consisting of two parallel microring resonators,” Opt. Lett. 36, 1650–1652 (2011).
[CrossRef]

Elias, P.

P. Elias, “Optics in communication theory,” J. Opt. Soc. Am. 43, 229–232 (1953).
[CrossRef]

P. Elias, D. S. Gray, and D. Z. Robinson, “Fourier treatment of optical processes,” J. Opt. Soc. Am. 42, 127–134 (1952).
[CrossRef]

Esman, R. D.

T. R. Clark, J. U. Kang, and R. D. Esman, “Performance of a time- and wavelength-interleaved photonic sampler for analog-digital conversion,” IEEE Photonics Technol. Lett. 11, 1168–1170 (1999).
[CrossRef]

Fainman, S. Y.

C.-S. Pang, K. Oba, Y. T. Mazurenko, and S. Y. Fainman, “Space-time processing with photorefractive volume holography,” Proc. IEEE 87, 2086–2097 (1999).
[CrossRef]

Fang, Q.

Y. H. Tian, L. Zhang, R. Q. Ji, L. Yang, P. Zhou, H. T. Chen, J. F. Ding, W. W. Zhu, Y. Y. Lu, L. X. Jia, Q. Fang, and M. B. Yu, “Proof of concept of directed OR/NOR and AND/NAND logic circuit consisting of two parallel microring resonators,” Opt. Lett. 36, 1650–1652 (2011).
[CrossRef]

L. Zhang, R. Q. Ji, Y. H. Tian, L. Yang, P. Zhou, Y. Y. Lu, W. W. Zhu, Y. L. Liu, X. L. Jia, Q. Fang, and M. B. Yu, “Simultaneous implementation of XOR and XNOR operations using a directed logic circuit based on two microring resonators,” Opt. Express 19, 6524–6540 (2011).
[CrossRef]

L. Zhang, R. Q. Ji, L. X. Jia, L. Yang, P. Zhou, Y. H. Tian, P. Chen, Y. Y. Lu, Z. Y. Jiang, Y. L. Liu, Q. Fang, and M. B. Yu, “Demonstration of directed XOR/XNOR logic gates using two cascaded microring resonators,” Opt. Lett. 35, 1620–1622(2010).
[CrossRef]

Farhat, N. H.

N. H. Farhat, “Optoelectronic analogs of self programming neural nets: architecture and methodologies for implementing fast stochastic learning by simulated annealing,” Appl. Opt. 26, 5093–5103 (1987).
[CrossRef]

Feynman, R. P.

R. P. Feynman, “Quantum mechanical computing,” Opt. News 11, 11–20 (1985).
[CrossRef]

Fredkin, E.

E. Fredkin and T. Toffoli, “Conservative logic,” Int. J. Theor. Phys. 21, 219–253 (1982).
[CrossRef]

Gabor, D.

D. Gabor, “Light and information,” in Progress in Optics, E. Wolf, ed. (Elsevier, 1964), Vol. 1, pp. 109–153.

Goodman, J. W.

J. W. Goodman, F. I. Leonberger, S. Kung, and R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

Gray, D. S.

P. Elias, D. S. Gray, and D. Z. Robinson, “Fourier treatment of optical processes,” J. Opt. Soc. Am. 42, 127–134 (1952).
[CrossRef]

Hardy, J.

J. Hardy and J. Shamir, “Optics inspired logic architecture,” Opt. Express 15, 150–165 (2007).
[CrossRef]

Hassan, K.

S. Papaioannou, K. Vyrsokinos, O. Tsilipakos, A. Pitilakis, K. Hassan, J.-C. Weeber, L. Markey, A. Dereux, S. I. Bozhevolnyi, A. Miliou, E. E. Kriezis, and N. Pleros, “A 320  Gb/s-throughput capable 2×2 silicon-plasmonic router architecture for optical interconnects,” J. Lightwave Technol. 29, 3185–3195 (2011).
[CrossRef]

Hauch, R.

B. Braunecker, R. Hauch, and A. W. Lohmann, “Optical character recognition based on nonredundant correlation measurements,” Appl. Opt. 18, 2746–2753 (1979).
[CrossRef]

Herzig, H. P.

H. P. Herzig, Micro-Optics (Taylor & Francis, 1997).

Hester, C.

H.-I. Jeon, J. Shamir, R. B. Johnson, H. J. Caulfield, J. Kinser, C. Hester, and M. Temmen, “The use of fixed holograms for massively-interconnected, low-power neural networks,” in Neural Networks for Perception, H. Wechsler, ed. (Academic, 1992), Vol. 2, pp. 282–309.

Hester, C. F.

C. F. Hester and D. Casasent, “Multivariant technique for multiclass pattern recognition,” Appl. Opt. 19, 1758–1761 (1980).
[CrossRef]

Hsu, Y.

Y. Hsu and H. Arsenault, “Optical pattern recognition using circular harmonic expansion,” Appl. Opt. 21, 4016–4019 (1982).
[CrossRef]

Hulburd, W. G.

P. L. Wizinowich, M. Lloyd-Hart, B. A. McLeod, D. Colucci, R. G. Dekany, D. M. Wittman, J. R. P. Angel, D. W. McCarthy, W. G. Hulburd, and D. G. Sandler, “Neural network adaptive optics for the multimirror telescope,” Proc. SPIE 1542, 148–158 (1991).
[CrossRef]

Indebetouw, G.

G. Indebetouw, “Scanning holographic microscopy with spatially incoherent sources: reconciling the holographic advantage with the sectioning advantage,” J. Opt. Soc. Am. A 26, 252–258 (2009).
[CrossRef]

Jeon, H.-I.

H.-I. Jeon, J. Shamir, R. B. Johnson, H. J. Caulfield, J. Kinser, C. Hester, and M. Temmen, “The use of fixed holograms for massively-interconnected, low-power neural networks,” in Neural Networks for Perception, H. Wechsler, ed. (Academic, 1992), Vol. 2, pp. 282–309.

Ji, R. Q.

Y. H. Tian, L. Zhang, R. Q. Ji, L. Yang, P. Zhou, H. T. Chen, J. F. Ding, W. W. Zhu, Y. Y. Lu, L. X. Jia, Q. Fang, and M. B. Yu, “Proof of concept of directed OR/NOR and AND/NAND logic circuit consisting of two parallel microring resonators,” Opt. Lett. 36, 1650–1652 (2011).
[CrossRef]

L. Zhang, R. Q. Ji, Y. H. Tian, L. Yang, P. Zhou, Y. Y. Lu, W. W. Zhu, Y. L. Liu, X. L. Jia, Q. Fang, and M. B. Yu, “Simultaneous implementation of XOR and XNOR operations using a directed logic circuit based on two microring resonators,” Opt. Express 19, 6524–6540 (2011).
[CrossRef]

L. Zhang, R. Q. Ji, L. X. Jia, L. Yang, P. Zhou, Y. H. Tian, P. Chen, Y. Y. Lu, Z. Y. Jiang, Y. L. Liu, Q. Fang, and M. B. Yu, “Demonstration of directed XOR/XNOR logic gates using two cascaded microring resonators,” Opt. Lett. 35, 1620–1622(2010).
[CrossRef]

Jia, L. X.

Y. H. Tian, L. Zhang, R. Q. Ji, L. Yang, P. Zhou, H. T. Chen, J. F. Ding, W. W. Zhu, Y. Y. Lu, L. X. Jia, Q. Fang, and M. B. Yu, “Proof of concept of directed OR/NOR and AND/NAND logic circuit consisting of two parallel microring resonators,” Opt. Lett. 36, 1650–1652 (2011).
[CrossRef]

L. Zhang, R. Q. Ji, L. X. Jia, L. Yang, P. Zhou, Y. H. Tian, P. Chen, Y. Y. Lu, Z. Y. Jiang, Y. L. Liu, Q. Fang, and M. B. Yu, “Demonstration of directed XOR/XNOR logic gates using two cascaded microring resonators,” Opt. Lett. 35, 1620–1622(2010).
[CrossRef]

Jia, X. L.

L. Zhang, R. Q. Ji, Y. H. Tian, L. Yang, P. Zhou, Y. Y. Lu, W. W. Zhu, Y. L. Liu, X. L. Jia, Q. Fang, and M. B. Yu, “Simultaneous implementation of XOR and XNOR operations using a directed logic circuit based on two microring resonators,” Opt. Express 19, 6524–6540 (2011).
[CrossRef]

Jiang, Z. Y.

L. Zhang, R. Q. Ji, L. X. Jia, L. Yang, P. Zhou, Y. H. Tian, P. Chen, Y. Y. Lu, Z. Y. Jiang, Y. L. Liu, Q. Fang, and M. B. Yu, “Demonstration of directed XOR/XNOR logic gates using two cascaded microring resonators,” Opt. Lett. 35, 1620–1622(2010).
[CrossRef]

Johnson, R. B.

J. Shamir, H. J. Caulfield, and R. B. Johnson, “Massive holographic interconnection networks and their limitations,” Appl. Opt. 28, 311–324 (1989).
[CrossRef]

H.-I. Jeon, J. Shamir, R. B. Johnson, H. J. Caulfield, J. Kinser, C. Hester, and M. Temmen, “The use of fixed holograms for massively-interconnected, low-power neural networks,” in Neural Networks for Perception, H. Wechsler, ed. (Academic, 1992), Vol. 2, pp. 282–309.

Kang, J. U.

T. R. Clark, J. U. Kang, and R. D. Esman, “Performance of a time- and wavelength-interleaved photonic sampler for analog-digital conversion,” IEEE Photonics Technol. Lett. 11, 1168–1170 (1999).
[CrossRef]

Kinser, J.

H.-I. Jeon, J. Shamir, R. B. Johnson, H. J. Caulfield, J. Kinser, C. Hester, and M. Temmen, “The use of fixed holograms for massively-interconnected, low-power neural networks,” in Neural Networks for Perception, H. Wechsler, ed. (Academic, 1992), Vol. 2, pp. 282–309.

Kiryati, N.

D. Caspi, N. Kiryati, and J. Shamir, “Range imaging with adaptive color structured sight,” IEEE Trans. Pattern Anal. Mach. Intell. 20, 470–480 (1998).
[CrossRef]

Korpel, A.

A. Korpel, Acousto-Optics (Marcel Dekker, 1997).

Kriezis, E. E.

S. Papaioannou, K. Vyrsokinos, O. Tsilipakos, A. Pitilakis, K. Hassan, J.-C. Weeber, L. Markey, A. Dereux, S. I. Bozhevolnyi, A. Miliou, E. E. Kriezis, and N. Pleros, “A 320  Gb/s-throughput capable 2×2 silicon-plasmonic router architecture for optical interconnects,” J. Lightwave Technol. 29, 3185–3195 (2011).
[CrossRef]

Kung, S.

J. W. Goodman, F. I. Leonberger, S. Kung, and R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

Landauer, R.

R. Landauer, “Irreversibility and heat generation in the computing process,” IBM J. Res. Dev. 5, 183–191(1961).
[CrossRef]

Leith, E. N.

L. J. Cutrona, E. N. Leith, C. J. Palermo, and L. J. Porcello, “Optical data processing and filtering systems,” IRE Trans. Inf. Theory IT-6, 386–400 (1960).

Leonberger, F. I.

J. W. Goodman, F. I. Leonberger, S. Kung, and R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

Liu, Y. L.

L. Zhang, R. Q. Ji, Y. H. Tian, L. Yang, P. Zhou, Y. Y. Lu, W. W. Zhu, Y. L. Liu, X. L. Jia, Q. Fang, and M. B. Yu, “Simultaneous implementation of XOR and XNOR operations using a directed logic circuit based on two microring resonators,” Opt. Express 19, 6524–6540 (2011).
[CrossRef]

L. Zhang, R. Q. Ji, L. X. Jia, L. Yang, P. Zhou, Y. H. Tian, P. Chen, Y. Y. Lu, Z. Y. Jiang, Y. L. Liu, Q. Fang, and M. B. Yu, “Demonstration of directed XOR/XNOR logic gates using two cascaded microring resonators,” Opt. Lett. 35, 1620–1622(2010).
[CrossRef]

Lloyd-Hart, M.

P. L. Wizinowich, M. Lloyd-Hart, B. A. McLeod, D. Colucci, R. G. Dekany, D. M. Wittman, J. R. P. Angel, D. W. McCarthy, W. G. Hulburd, and D. G. Sandler, “Neural network adaptive optics for the multimirror telescope,” Proc. SPIE 1542, 148–158 (1991).
[CrossRef]

Lohmann, A. W.

A. W. Lohmann and A. S. Marathay, “Globality and speed of optical parallel processors,” Appl. Opt. 28, 3838–3842 (1989).
[CrossRef]

B. Braunecker, R. Hauch, and A. W. Lohmann, “Optical character recognition based on nonredundant correlation measurements,” Appl. Opt. 18, 2746–2753 (1979).
[CrossRef]

Lu, Y. Y.

Y. H. Tian, L. Zhang, R. Q. Ji, L. Yang, P. Zhou, H. T. Chen, J. F. Ding, W. W. Zhu, Y. Y. Lu, L. X. Jia, Q. Fang, and M. B. Yu, “Proof of concept of directed OR/NOR and AND/NAND logic circuit consisting of two parallel microring resonators,” Opt. Lett. 36, 1650–1652 (2011).
[CrossRef]

L. Zhang, R. Q. Ji, Y. H. Tian, L. Yang, P. Zhou, Y. Y. Lu, W. W. Zhu, Y. L. Liu, X. L. Jia, Q. Fang, and M. B. Yu, “Simultaneous implementation of XOR and XNOR operations using a directed logic circuit based on two microring resonators,” Opt. Express 19, 6524–6540 (2011).
[CrossRef]

L. Zhang, R. Q. Ji, L. X. Jia, L. Yang, P. Zhou, Y. H. Tian, P. Chen, Y. Y. Lu, Z. Y. Jiang, Y. L. Liu, Q. Fang, and M. B. Yu, “Demonstration of directed XOR/XNOR logic gates using two cascaded microring resonators,” Opt. Lett. 35, 1620–1622(2010).
[CrossRef]

Lyszyk, D.

D. Lyszyk and J. Shamir, “Signal processing under uncertain conditions by parallel projections onto fuzzy sets,” J. Opt. Soc. Am A 16, 1602–1611 (1999).
[CrossRef]

Mahlab, U.

U. Mahlab and J. Shamir, “Optical pattern recognition based on convex functions,” J. Opt. Soc. Am. A 8, 1233–1239 (1991).
[CrossRef]

J. Rosen, U. Mahlab, and J. Shamir, “Adaptive learning with joint transform correlators,” Opt. Eng. 29, 1101–1106 (1990).
[CrossRef]

U. Mahlab and J. Shamir, “Phase-only entropy-optimized filter by simulated annealing,” Opt. Lett. 14, 1168–1170 (1989).
[CrossRef]

Maloney, W. T.

H. J. Caulfield and W. T. Maloney, “Improved discrimination in optical character recognition,” Appl. Opt. 8, 2354–2356 (1969).
[CrossRef]

Marathay, A. S.

A. W. Lohmann and A. S. Marathay, “Globality and speed of optical parallel processors,” Appl. Opt. 28, 3838–3842 (1989).
[CrossRef]

Markey, L.

S. Papaioannou, K. Vyrsokinos, O. Tsilipakos, A. Pitilakis, K. Hassan, J.-C. Weeber, L. Markey, A. Dereux, S. I. Bozhevolnyi, A. Miliou, E. E. Kriezis, and N. Pleros, “A 320  Gb/s-throughput capable 2×2 silicon-plasmonic router architecture for optical interconnects,” J. Lightwave Technol. 29, 3185–3195 (2011).
[CrossRef]

Mazurenko, Y. T.

C.-S. Pang, K. Oba, Y. T. Mazurenko, and S. Y. Fainman, “Space-time processing with photorefractive volume holography,” Proc. IEEE 87, 2086–2097 (1999).
[CrossRef]

McCarthy, D. W.

P. L. Wizinowich, M. Lloyd-Hart, B. A. McLeod, D. Colucci, R. G. Dekany, D. M. Wittman, J. R. P. Angel, D. W. McCarthy, W. G. Hulburd, and D. G. Sandler, “Neural network adaptive optics for the multimirror telescope,” Proc. SPIE 1542, 148–158 (1991).
[CrossRef]

McLeod, B. A.

P. L. Wizinowich, M. Lloyd-Hart, B. A. McLeod, D. Colucci, R. G. Dekany, D. M. Wittman, J. R. P. Angel, D. W. McCarthy, W. G. Hulburd, and D. G. Sandler, “Neural network adaptive optics for the multimirror telescope,” Proc. SPIE 1542, 148–158 (1991).
[CrossRef]

Meshulach, D.

D. Meshulach, D. Yelin, and Y. Silberberg, “Adaptive real-time femtosecond pulse shaping,” J. Opt. Soc. Am. B 15, 1615–1619 (1998).
[CrossRef]

Miceli, W.

J. Shamir, H. J. Caulfield, W. Miceli, and R. J. Seymour, “Optical computing and the Fredkin gate,” Appl. Opt. 25, 1604–1607 (1986).
[CrossRef]

Miliou, A.

S. Papaioannou, K. Vyrsokinos, O. Tsilipakos, A. Pitilakis, K. Hassan, J.-C. Weeber, L. Markey, A. Dereux, S. I. Bozhevolnyi, A. Miliou, E. E. Kriezis, and N. Pleros, “A 320  Gb/s-throughput capable 2×2 silicon-plasmonic router architecture for optical interconnects,” J. Lightwave Technol. 29, 3185–3195 (2011).
[CrossRef]

Mirsalehi, M. M.

M. M. Mirsalehi, J. Shamir, and H. J. Caulfield, “Residue arithmetic processing utilizing optical Fredkin gate arrays,” Appl. Opt. 26, 3940–3946 (1987).
[CrossRef]

Oba, K.

C.-S. Pang, K. Oba, Y. T. Mazurenko, and S. Y. Fainman, “Space-time processing with photorefractive volume holography,” Proc. IEEE 87, 2086–2097 (1999).
[CrossRef]

Palermo, C. J.

L. J. Cutrona, E. N. Leith, C. J. Palermo, and L. J. Porcello, “Optical data processing and filtering systems,” IRE Trans. Inf. Theory IT-6, 386–400 (1960).

Pang, C.-S.

C.-S. Pang, K. Oba, Y. T. Mazurenko, and S. Y. Fainman, “Space-time processing with photorefractive volume holography,” Proc. IEEE 87, 2086–2097 (1999).
[CrossRef]

Papaioannou, S.

S. Papaioannou, K. Vyrsokinos, O. Tsilipakos, A. Pitilakis, K. Hassan, J.-C. Weeber, L. Markey, A. Dereux, S. I. Bozhevolnyi, A. Miliou, E. E. Kriezis, and N. Pleros, “A 320  Gb/s-throughput capable 2×2 silicon-plasmonic router architecture for optical interconnects,” J. Lightwave Technol. 29, 3185–3195 (2011).
[CrossRef]

Piestun, R.

R. Piestun and J. Shamir, “Synthesis of three-dimensional light-fields and applications,” Proc. IEEE 90, 222–244 (2002).
[CrossRef]

R. Piestun, B. Spektor, and J. Shamir, “Wave fields in three dimensions: analysis and synthesis,” J. Opt. Soc. Am. A 13, 1837–1848 (1996).
[CrossRef]

Pitilakis, A.

S. Papaioannou, K. Vyrsokinos, O. Tsilipakos, A. Pitilakis, K. Hassan, J.-C. Weeber, L. Markey, A. Dereux, S. I. Bozhevolnyi, A. Miliou, E. E. Kriezis, and N. Pleros, “A 320  Gb/s-throughput capable 2×2 silicon-plasmonic router architecture for optical interconnects,” J. Lightwave Technol. 29, 3185–3195 (2011).
[CrossRef]

Pleros, N.

S. Papaioannou, K. Vyrsokinos, O. Tsilipakos, A. Pitilakis, K. Hassan, J.-C. Weeber, L. Markey, A. Dereux, S. I. Bozhevolnyi, A. Miliou, E. E. Kriezis, and N. Pleros, “A 320  Gb/s-throughput capable 2×2 silicon-plasmonic router architecture for optical interconnects,” J. Lightwave Technol. 29, 3185–3195 (2011).
[CrossRef]

Porcello, L. J.

L. J. Cutrona, E. N. Leith, C. J. Palermo, and L. J. Porcello, “Optical data processing and filtering systems,” IRE Trans. Inf. Theory IT-6, 386–400 (1960).

Psaltis, D.

D. Casasent and D. Psaltis, “New optical transforms for pattern recognition,” Proc. IEEE 65, 77–84 (1977).
[CrossRef]

Robinson, D. Z.

P. Elias, D. S. Gray, and D. Z. Robinson, “Fourier treatment of optical processes,” J. Opt. Soc. Am. 42, 127–134 (1952).
[CrossRef]

Rosen, J.

J. Rosen, U. Mahlab, and J. Shamir, “Adaptive learning with joint transform correlators,” Opt. Eng. 29, 1101–1106 (1990).
[CrossRef]

J. Rosen and J. Shamir, “Scale invariant pattern recognition with logarithmic radial harmonic filters,” Appl. Opt. 28, 240–244 (1989).
[CrossRef]

J. Rosen and J. Shamir, “Circular harmonic phase filters for efficient rotation-invariant pattern recognition,” Appl. Opt. 27, 2895–2899 (1988).
[CrossRef]

Sandler, D. G.

P. L. Wizinowich, M. Lloyd-Hart, B. A. McLeod, D. Colucci, R. G. Dekany, D. M. Wittman, J. R. P. Angel, D. W. McCarthy, W. G. Hulburd, and D. G. Sandler, “Neural network adaptive optics for the multimirror telescope,” Proc. SPIE 1542, 148–158 (1991).
[CrossRef]

Seymour, R. J.

J. Shamir, H. J. Caulfield, W. Miceli, and R. J. Seymour, “Optical computing and the Fredkin gate,” Appl. Opt. 25, 1604–1607 (1986).
[CrossRef]

Shamir, J.

J. Hardy and J. Shamir, “Optics inspired logic architecture,” Opt. Express 15, 150–165 (2007).
[CrossRef]

J. Shamir, “Paradigms for bit-oriented holographic information storage,” Appl. Opt. 45, 5212–5222 (2006).
[CrossRef]

R. Piestun and J. Shamir, “Synthesis of three-dimensional light-fields and applications,” Proc. IEEE 90, 222–244 (2002).
[CrossRef]

D. Lyszyk and J. Shamir, “Signal processing under uncertain conditions by parallel projections onto fuzzy sets,” J. Opt. Soc. Am A 16, 1602–1611 (1999).
[CrossRef]

D. Caspi, N. Kiryati, and J. Shamir, “Range imaging with adaptive color structured sight,” IEEE Trans. Pattern Anal. Mach. Intell. 20, 470–480 (1998).
[CrossRef]

J. Shamir, “Adaptive pattern recognition correlators,” Opt. Eng. 36, 2675–2689 (1997).
[CrossRef]

R. Piestun, B. Spektor, and J. Shamir, “Wave fields in three dimensions: analysis and synthesis,” J. Opt. Soc. Am. A 13, 1837–1848 (1996).
[CrossRef]

J. Shamir, D. G. Crowe, and J. W. Beletic, “Improved compensation of atmospheric turbulence effects by multiple adaptive mirror systems,” Appl. Opt. 32, 4618–4628 (1993).
[CrossRef]

U. Mahlab and J. Shamir, “Optical pattern recognition based on convex functions,” J. Opt. Soc. Am. A 8, 1233–1239 (1991).
[CrossRef]

J. Shamir and H. J. Caulfield, “Parallel optical processors—some basic considerations,” Int. J. Opt. Comp. 2, 73–78 (1991).

H. J. Caulfield and J. Shamir, “Wave-particle duality processors—characteristics, requirements and applications,” J. Opt. Soc. Am. A 7, 1314–1323 (1990).
[CrossRef]

J. Rosen, U. Mahlab, and J. Shamir, “Adaptive learning with joint transform correlators,” Opt. Eng. 29, 1101–1106 (1990).
[CrossRef]

U. Mahlab and J. Shamir, “Phase-only entropy-optimized filter by simulated annealing,” Opt. Lett. 14, 1168–1170 (1989).
[CrossRef]

J. Rosen and J. Shamir, “Scale invariant pattern recognition with logarithmic radial harmonic filters,” Appl. Opt. 28, 240–244 (1989).
[CrossRef]

H. J. Caulfield and J. Shamir, “Wave-particle duality considerations in optical computing,” Appl. Opt. 28, 2184–2186 (1989).
[CrossRef]

J. Shamir, H. J. Caulfield, and R. B. Johnson, “Massive holographic interconnection networks and their limitations,” Appl. Opt. 28, 311–324 (1989).
[CrossRef]

J. Rosen and J. Shamir, “Circular harmonic phase filters for efficient rotation-invariant pattern recognition,” Appl. Opt. 27, 2895–2899 (1988).
[CrossRef]

J. Shamir, “Fundamental speed limitations on parallel processing,” Appl. Opt. 26, 1567–1593 (1987).
[CrossRef]

J. Shamir and H. J. Caulfield, “High-efficiency rapidly programmable optical interconnections,” Appl. Opt. 26, 1032–1037 (1987).
[CrossRef]

M. M. Mirsalehi, J. Shamir, and H. J. Caulfield, “Residue arithmetic processing utilizing optical Fredkin gate arrays,” Appl. Opt. 26, 3940–3946 (1987).
[CrossRef]

J. Shamir, “Three-dimensional optical interconnection gate array,” Appl. Opt. 26, 3455–3457 (1987).
[CrossRef]

J. Shamir, H. J. Caulfield, W. Miceli, and R. J. Seymour, “Optical computing and the Fredkin gate,” Appl. Opt. 25, 1604–1607 (1986).
[CrossRef]

J. Shamir, “Moire gauging by projected interference fringes,” Opt. Laser Technol. 5, 78–86 (1973).
[CrossRef]

J. Shamir, “Iterative procedures in electro-optical pattern recognition,” in Optical Pattern Recognition, F. T. S. Yu, ed. (Cambridge University, 1998), pp. 221–261.

H.-I. Jeon, J. Shamir, R. B. Johnson, H. J. Caulfield, J. Kinser, C. Hester, and M. Temmen, “The use of fixed holograms for massively-interconnected, low-power neural networks,” in Neural Networks for Perception, H. Wechsler, ed. (Academic, 1992), Vol. 2, pp. 282–309.

H. J. Caulfield and J. Shamir, “Fixed hologram neural networks,” in Real-Time Optical Information Processing, B. Javidi and J. L. Horner, eds. (Academic, 1994), pp. 255–305.

J. Shamir, Optical Systems and Processes (SPIE, 1999). Reprinted by Prentice-Hall India, 2004.

J. Shamir, “Parallel optical logic operations on reversible networks,” Opt. Commun. (to be published).

Silberberg, Y.

D. Meshulach, D. Yelin, and Y. Silberberg, “Adaptive real-time femtosecond pulse shaping,” J. Opt. Soc. Am. B 15, 1615–1619 (1998).
[CrossRef]

Soref, R.

Q. Xu and R. Soref, “Reconfigurable optical directed-logic circuits using microresonator-based optical switches,” Opt. Express 19, 5244–5259 (2011).
[CrossRef]

Spektor, B.

R. Piestun, B. Spektor, and J. Shamir, “Wave fields in three dimensions: analysis and synthesis,” J. Opt. Soc. Am. A 13, 1837–1848 (1996).
[CrossRef]

Strutt, J. W.

J. W. Strutt (Lord Rayleigh), “Investigations in optics, with special reference to the spectroscope,” Philos. Mag. 8, 40–55 (1880). Reprinted in The Collection of Optics Papers of Lord Rayleigh, J. W. Strutt, ed. (Optical Society of America, 1994), pp. 117–130.

Temmen, M.

H.-I. Jeon, J. Shamir, R. B. Johnson, H. J. Caulfield, J. Kinser, C. Hester, and M. Temmen, “The use of fixed holograms for massively-interconnected, low-power neural networks,” in Neural Networks for Perception, H. Wechsler, ed. (Academic, 1992), Vol. 2, pp. 282–309.

Tian, Y. H.

L. Zhang, R. Q. Ji, Y. H. Tian, L. Yang, P. Zhou, Y. Y. Lu, W. W. Zhu, Y. L. Liu, X. L. Jia, Q. Fang, and M. B. Yu, “Simultaneous implementation of XOR and XNOR operations using a directed logic circuit based on two microring resonators,” Opt. Express 19, 6524–6540 (2011).
[CrossRef]

Y. H. Tian, L. Zhang, R. Q. Ji, L. Yang, P. Zhou, H. T. Chen, J. F. Ding, W. W. Zhu, Y. Y. Lu, L. X. Jia, Q. Fang, and M. B. Yu, “Proof of concept of directed OR/NOR and AND/NAND logic circuit consisting of two parallel microring resonators,” Opt. Lett. 36, 1650–1652 (2011).
[CrossRef]

L. Zhang, R. Q. Ji, L. X. Jia, L. Yang, P. Zhou, Y. H. Tian, P. Chen, Y. Y. Lu, Z. Y. Jiang, Y. L. Liu, Q. Fang, and M. B. Yu, “Demonstration of directed XOR/XNOR logic gates using two cascaded microring resonators,” Opt. Lett. 35, 1620–1622(2010).
[CrossRef]

Toffoli, T.

E. Fredkin and T. Toffoli, “Conservative logic,” Int. J. Theor. Phys. 21, 219–253 (1982).
[CrossRef]

Tsilipakos, O.

S. Papaioannou, K. Vyrsokinos, O. Tsilipakos, A. Pitilakis, K. Hassan, J.-C. Weeber, L. Markey, A. Dereux, S. I. Bozhevolnyi, A. Miliou, E. E. Kriezis, and N. Pleros, “A 320  Gb/s-throughput capable 2×2 silicon-plasmonic router architecture for optical interconnects,” J. Lightwave Technol. 29, 3185–3195 (2011).
[CrossRef]

Tyson, R. K.

R. K. Tyson, Principles of Adaptive Optics (Academic, 1991).

VanderLugt, A. B.

A. B. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory 10, 139–145 (1964).
[CrossRef]

Vijaya Kumar, B. V. K.

B. V. K. Vijaya Kumar, “Tutorial survey of composite filter designs for optical correlators,” Appl. Opt. 31, 4773–4801 (1992).
[CrossRef]

Vyrsokinos, K.

S. Papaioannou, K. Vyrsokinos, O. Tsilipakos, A. Pitilakis, K. Hassan, J.-C. Weeber, L. Markey, A. Dereux, S. I. Bozhevolnyi, A. Miliou, E. E. Kriezis, and N. Pleros, “A 320  Gb/s-throughput capable 2×2 silicon-plasmonic router architecture for optical interconnects,” J. Lightwave Technol. 29, 3185–3195 (2011).
[CrossRef]

Weeber, J.-C.

S. Papaioannou, K. Vyrsokinos, O. Tsilipakos, A. Pitilakis, K. Hassan, J.-C. Weeber, L. Markey, A. Dereux, S. I. Bozhevolnyi, A. Miliou, E. E. Kriezis, and N. Pleros, “A 320  Gb/s-throughput capable 2×2 silicon-plasmonic router architecture for optical interconnects,” J. Lightwave Technol. 29, 3185–3195 (2011).
[CrossRef]

Wittman, D. M.

P. L. Wizinowich, M. Lloyd-Hart, B. A. McLeod, D. Colucci, R. G. Dekany, D. M. Wittman, J. R. P. Angel, D. W. McCarthy, W. G. Hulburd, and D. G. Sandler, “Neural network adaptive optics for the multimirror telescope,” Proc. SPIE 1542, 148–158 (1991).
[CrossRef]

Wizinowich, P. L.

P. L. Wizinowich, M. Lloyd-Hart, B. A. McLeod, D. Colucci, R. G. Dekany, D. M. Wittman, J. R. P. Angel, D. W. McCarthy, W. G. Hulburd, and D. G. Sandler, “Neural network adaptive optics for the multimirror telescope,” Proc. SPIE 1542, 148–158 (1991).
[CrossRef]

Xu, Q.

Q. Xu and R. Soref, “Reconfigurable optical directed-logic circuits using microresonator-based optical switches,” Opt. Express 19, 5244–5259 (2011).
[CrossRef]

Yang, L.

Y. H. Tian, L. Zhang, R. Q. Ji, L. Yang, P. Zhou, H. T. Chen, J. F. Ding, W. W. Zhu, Y. Y. Lu, L. X. Jia, Q. Fang, and M. B. Yu, “Proof of concept of directed OR/NOR and AND/NAND logic circuit consisting of two parallel microring resonators,” Opt. Lett. 36, 1650–1652 (2011).
[CrossRef]

L. Zhang, R. Q. Ji, Y. H. Tian, L. Yang, P. Zhou, Y. Y. Lu, W. W. Zhu, Y. L. Liu, X. L. Jia, Q. Fang, and M. B. Yu, “Simultaneous implementation of XOR and XNOR operations using a directed logic circuit based on two microring resonators,” Opt. Express 19, 6524–6540 (2011).
[CrossRef]

L. Zhang, R. Q. Ji, L. X. Jia, L. Yang, P. Zhou, Y. H. Tian, P. Chen, Y. Y. Lu, Z. Y. Jiang, Y. L. Liu, Q. Fang, and M. B. Yu, “Demonstration of directed XOR/XNOR logic gates using two cascaded microring resonators,” Opt. Lett. 35, 1620–1622(2010).
[CrossRef]

Yelin, D.

D. Meshulach, D. Yelin, and Y. Silberberg, “Adaptive real-time femtosecond pulse shaping,” J. Opt. Soc. Am. B 15, 1615–1619 (1998).
[CrossRef]

Yu, M. B.

Y. H. Tian, L. Zhang, R. Q. Ji, L. Yang, P. Zhou, H. T. Chen, J. F. Ding, W. W. Zhu, Y. Y. Lu, L. X. Jia, Q. Fang, and M. B. Yu, “Proof of concept of directed OR/NOR and AND/NAND logic circuit consisting of two parallel microring resonators,” Opt. Lett. 36, 1650–1652 (2011).
[CrossRef]

L. Zhang, R. Q. Ji, Y. H. Tian, L. Yang, P. Zhou, Y. Y. Lu, W. W. Zhu, Y. L. Liu, X. L. Jia, Q. Fang, and M. B. Yu, “Simultaneous implementation of XOR and XNOR operations using a directed logic circuit based on two microring resonators,” Opt. Express 19, 6524–6540 (2011).
[CrossRef]

L. Zhang, R. Q. Ji, L. X. Jia, L. Yang, P. Zhou, Y. H. Tian, P. Chen, Y. Y. Lu, Z. Y. Jiang, Y. L. Liu, Q. Fang, and M. B. Yu, “Demonstration of directed XOR/XNOR logic gates using two cascaded microring resonators,” Opt. Lett. 35, 1620–1622(2010).
[CrossRef]

Zhang, L.

Y. H. Tian, L. Zhang, R. Q. Ji, L. Yang, P. Zhou, H. T. Chen, J. F. Ding, W. W. Zhu, Y. Y. Lu, L. X. Jia, Q. Fang, and M. B. Yu, “Proof of concept of directed OR/NOR and AND/NAND logic circuit consisting of two parallel microring resonators,” Opt. Lett. 36, 1650–1652 (2011).
[CrossRef]

L. Zhang, R. Q. Ji, Y. H. Tian, L. Yang, P. Zhou, Y. Y. Lu, W. W. Zhu, Y. L. Liu, X. L. Jia, Q. Fang, and M. B. Yu, “Simultaneous implementation of XOR and XNOR operations using a directed logic circuit based on two microring resonators,” Opt. Express 19, 6524–6540 (2011).
[CrossRef]

L. Zhang, R. Q. Ji, L. X. Jia, L. Yang, P. Zhou, Y. H. Tian, P. Chen, Y. Y. Lu, Z. Y. Jiang, Y. L. Liu, Q. Fang, and M. B. Yu, “Demonstration of directed XOR/XNOR logic gates using two cascaded microring resonators,” Opt. Lett. 35, 1620–1622(2010).
[CrossRef]

Zhou, P.

Y. H. Tian, L. Zhang, R. Q. Ji, L. Yang, P. Zhou, H. T. Chen, J. F. Ding, W. W. Zhu, Y. Y. Lu, L. X. Jia, Q. Fang, and M. B. Yu, “Proof of concept of directed OR/NOR and AND/NAND logic circuit consisting of two parallel microring resonators,” Opt. Lett. 36, 1650–1652 (2011).
[CrossRef]

L. Zhang, R. Q. Ji, Y. H. Tian, L. Yang, P. Zhou, Y. Y. Lu, W. W. Zhu, Y. L. Liu, X. L. Jia, Q. Fang, and M. B. Yu, “Simultaneous implementation of XOR and XNOR operations using a directed logic circuit based on two microring resonators,” Opt. Express 19, 6524–6540 (2011).
[CrossRef]

L. Zhang, R. Q. Ji, L. X. Jia, L. Yang, P. Zhou, Y. H. Tian, P. Chen, Y. Y. Lu, Z. Y. Jiang, Y. L. Liu, Q. Fang, and M. B. Yu, “Demonstration of directed XOR/XNOR logic gates using two cascaded microring resonators,” Opt. Lett. 35, 1620–1622(2010).
[CrossRef]

Zhu, W. W.

Y. H. Tian, L. Zhang, R. Q. Ji, L. Yang, P. Zhou, H. T. Chen, J. F. Ding, W. W. Zhu, Y. Y. Lu, L. X. Jia, Q. Fang, and M. B. Yu, “Proof of concept of directed OR/NOR and AND/NAND logic circuit consisting of two parallel microring resonators,” Opt. Lett. 36, 1650–1652 (2011).
[CrossRef]

L. Zhang, R. Q. Ji, Y. H. Tian, L. Yang, P. Zhou, Y. Y. Lu, W. W. Zhu, Y. L. Liu, X. L. Jia, Q. Fang, and M. B. Yu, “Simultaneous implementation of XOR and XNOR operations using a directed logic circuit based on two microring resonators,” Opt. Express 19, 6524–6540 (2011).
[CrossRef]

Appl. Opt.

H. J. Caulfield and J. Shamir, “Wave-particle duality considerations in optical computing,” Appl. Opt. 28, 2184–2186 (1989).
[CrossRef]

J. Shamir, H. J. Caulfield, and R. B. Johnson, “Massive holographic interconnection networks and their limitations,” Appl. Opt. 28, 311–324 (1989).
[CrossRef]

H. J. Caulfield, “Parallel N4 weighted optical interconnections,” Appl. Opt. 26, 4039–4040 (1987).
[CrossRef]

J. Shamir, “Paradigms for bit-oriented holographic information storage,” Appl. Opt. 45, 5212–5222 (2006).
[CrossRef]

H. J. Caulfield and W. T. Maloney, “Improved discrimination in optical character recognition,” Appl. Opt. 8, 2354–2356 (1969).
[CrossRef]

B. Braunecker, R. Hauch, and A. W. Lohmann, “Optical character recognition based on nonredundant correlation measurements,” Appl. Opt. 18, 2746–2753 (1979).
[CrossRef]

C. F. Hester and D. Casasent, “Multivariant technique for multiclass pattern recognition,” Appl. Opt. 19, 1758–1761 (1980).
[CrossRef]

Y. Hsu and H. Arsenault, “Optical pattern recognition using circular harmonic expansion,” Appl. Opt. 21, 4016–4019 (1982).
[CrossRef]

J. Rosen and J. Shamir, “Circular harmonic phase filters for efficient rotation-invariant pattern recognition,” Appl. Opt. 27, 2895–2899 (1988).
[CrossRef]

J. Rosen and J. Shamir, “Scale invariant pattern recognition with logarithmic radial harmonic filters,” Appl. Opt. 28, 240–244 (1989).
[CrossRef]

D. Casasent, “Unified synthetic discriminant function computational formulation,” Appl. Opt. 23, 1620–1627 (1984).
[CrossRef]

B. V. K. Vijaya Kumar, “Tutorial survey of composite filter designs for optical correlators,” Appl. Opt. 31, 4773–4801 (1992).
[CrossRef]

J. Shamir, “Fundamental speed limitations on parallel processing,” Appl. Opt. 26, 1567–1593 (1987).
[CrossRef]

A. W. Lohmann and A. S. Marathay, “Globality and speed of optical parallel processors,” Appl. Opt. 28, 3838–3842 (1989).
[CrossRef]

J. Shamir, D. G. Crowe, and J. W. Beletic, “Improved compensation of atmospheric turbulence effects by multiple adaptive mirror systems,” Appl. Opt. 32, 4618–4628 (1993).
[CrossRef]

J. Shamir, H. J. Caulfield, W. Miceli, and R. J. Seymour, “Optical computing and the Fredkin gate,” Appl. Opt. 25, 1604–1607 (1986).
[CrossRef]

N. H. Farhat, “Optoelectronic analogs of self programming neural nets: architecture and methodologies for implementing fast stochastic learning by simulated annealing,” Appl. Opt. 26, 5093–5103 (1987).
[CrossRef]

J. Shamir and H. J. Caulfield, “High-efficiency rapidly programmable optical interconnections,” Appl. Opt. 26, 1032–1037 (1987).
[CrossRef]

J. Shamir, “Three-dimensional optical interconnection gate array,” Appl. Opt. 26, 3455–3457 (1987).
[CrossRef]

M. M. Mirsalehi, J. Shamir, and H. J. Caulfield, “Residue arithmetic processing utilizing optical Fredkin gate arrays,” Appl. Opt. 26, 3940–3946 (1987).
[CrossRef]

IBM J. Res. Dev.

R. Landauer, “Irreversibility and heat generation in the computing process,” IBM J. Res. Dev. 5, 183–191(1961).
[CrossRef]

C. H. Bennett, “Logical reversibility of computation,” IBM J. Res. Dev. 17, 525–532 (1973).
[CrossRef]

IEEE Photonics Technol. Lett.

T. R. Clark, J. U. Kang, and R. D. Esman, “Performance of a time- and wavelength-interleaved photonic sampler for analog-digital conversion,” IEEE Photonics Technol. Lett. 11, 1168–1170 (1999).
[CrossRef]

IEEE Trans. Fuzzy Syst.

H. J. Caulfield, “Fuzzy optical metrology,” IEEE Trans. Fuzzy Syst. 4, 206–207 (1996).
[CrossRef]

IEEE Trans. Inf. Theory

A. B. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory 10, 139–145 (1964).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell.

D. Caspi, N. Kiryati, and J. Shamir, “Range imaging with adaptive color structured sight,” IEEE Trans. Pattern Anal. Mach. Intell. 20, 470–480 (1998).
[CrossRef]

Int. J. Opt. Comp.

J. Shamir and H. J. Caulfield, “Parallel optical processors—some basic considerations,” Int. J. Opt. Comp. 2, 73–78 (1991).

Int. J. Theor. Phys.

E. Fredkin and T. Toffoli, “Conservative logic,” Int. J. Theor. Phys. 21, 219–253 (1982).
[CrossRef]

IRE Trans. Inf. Theory

L. J. Cutrona, E. N. Leith, C. J. Palermo, and L. J. Porcello, “Optical data processing and filtering systems,” IRE Trans. Inf. Theory IT-6, 386–400 (1960).

J. Lightwave Technol.

S. Papaioannou, K. Vyrsokinos, O. Tsilipakos, A. Pitilakis, K. Hassan, J.-C. Weeber, L. Markey, A. Dereux, S. I. Bozhevolnyi, A. Miliou, E. E. Kriezis, and N. Pleros, “A 320  Gb/s-throughput capable 2×2 silicon-plasmonic router architecture for optical interconnects,” J. Lightwave Technol. 29, 3185–3195 (2011).
[CrossRef]

J. Opt. Soc. Am A

D. Lyszyk and J. Shamir, “Signal processing under uncertain conditions by parallel projections onto fuzzy sets,” J. Opt. Soc. Am A 16, 1602–1611 (1999).
[CrossRef]

J. Opt. Soc. Am.

P. Elias, D. S. Gray, and D. Z. Robinson, “Fourier treatment of optical processes,” J. Opt. Soc. Am. 42, 127–134 (1952).
[CrossRef]

P. Elias, “Optics in communication theory,” J. Opt. Soc. Am. 43, 229–232 (1953).
[CrossRef]

J. Opt. Soc. Am. A

H. J. Caulfield and J. Shamir, “Wave-particle duality processors—characteristics, requirements and applications,” J. Opt. Soc. Am. A 7, 1314–1323 (1990).
[CrossRef]

U. Mahlab and J. Shamir, “Optical pattern recognition based on convex functions,” J. Opt. Soc. Am. A 8, 1233–1239 (1991).
[CrossRef]

G. Indebetouw, “Scanning holographic microscopy with spatially incoherent sources: reconciling the holographic advantage with the sectioning advantage,” J. Opt. Soc. Am. A 26, 252–258 (2009).
[CrossRef]

R. Piestun, B. Spektor, and J. Shamir, “Wave fields in three dimensions: analysis and synthesis,” J. Opt. Soc. Am. A 13, 1837–1848 (1996).
[CrossRef]

J. Opt. Soc. Am. B

D. Meshulach, D. Yelin, and Y. Silberberg, “Adaptive real-time femtosecond pulse shaping,” J. Opt. Soc. Am. B 15, 1615–1619 (1998).
[CrossRef]

Opt. Eng.

J. Rosen, U. Mahlab, and J. Shamir, “Adaptive learning with joint transform correlators,” Opt. Eng. 29, 1101–1106 (1990).
[CrossRef]

J. Shamir, “Adaptive pattern recognition correlators,” Opt. Eng. 36, 2675–2689 (1997).
[CrossRef]

Opt. Express

J. Hardy and J. Shamir, “Optics inspired logic architecture,” Opt. Express 15, 150–165 (2007).
[CrossRef]

Q. Xu and R. Soref, “Reconfigurable optical directed-logic circuits using microresonator-based optical switches,” Opt. Express 19, 5244–5259 (2011).
[CrossRef]

L. Zhang, R. Q. Ji, Y. H. Tian, L. Yang, P. Zhou, Y. Y. Lu, W. W. Zhu, Y. L. Liu, X. L. Jia, Q. Fang, and M. B. Yu, “Simultaneous implementation of XOR and XNOR operations using a directed logic circuit based on two microring resonators,” Opt. Express 19, 6524–6540 (2011).
[CrossRef]

Opt. Laser Technol.

J. Shamir, “Moire gauging by projected interference fringes,” Opt. Laser Technol. 5, 78–86 (1973).
[CrossRef]

Opt. Lett.

L. Zhang, R. Q. Ji, L. X. Jia, L. Yang, P. Zhou, Y. H. Tian, P. Chen, Y. Y. Lu, Z. Y. Jiang, Y. L. Liu, Q. Fang, and M. B. Yu, “Demonstration of directed XOR/XNOR logic gates using two cascaded microring resonators,” Opt. Lett. 35, 1620–1622(2010).
[CrossRef]

Y. H. Tian, L. Zhang, R. Q. Ji, L. Yang, P. Zhou, H. T. Chen, J. F. Ding, W. W. Zhu, Y. Y. Lu, L. X. Jia, Q. Fang, and M. B. Yu, “Proof of concept of directed OR/NOR and AND/NAND logic circuit consisting of two parallel microring resonators,” Opt. Lett. 36, 1650–1652 (2011).
[CrossRef]

U. Mahlab and J. Shamir, “Phase-only entropy-optimized filter by simulated annealing,” Opt. Lett. 14, 1168–1170 (1989).
[CrossRef]

Opt. News

R. P. Feynman, “Quantum mechanical computing,” Opt. News 11, 11–20 (1985).
[CrossRef]

Opt. Photonics News

P. Daukantas, “Photography in the American Civil War,” Opt. Photonics News 23(6), 24–29 (2012).
[CrossRef]

Philos. Mag.

J. W. Strutt (Lord Rayleigh), “Investigations in optics, with special reference to the spectroscope,” Philos. Mag. 8, 40–55 (1880). Reprinted in The Collection of Optics Papers of Lord Rayleigh, J. W. Strutt, ed. (Optical Society of America, 1994), pp. 117–130.

Proc. IEEE

D. Casasent and D. Psaltis, “New optical transforms for pattern recognition,” Proc. IEEE 65, 77–84 (1977).
[CrossRef]

C.-S. Pang, K. Oba, Y. T. Mazurenko, and S. Y. Fainman, “Space-time processing with photorefractive volume holography,” Proc. IEEE 87, 2086–2097 (1999).
[CrossRef]

J. W. Goodman, F. I. Leonberger, S. Kung, and R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

R. Piestun and J. Shamir, “Synthesis of three-dimensional light-fields and applications,” Proc. IEEE 90, 222–244 (2002).
[CrossRef]

L. J. Cutrona, “On the application of coherent optical processing techniques to synthetic-aperture radar,” Proc. IEEE 54, 1026–1032 (1966).
[CrossRef]

Proc. SPIE

P. L. Wizinowich, M. Lloyd-Hart, B. A. McLeod, D. Colucci, R. G. Dekany, D. M. Wittman, J. R. P. Angel, D. W. McCarthy, W. G. Hulburd, and D. G. Sandler, “Neural network adaptive optics for the multimirror telescope,” Proc. SPIE 1542, 148–158 (1991).
[CrossRef]

Other

R. K. Tyson, Principles of Adaptive Optics (Academic, 1991).

H. P. Herzig, Micro-Optics (Taylor & Francis, 1997).

J. Shamir, “Parallel optical logic operations on reversible networks,” Opt. Commun. (to be published).

D. Gabor, “Light and information,” in Progress in Optics, E. Wolf, ed. (Elsevier, 1964), Vol. 1, pp. 109–153.

J. Shamir, “Iterative procedures in electro-optical pattern recognition,” in Optical Pattern Recognition, F. T. S. Yu, ed. (Cambridge University, 1998), pp. 221–261.

A. Korpel, Acousto-Optics (Marcel Dekker, 1997).

H.-I. Jeon, J. Shamir, R. B. Johnson, H. J. Caulfield, J. Kinser, C. Hester, and M. Temmen, “The use of fixed holograms for massively-interconnected, low-power neural networks,” in Neural Networks for Perception, H. Wechsler, ed. (Academic, 1992), Vol. 2, pp. 282–309.

H. J. Caulfield and J. Shamir, “Fixed hologram neural networks,” in Real-Time Optical Information Processing, B. Javidi and J. L. Horner, eds. (Academic, 1994), pp. 255–305.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

J. Shamir, Optical Systems and Processes (SPIE, 1999). Reprinted by Prentice-Hall India, 2004.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (13)

Fig. 1.
Fig. 1.

A photon arriving at point B from a source at point A traveled the quickest path (Fermat’s principle). In free space it is a straight line.

Fig. 2.
Fig. 2.

Simple, single lens optical system.

Fig. 3.
Fig. 3.

Optical correlator.

Fig. 4.
Fig. 4.

Matrix-matrix multiplier or an n4 interconnection network.

Fig. 5.
Fig. 5.

Time skew in free space.

Fig. 6.
Fig. 6.

Hybrid correlator for the implementation of optimization algorithms.

Fig. 7.
Fig. 7.

Basic definition of the Fredkin gate.

Fig. 8.
Fig. 8.

Implementation of logic elements using a Fredkin gate. (a) NOT gate, (b) AND gate, and (c) OR gate.

Fig. 9.
Fig. 9.

DL implementation of an OR gate.

Fig. 10.
Fig. 10.

Waveguide coupler as Fredkin gate. The two waveguide channels are coupled by a controllable element represented by the ellipse.

Fig. 11.
Fig. 11.

Generic interconnection network. Each dashed rectangle delineates a single switching layer.

Fig. 12.
Fig. 12.

4×4 interconnection network implementing logic operations (see text for detail).

Fig. 13.
Fig. 13.

Implementation of a full adder (see text for detail).

Equations (9)

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

δ=RL=D2+L2L=L(4tan2θ+11),
b1=a1;b2=a2IfC=0;b1=a2;b2=a1IfC=1.
(b1b2)=M(a1a2),
M=(1001)forC=0;M=(0110)forC=1.
M(1,0)=(1000010000100001)(1000010000100001)(1000001001000001)×(0100100000100001)=(0100001010000001)=M(0,1).
M(1,1)=(0010100001000001).
(b1(0,0)b2(0,0)b3(0,0)b4(0,0))=(a1a2a3a4);(b1(1,1)b2(1,1)b3(1,1)b4(1,1))=(a3a1a2a4);(b1(1,0)b2(1,0)b3(1,0)b4(1,0))=(b1(0,1)b2(0,1)b3(0,1)b4(0,1))=(a2a3a1a4).
S=(ABC)+A·B·C,
Cout=C1+C2=(A·B+A·C+B·C)+A·B·C.

Metrics