Abstract

Galois field (GF) algebraic expressions have been found to be promising choices for reversible and quantum implementation of multivalued logic. For the first time to our knowledge, we developed GF(4) adder multivalued (four valued) logic circuits in an all-optical domain. The principle and possibilities of an all-optical GF(4) adder circuit are described. The theoretical model is presented and verified through numerical simulation. The quaternary inverter, successor, clockwise cycle, and counterclockwise cycle gates are proposed with the help of the all-optical GF(4) adder circuit. In this scheme different quaternary logical states are represented by different polarized light. A terahertz optical asymmetric demultiplexer interferometric switch plays an important role in this scheme.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. C. Smith, “The prospects for multivalued logic: a technology and applications view,” IEEE Trans. Comput. C-30, 1160-1179 (1984).
  2. Y. Yasuda, Y. Tokuda, S. Zaima, K. Pak, T. Nakamura, and A. Yoshida, “Realization of quaternary logic circuits by n-channel MOS devices,” IEEE J. Solid-State Circuits SSC-21, 162-168(1986)
    [CrossRef]
  3. A. A. S. Awwal, M. A. Karim, and A. K. Cherri, “Polarization-encoded optical shadow-casting scheme: design of multioutput trinary combinational logic units,” Appl. Opt. 26, 4814-4818(1987)
    [CrossRef]
  4. S. Liu, C. Li, J. Wu, and Y. Lin, “Optoelectronic multiple-valued logic implementation,” Opt. Lett. 14, 713-715(1989).
    [CrossRef]
  5. J. Yi, H. He, and Y. Lu, “Ternary optical computer architecture,” Phys. Scr. T118, 98-101 (2005).
  6. C. S. Vikram and H. J. Caulfield, “Position-sensing detector for logical operations using incoherent light,” Opt. Eng. 44, 115201 (2005).
  7. T. Chattopadhyay and J. N. Roy, “Polarization encoded all-optical quaternary multiplexer and demultiplexer -a proposal,” Optik (Jena) , doi:10.1016/j.ijleo.2008.03.030 [In press].
    [CrossRef]
  8. T. Chattopadhyay and J. N. Roy, “All-optical conversion scheme: binary to quaternary and quaternary to binary number,” Opt. Laser Technol. 41, 289-294 (2009).
  9. T. Chattopadhyay and J. N. Roy, “Polarization encoded TOAD based all-optical quaternary Literals,” Optik (Jena) [doi: 10.1016/j.ijleo.2008.09.014]
    [CrossRef]
  10. J. N. Roy and D. K. Gayen, “Integrated all-optical logic and arithmetic operations with the help of a TOAD-based interferometer device--alternative approach,” Appl. Opt. 46, 5304-5310 (2007).
    [CrossRef]
  11. M. H. A. Khan and M. A. Perkowski, “GF(4) based synthesis of quaternary reversible/ quantum logic circuits,” in Proceedings of the International Symposia on Multiple-Valued Logic (IEEE Computer Society, 2007).
  12. N. A. Khader and P. Siy, “Inversion/division in Galois field using multiple-valued logic,” in Proceedings of the International Symposia on Multiple-Valued Logic (IEEE Computer Society, 2007)
  13. M. H. A. Khan, N. K. Siddika, and M. A. Perkowski, “Minimization of quaternary Galois field sum of products expression for multi-output quaternary logic function using quaternary Galois field decision diagram,” in Proceedings of the International Symposia on Multiple-Valued Logic (IEEE Computer Society, 2008), pp. 125-130.
    [CrossRef]
  14. J. P. Sokoloff, P. R. Prucnal, I. Glesk, and M. Kane, “A terahertz optical asymmetric demultiplexer (TOAD),” IEEE Photon. Technol. Lett. 5, 787-790 (1993).
  15. M. Eiselt, W. Pieper, and H. G. Weber, “SLALOM: semiconductor laser amplifier in a loop mirror,” J. Lightwave Technol. 13, 2099-2112 (1995).
    [CrossRef]
  16. B. C. Wang, V. Baby, W. Tong, L. Xu, M. Friedman, R. J. Runser, I. Glesk, and P. R. Prucnal, “A novel fast optical switch based on two cascaded terahertz optical asymmetric demultiplexers (TOAD),” Opt. Express 10, 15-23 (2002).
  17. Y. K. Huang, I. Glesk, R. Shankar, and P. R. Prucnal, “Simultaneous all-optical 3R regeneration scheme with improved scalability using TOAD,” Opt. Express 14, 10339-10344 (2006).
    [CrossRef]
  18. Y. J. Jung, S. Lee, and N. Park, “All-optical 4-bit gray code to binary coded decimal converter,” Proc. of SPIE 6890, 68900S (2008).
    [CrossRef]
  19. Z. Y. Shen and L. L. Wu, “Reconfigurable optical logic unit with a terahertz optical asymmetric demultiplexer and electro-optic switches,” Appl. Opt. 47, 3737-3742 (2008).
    [CrossRef]
  20. D. K. Gayen and J. N. Roy, “All-optical arithmetic unit with the help of terahertz optical asymmetric demultiplexer-based tree architecture,” Appl. Opt. 47, 933-943 (2008).
    [CrossRef]
  21. J. N. Roy, G. K. Maity, D. K. Gayen, and T. Chattopadhyay, “Terahertz optical asymmetric demultiplexer based tree-net architecture for all-optical conversion scheme from binary to its other 2n radix based form,” Chin. Opt. Lett. 6, 536-540(2008).
  22. T. Yang, C. Shu, and C. Lin, “Depolarization technique for wavelength conversion using four-wave mixing in a dispersion-flattened photonic crystal fiber,” Opt. Express 13, 5409-5415 (2005).
  23. T. Chattopadhyay and J. N. Roy, “An all-optical technique for a binary-to-quaternary encoder and a quaternary-to-binary decoder,” J. Opt. A 11, 075501(2009), .
    [CrossRef]
  24. T. Houbavlis and K. E. Zoiros, “Numerical simulation of semiconductor optical amplifier assisted Sagnac gate and investigation of its switching characteristics,” Opt. Eng. 43, 1622-1627 (2004).
  25. K. E. Zoiros, R. Chasioti, C. S. Koukourlis, and T. Houbavlis, “On the output characteristics of a semiconductor optical amplifier driven by an ultrafast optical time division multiplexing pulse train,” Optik (Jena) 118, 134-146 (2007).
    [CrossRef]
  26. K. E. Zoiros, T. Houbavlis, and M. Kalyvas, “Ultra-high speed all-optical shift registers and their applications in OTDM networks,” Opt. Quantum Electron. 36 (11), 1005-1053 (2004).
    [CrossRef]
  27. K. E. Zoiros, G. Papadopopoulos, T. Houbavlis, and G. T. Kanellos, “Theoretical analysis and performance investigation of ultrafast all-optical Boolean xor gate with semiconductor optical amplifier-assisted Sagnac interferometer,” Opt. Commun. 258, 114-134 (2006).
    [CrossRef]
  28. W. Li, M. Zhang, and P. Ye, “Simulation of an all-optical xor gate with a semiconductor optical amplifier Mach-Zehnder interferometer sped up by a continuous-wave assistant light,” J. Opt. Networking 4, 524-530 (2005).
  29. G. P. Agrawal, Applications of Nonlinear Fibre Optics (Academic , India [an imprint of Elsevier, 2001]).
  30. A. Mecozzi and M. Shtaif, “The statistics of polarization dependent loss in optical communication systems,” IEEE Photon. Technol. Lett. 14, 313-315 (2002).
  31. S. Yamashita and K. Hotate, “Polarization-independent depolarizers for highly coherent light using Faraday rotator mirrors,” J. Lightwave Technol. 15, 900-905 (1997).
    [CrossRef]
  32. L. E. Nelson, T. N. Nielson, and H. Kogelnik, “Observation of PMD-induced coherent crosstalk in polarization-multiplexed transmission,” IEEE Photon. Techol. Lett. 13, 738-740 (2001).
  33. J. M. Tang and K. A. Shore, “Strong picosecond optical pulse propagating in semiconductor optical amplifiers at transparency,” IEEE J. Quantum Electron. 34, 1263-1269 (1998).
    [CrossRef]
  34. T. Houbavlis and K. E. Zoiros, “SOA-assisted Sagnac switch and investigation of its roadmap from 10 to 40 GHz,” Opt. Quantum Electron. 35, 1175-1203 (2003).
    [CrossRef]
  35. T. Houbavlis and K. E. Zoiros, “Ultrafast pattern-operated all-optical Boolean xor with semiconductor optical amplifier-assisted Sagnac switch,” Opt. Eng. 42, 3415-3416 (2003).
  36. S. M. Reddy, “Easily testable realization for logic functions,” IEEE Trans. Comput. C-21, 1183-1188 (1972).
    [CrossRef]

2009 (1)

T. Chattopadhyay and J. N. Roy, “All-optical conversion scheme: binary to quaternary and quaternary to binary number,” Opt. Laser Technol. 41, 289-294 (2009).

2008 (4)

Y. J. Jung, S. Lee, and N. Park, “All-optical 4-bit gray code to binary coded decimal converter,” Proc. of SPIE 6890, 68900S (2008).
[CrossRef]

D. K. Gayen and J. N. Roy, “All-optical arithmetic unit with the help of terahertz optical asymmetric demultiplexer-based tree architecture,” Appl. Opt. 47, 933-943 (2008).
[CrossRef]

Z. Y. Shen and L. L. Wu, “Reconfigurable optical logic unit with a terahertz optical asymmetric demultiplexer and electro-optic switches,” Appl. Opt. 47, 3737-3742 (2008).
[CrossRef]

J. N. Roy, G. K. Maity, D. K. Gayen, and T. Chattopadhyay, “Terahertz optical asymmetric demultiplexer based tree-net architecture for all-optical conversion scheme from binary to its other 2n radix based form,” Chin. Opt. Lett. 6, 536-540(2008).

2007 (2)

J. N. Roy and D. K. Gayen, “Integrated all-optical logic and arithmetic operations with the help of a TOAD-based interferometer device--alternative approach,” Appl. Opt. 46, 5304-5310 (2007).
[CrossRef]

K. E. Zoiros, R. Chasioti, C. S. Koukourlis, and T. Houbavlis, “On the output characteristics of a semiconductor optical amplifier driven by an ultrafast optical time division multiplexing pulse train,” Optik (Jena) 118, 134-146 (2007).
[CrossRef]

2006 (2)

K. E. Zoiros, G. Papadopopoulos, T. Houbavlis, and G. T. Kanellos, “Theoretical analysis and performance investigation of ultrafast all-optical Boolean xor gate with semiconductor optical amplifier-assisted Sagnac interferometer,” Opt. Commun. 258, 114-134 (2006).
[CrossRef]

Y. K. Huang, I. Glesk, R. Shankar, and P. R. Prucnal, “Simultaneous all-optical 3R regeneration scheme with improved scalability using TOAD,” Opt. Express 14, 10339-10344 (2006).
[CrossRef]

2005 (4)

W. Li, M. Zhang, and P. Ye, “Simulation of an all-optical xor gate with a semiconductor optical amplifier Mach-Zehnder interferometer sped up by a continuous-wave assistant light,” J. Opt. Networking 4, 524-530 (2005).

T. Yang, C. Shu, and C. Lin, “Depolarization technique for wavelength conversion using four-wave mixing in a dispersion-flattened photonic crystal fiber,” Opt. Express 13, 5409-5415 (2005).

J. Yi, H. He, and Y. Lu, “Ternary optical computer architecture,” Phys. Scr. T118, 98-101 (2005).

C. S. Vikram and H. J. Caulfield, “Position-sensing detector for logical operations using incoherent light,” Opt. Eng. 44, 115201 (2005).

2004 (2)

T. Houbavlis and K. E. Zoiros, “Numerical simulation of semiconductor optical amplifier assisted Sagnac gate and investigation of its switching characteristics,” Opt. Eng. 43, 1622-1627 (2004).

K. E. Zoiros, T. Houbavlis, and M. Kalyvas, “Ultra-high speed all-optical shift registers and their applications in OTDM networks,” Opt. Quantum Electron. 36 (11), 1005-1053 (2004).
[CrossRef]

2003 (2)

T. Houbavlis and K. E. Zoiros, “SOA-assisted Sagnac switch and investigation of its roadmap from 10 to 40 GHz,” Opt. Quantum Electron. 35, 1175-1203 (2003).
[CrossRef]

T. Houbavlis and K. E. Zoiros, “Ultrafast pattern-operated all-optical Boolean xor with semiconductor optical amplifier-assisted Sagnac switch,” Opt. Eng. 42, 3415-3416 (2003).

2002 (2)

A. Mecozzi and M. Shtaif, “The statistics of polarization dependent loss in optical communication systems,” IEEE Photon. Technol. Lett. 14, 313-315 (2002).

B. C. Wang, V. Baby, W. Tong, L. Xu, M. Friedman, R. J. Runser, I. Glesk, and P. R. Prucnal, “A novel fast optical switch based on two cascaded terahertz optical asymmetric demultiplexers (TOAD),” Opt. Express 10, 15-23 (2002).

2001 (1)

L. E. Nelson, T. N. Nielson, and H. Kogelnik, “Observation of PMD-induced coherent crosstalk in polarization-multiplexed transmission,” IEEE Photon. Techol. Lett. 13, 738-740 (2001).

1998 (1)

J. M. Tang and K. A. Shore, “Strong picosecond optical pulse propagating in semiconductor optical amplifiers at transparency,” IEEE J. Quantum Electron. 34, 1263-1269 (1998).
[CrossRef]

1997 (1)

S. Yamashita and K. Hotate, “Polarization-independent depolarizers for highly coherent light using Faraday rotator mirrors,” J. Lightwave Technol. 15, 900-905 (1997).
[CrossRef]

1995 (1)

M. Eiselt, W. Pieper, and H. G. Weber, “SLALOM: semiconductor laser amplifier in a loop mirror,” J. Lightwave Technol. 13, 2099-2112 (1995).
[CrossRef]

1993 (1)

J. P. Sokoloff, P. R. Prucnal, I. Glesk, and M. Kane, “A terahertz optical asymmetric demultiplexer (TOAD),” IEEE Photon. Technol. Lett. 5, 787-790 (1993).

1989 (1)

1987 (1)

1986 (1)

Y. Yasuda, Y. Tokuda, S. Zaima, K. Pak, T. Nakamura, and A. Yoshida, “Realization of quaternary logic circuits by n-channel MOS devices,” IEEE J. Solid-State Circuits SSC-21, 162-168(1986)
[CrossRef]

1984 (1)

K. C. Smith, “The prospects for multivalued logic: a technology and applications view,” IEEE Trans. Comput. C-30, 1160-1179 (1984).

1972 (1)

S. M. Reddy, “Easily testable realization for logic functions,” IEEE Trans. Comput. C-21, 1183-1188 (1972).
[CrossRef]

Wu, L. L.

Agrawal, G. P.

G. P. Agrawal, Applications of Nonlinear Fibre Optics (Academic , India [an imprint of Elsevier, 2001]).

Awwal, A. A. S.

Baby, V.

Caulfield, H. J.

C. S. Vikram and H. J. Caulfield, “Position-sensing detector for logical operations using incoherent light,” Opt. Eng. 44, 115201 (2005).

Chasioti, R.

K. E. Zoiros, R. Chasioti, C. S. Koukourlis, and T. Houbavlis, “On the output characteristics of a semiconductor optical amplifier driven by an ultrafast optical time division multiplexing pulse train,” Optik (Jena) 118, 134-146 (2007).
[CrossRef]

Chattopadhyay, T.

T. Chattopadhyay and J. N. Roy, “All-optical conversion scheme: binary to quaternary and quaternary to binary number,” Opt. Laser Technol. 41, 289-294 (2009).

J. N. Roy, G. K. Maity, D. K. Gayen, and T. Chattopadhyay, “Terahertz optical asymmetric demultiplexer based tree-net architecture for all-optical conversion scheme from binary to its other 2n radix based form,” Chin. Opt. Lett. 6, 536-540(2008).

T. Chattopadhyay and J. N. Roy, “Polarization encoded TOAD based all-optical quaternary Literals,” Optik (Jena) [doi: 10.1016/j.ijleo.2008.09.014]
[CrossRef]

T. Chattopadhyay and J. N. Roy, “Polarization encoded all-optical quaternary multiplexer and demultiplexer -a proposal,” Optik (Jena) , doi:10.1016/j.ijleo.2008.03.030 [In press].
[CrossRef]

T. Chattopadhyay and J. N. Roy, “An all-optical technique for a binary-to-quaternary encoder and a quaternary-to-binary decoder,” J. Opt. A 11, 075501(2009), .
[CrossRef]

Cherri, A. K.

Eiselt, M.

M. Eiselt, W. Pieper, and H. G. Weber, “SLALOM: semiconductor laser amplifier in a loop mirror,” J. Lightwave Technol. 13, 2099-2112 (1995).
[CrossRef]

Friedman, M.

Gayen, D. K.

Glesk, I.

He, H.

J. Yi, H. He, and Y. Lu, “Ternary optical computer architecture,” Phys. Scr. T118, 98-101 (2005).

Hotate, K.

S. Yamashita and K. Hotate, “Polarization-independent depolarizers for highly coherent light using Faraday rotator mirrors,” J. Lightwave Technol. 15, 900-905 (1997).
[CrossRef]

Houbavlis, T.

K. E. Zoiros, R. Chasioti, C. S. Koukourlis, and T. Houbavlis, “On the output characteristics of a semiconductor optical amplifier driven by an ultrafast optical time division multiplexing pulse train,” Optik (Jena) 118, 134-146 (2007).
[CrossRef]

K. E. Zoiros, G. Papadopopoulos, T. Houbavlis, and G. T. Kanellos, “Theoretical analysis and performance investigation of ultrafast all-optical Boolean xor gate with semiconductor optical amplifier-assisted Sagnac interferometer,” Opt. Commun. 258, 114-134 (2006).
[CrossRef]

K. E. Zoiros, T. Houbavlis, and M. Kalyvas, “Ultra-high speed all-optical shift registers and their applications in OTDM networks,” Opt. Quantum Electron. 36 (11), 1005-1053 (2004).
[CrossRef]

T. Houbavlis and K. E. Zoiros, “Numerical simulation of semiconductor optical amplifier assisted Sagnac gate and investigation of its switching characteristics,” Opt. Eng. 43, 1622-1627 (2004).

T. Houbavlis and K. E. Zoiros, “SOA-assisted Sagnac switch and investigation of its roadmap from 10 to 40 GHz,” Opt. Quantum Electron. 35, 1175-1203 (2003).
[CrossRef]

T. Houbavlis and K. E. Zoiros, “Ultrafast pattern-operated all-optical Boolean xor with semiconductor optical amplifier-assisted Sagnac switch,” Opt. Eng. 42, 3415-3416 (2003).

Huang, Y. K.

Jung, Y. J.

Y. J. Jung, S. Lee, and N. Park, “All-optical 4-bit gray code to binary coded decimal converter,” Proc. of SPIE 6890, 68900S (2008).
[CrossRef]

Kalyvas, M.

K. E. Zoiros, T. Houbavlis, and M. Kalyvas, “Ultra-high speed all-optical shift registers and their applications in OTDM networks,” Opt. Quantum Electron. 36 (11), 1005-1053 (2004).
[CrossRef]

Kane, M.

J. P. Sokoloff, P. R. Prucnal, I. Glesk, and M. Kane, “A terahertz optical asymmetric demultiplexer (TOAD),” IEEE Photon. Technol. Lett. 5, 787-790 (1993).

Kanellos, G. T.

K. E. Zoiros, G. Papadopopoulos, T. Houbavlis, and G. T. Kanellos, “Theoretical analysis and performance investigation of ultrafast all-optical Boolean xor gate with semiconductor optical amplifier-assisted Sagnac interferometer,” Opt. Commun. 258, 114-134 (2006).
[CrossRef]

Karim, M. A.

Khader, N. A.

N. A. Khader and P. Siy, “Inversion/division in Galois field using multiple-valued logic,” in Proceedings of the International Symposia on Multiple-Valued Logic (IEEE Computer Society, 2007)

Khan, M. H. A.

M. H. A. Khan and M. A. Perkowski, “GF(4) based synthesis of quaternary reversible/ quantum logic circuits,” in Proceedings of the International Symposia on Multiple-Valued Logic (IEEE Computer Society, 2007).

M. H. A. Khan, N. K. Siddika, and M. A. Perkowski, “Minimization of quaternary Galois field sum of products expression for multi-output quaternary logic function using quaternary Galois field decision diagram,” in Proceedings of the International Symposia on Multiple-Valued Logic (IEEE Computer Society, 2008), pp. 125-130.
[CrossRef]

Kogelnik, H.

L. E. Nelson, T. N. Nielson, and H. Kogelnik, “Observation of PMD-induced coherent crosstalk in polarization-multiplexed transmission,” IEEE Photon. Techol. Lett. 13, 738-740 (2001).

Koukourlis, C. S.

K. E. Zoiros, R. Chasioti, C. S. Koukourlis, and T. Houbavlis, “On the output characteristics of a semiconductor optical amplifier driven by an ultrafast optical time division multiplexing pulse train,” Optik (Jena) 118, 134-146 (2007).
[CrossRef]

Lee, S.

Y. J. Jung, S. Lee, and N. Park, “All-optical 4-bit gray code to binary coded decimal converter,” Proc. of SPIE 6890, 68900S (2008).
[CrossRef]

Li, C.

Li, W.

W. Li, M. Zhang, and P. Ye, “Simulation of an all-optical xor gate with a semiconductor optical amplifier Mach-Zehnder interferometer sped up by a continuous-wave assistant light,” J. Opt. Networking 4, 524-530 (2005).

Lin, C.

T. Yang, C. Shu, and C. Lin, “Depolarization technique for wavelength conversion using four-wave mixing in a dispersion-flattened photonic crystal fiber,” Opt. Express 13, 5409-5415 (2005).

Lin, Y.

Liu, S.

Lu, Y.

J. Yi, H. He, and Y. Lu, “Ternary optical computer architecture,” Phys. Scr. T118, 98-101 (2005).

Maity, G. K.

Mecozzi, A.

A. Mecozzi and M. Shtaif, “The statistics of polarization dependent loss in optical communication systems,” IEEE Photon. Technol. Lett. 14, 313-315 (2002).

Nakamura, T.

Y. Yasuda, Y. Tokuda, S. Zaima, K. Pak, T. Nakamura, and A. Yoshida, “Realization of quaternary logic circuits by n-channel MOS devices,” IEEE J. Solid-State Circuits SSC-21, 162-168(1986)
[CrossRef]

Nelson, L. E.

L. E. Nelson, T. N. Nielson, and H. Kogelnik, “Observation of PMD-induced coherent crosstalk in polarization-multiplexed transmission,” IEEE Photon. Techol. Lett. 13, 738-740 (2001).

Nielson, T. N.

L. E. Nelson, T. N. Nielson, and H. Kogelnik, “Observation of PMD-induced coherent crosstalk in polarization-multiplexed transmission,” IEEE Photon. Techol. Lett. 13, 738-740 (2001).

Pak, K.

Y. Yasuda, Y. Tokuda, S. Zaima, K. Pak, T. Nakamura, and A. Yoshida, “Realization of quaternary logic circuits by n-channel MOS devices,” IEEE J. Solid-State Circuits SSC-21, 162-168(1986)
[CrossRef]

Papadopopoulos, G.

K. E. Zoiros, G. Papadopopoulos, T. Houbavlis, and G. T. Kanellos, “Theoretical analysis and performance investigation of ultrafast all-optical Boolean xor gate with semiconductor optical amplifier-assisted Sagnac interferometer,” Opt. Commun. 258, 114-134 (2006).
[CrossRef]

Park, N.

Y. J. Jung, S. Lee, and N. Park, “All-optical 4-bit gray code to binary coded decimal converter,” Proc. of SPIE 6890, 68900S (2008).
[CrossRef]

Perkowski, M. A.

M. H. A. Khan, N. K. Siddika, and M. A. Perkowski, “Minimization of quaternary Galois field sum of products expression for multi-output quaternary logic function using quaternary Galois field decision diagram,” in Proceedings of the International Symposia on Multiple-Valued Logic (IEEE Computer Society, 2008), pp. 125-130.
[CrossRef]

M. H. A. Khan and M. A. Perkowski, “GF(4) based synthesis of quaternary reversible/ quantum logic circuits,” in Proceedings of the International Symposia on Multiple-Valued Logic (IEEE Computer Society, 2007).

Pieper, W.

M. Eiselt, W. Pieper, and H. G. Weber, “SLALOM: semiconductor laser amplifier in a loop mirror,” J. Lightwave Technol. 13, 2099-2112 (1995).
[CrossRef]

Prucnal, P. R.

Reddy, S. M.

S. M. Reddy, “Easily testable realization for logic functions,” IEEE Trans. Comput. C-21, 1183-1188 (1972).
[CrossRef]

Roy, J. N.

T. Chattopadhyay and J. N. Roy, “All-optical conversion scheme: binary to quaternary and quaternary to binary number,” Opt. Laser Technol. 41, 289-294 (2009).

J. N. Roy, G. K. Maity, D. K. Gayen, and T. Chattopadhyay, “Terahertz optical asymmetric demultiplexer based tree-net architecture for all-optical conversion scheme from binary to its other 2n radix based form,” Chin. Opt. Lett. 6, 536-540(2008).

D. K. Gayen and J. N. Roy, “All-optical arithmetic unit with the help of terahertz optical asymmetric demultiplexer-based tree architecture,” Appl. Opt. 47, 933-943 (2008).
[CrossRef]

J. N. Roy and D. K. Gayen, “Integrated all-optical logic and arithmetic operations with the help of a TOAD-based interferometer device--alternative approach,” Appl. Opt. 46, 5304-5310 (2007).
[CrossRef]

T. Chattopadhyay and J. N. Roy, “Polarization encoded TOAD based all-optical quaternary Literals,” Optik (Jena) [doi: 10.1016/j.ijleo.2008.09.014]
[CrossRef]

T. Chattopadhyay and J. N. Roy, “Polarization encoded all-optical quaternary multiplexer and demultiplexer -a proposal,” Optik (Jena) , doi:10.1016/j.ijleo.2008.03.030 [In press].
[CrossRef]

T. Chattopadhyay and J. N. Roy, “An all-optical technique for a binary-to-quaternary encoder and a quaternary-to-binary decoder,” J. Opt. A 11, 075501(2009), .
[CrossRef]

Runser, R. J.

Shankar, R.

Shen, Z. Y.

Shore, K. A.

J. M. Tang and K. A. Shore, “Strong picosecond optical pulse propagating in semiconductor optical amplifiers at transparency,” IEEE J. Quantum Electron. 34, 1263-1269 (1998).
[CrossRef]

Shtaif, M.

A. Mecozzi and M. Shtaif, “The statistics of polarization dependent loss in optical communication systems,” IEEE Photon. Technol. Lett. 14, 313-315 (2002).

Shu, C.

T. Yang, C. Shu, and C. Lin, “Depolarization technique for wavelength conversion using four-wave mixing in a dispersion-flattened photonic crystal fiber,” Opt. Express 13, 5409-5415 (2005).

Siddika, N. K.

M. H. A. Khan, N. K. Siddika, and M. A. Perkowski, “Minimization of quaternary Galois field sum of products expression for multi-output quaternary logic function using quaternary Galois field decision diagram,” in Proceedings of the International Symposia on Multiple-Valued Logic (IEEE Computer Society, 2008), pp. 125-130.
[CrossRef]

Siy, P.

N. A. Khader and P. Siy, “Inversion/division in Galois field using multiple-valued logic,” in Proceedings of the International Symposia on Multiple-Valued Logic (IEEE Computer Society, 2007)

Smith, K. C.

K. C. Smith, “The prospects for multivalued logic: a technology and applications view,” IEEE Trans. Comput. C-30, 1160-1179 (1984).

Sokoloff, J. P.

J. P. Sokoloff, P. R. Prucnal, I. Glesk, and M. Kane, “A terahertz optical asymmetric demultiplexer (TOAD),” IEEE Photon. Technol. Lett. 5, 787-790 (1993).

Tang, J. M.

J. M. Tang and K. A. Shore, “Strong picosecond optical pulse propagating in semiconductor optical amplifiers at transparency,” IEEE J. Quantum Electron. 34, 1263-1269 (1998).
[CrossRef]

Tokuda, Y.

Y. Yasuda, Y. Tokuda, S. Zaima, K. Pak, T. Nakamura, and A. Yoshida, “Realization of quaternary logic circuits by n-channel MOS devices,” IEEE J. Solid-State Circuits SSC-21, 162-168(1986)
[CrossRef]

Tong, W.

Vikram, C. S.

C. S. Vikram and H. J. Caulfield, “Position-sensing detector for logical operations using incoherent light,” Opt. Eng. 44, 115201 (2005).

Wang, B. C.

Weber, H. G.

M. Eiselt, W. Pieper, and H. G. Weber, “SLALOM: semiconductor laser amplifier in a loop mirror,” J. Lightwave Technol. 13, 2099-2112 (1995).
[CrossRef]

Wu, J.

Xu, L.

Yamashita, S.

S. Yamashita and K. Hotate, “Polarization-independent depolarizers for highly coherent light using Faraday rotator mirrors,” J. Lightwave Technol. 15, 900-905 (1997).
[CrossRef]

Yang, T.

T. Yang, C. Shu, and C. Lin, “Depolarization technique for wavelength conversion using four-wave mixing in a dispersion-flattened photonic crystal fiber,” Opt. Express 13, 5409-5415 (2005).

Yasuda, Y.

Y. Yasuda, Y. Tokuda, S. Zaima, K. Pak, T. Nakamura, and A. Yoshida, “Realization of quaternary logic circuits by n-channel MOS devices,” IEEE J. Solid-State Circuits SSC-21, 162-168(1986)
[CrossRef]

Ye, P.

W. Li, M. Zhang, and P. Ye, “Simulation of an all-optical xor gate with a semiconductor optical amplifier Mach-Zehnder interferometer sped up by a continuous-wave assistant light,” J. Opt. Networking 4, 524-530 (2005).

Yi, J.

J. Yi, H. He, and Y. Lu, “Ternary optical computer architecture,” Phys. Scr. T118, 98-101 (2005).

Yoshida, A.

Y. Yasuda, Y. Tokuda, S. Zaima, K. Pak, T. Nakamura, and A. Yoshida, “Realization of quaternary logic circuits by n-channel MOS devices,” IEEE J. Solid-State Circuits SSC-21, 162-168(1986)
[CrossRef]

Zaima, S.

Y. Yasuda, Y. Tokuda, S. Zaima, K. Pak, T. Nakamura, and A. Yoshida, “Realization of quaternary logic circuits by n-channel MOS devices,” IEEE J. Solid-State Circuits SSC-21, 162-168(1986)
[CrossRef]

Zhang, M.

W. Li, M. Zhang, and P. Ye, “Simulation of an all-optical xor gate with a semiconductor optical amplifier Mach-Zehnder interferometer sped up by a continuous-wave assistant light,” J. Opt. Networking 4, 524-530 (2005).

Zoiros, K. E.

K. E. Zoiros, R. Chasioti, C. S. Koukourlis, and T. Houbavlis, “On the output characteristics of a semiconductor optical amplifier driven by an ultrafast optical time division multiplexing pulse train,” Optik (Jena) 118, 134-146 (2007).
[CrossRef]

K. E. Zoiros, G. Papadopopoulos, T. Houbavlis, and G. T. Kanellos, “Theoretical analysis and performance investigation of ultrafast all-optical Boolean xor gate with semiconductor optical amplifier-assisted Sagnac interferometer,” Opt. Commun. 258, 114-134 (2006).
[CrossRef]

K. E. Zoiros, T. Houbavlis, and M. Kalyvas, “Ultra-high speed all-optical shift registers and their applications in OTDM networks,” Opt. Quantum Electron. 36 (11), 1005-1053 (2004).
[CrossRef]

T. Houbavlis and K. E. Zoiros, “Numerical simulation of semiconductor optical amplifier assisted Sagnac gate and investigation of its switching characteristics,” Opt. Eng. 43, 1622-1627 (2004).

T. Houbavlis and K. E. Zoiros, “SOA-assisted Sagnac switch and investigation of its roadmap from 10 to 40 GHz,” Opt. Quantum Electron. 35, 1175-1203 (2003).
[CrossRef]

T. Houbavlis and K. E. Zoiros, “Ultrafast pattern-operated all-optical Boolean xor with semiconductor optical amplifier-assisted Sagnac switch,” Opt. Eng. 42, 3415-3416 (2003).

Appl. Opt. (1)

D. K. Gayen and J. N. Roy, “All-optical arithmetic unit with the help of terahertz optical asymmetric demultiplexer-based tree architecture,” Appl. Opt. 47, 933-943 (2008).
[CrossRef]

Appl. Opt. (3)

Chin. Opt. Lett. (1)

IEEE J. Quantum Electron. (1)

J. M. Tang and K. A. Shore, “Strong picosecond optical pulse propagating in semiconductor optical amplifiers at transparency,” IEEE J. Quantum Electron. 34, 1263-1269 (1998).
[CrossRef]

IEEE J. Solid-State Circuits (1)

Y. Yasuda, Y. Tokuda, S. Zaima, K. Pak, T. Nakamura, and A. Yoshida, “Realization of quaternary logic circuits by n-channel MOS devices,” IEEE J. Solid-State Circuits SSC-21, 162-168(1986)
[CrossRef]

IEEE Photon. Technol. Lett. (2)

J. P. Sokoloff, P. R. Prucnal, I. Glesk, and M. Kane, “A terahertz optical asymmetric demultiplexer (TOAD),” IEEE Photon. Technol. Lett. 5, 787-790 (1993).

A. Mecozzi and M. Shtaif, “The statistics of polarization dependent loss in optical communication systems,” IEEE Photon. Technol. Lett. 14, 313-315 (2002).

IEEE Photon. Techol. Lett. (1)

L. E. Nelson, T. N. Nielson, and H. Kogelnik, “Observation of PMD-induced coherent crosstalk in polarization-multiplexed transmission,” IEEE Photon. Techol. Lett. 13, 738-740 (2001).

IEEE Trans. Comput. (2)

S. M. Reddy, “Easily testable realization for logic functions,” IEEE Trans. Comput. C-21, 1183-1188 (1972).
[CrossRef]

K. C. Smith, “The prospects for multivalued logic: a technology and applications view,” IEEE Trans. Comput. C-30, 1160-1179 (1984).

J. Lightwave Technol. (2)

S. Yamashita and K. Hotate, “Polarization-independent depolarizers for highly coherent light using Faraday rotator mirrors,” J. Lightwave Technol. 15, 900-905 (1997).
[CrossRef]

M. Eiselt, W. Pieper, and H. G. Weber, “SLALOM: semiconductor laser amplifier in a loop mirror,” J. Lightwave Technol. 13, 2099-2112 (1995).
[CrossRef]

J. Opt. A (1)

T. Chattopadhyay and J. N. Roy, “An all-optical technique for a binary-to-quaternary encoder and a quaternary-to-binary decoder,” J. Opt. A 11, 075501(2009), .
[CrossRef]

J. Opt. Networking (1)

W. Li, M. Zhang, and P. Ye, “Simulation of an all-optical xor gate with a semiconductor optical amplifier Mach-Zehnder interferometer sped up by a continuous-wave assistant light,” J. Opt. Networking 4, 524-530 (2005).

Opt. Commun. (1)

K. E. Zoiros, G. Papadopopoulos, T. Houbavlis, and G. T. Kanellos, “Theoretical analysis and performance investigation of ultrafast all-optical Boolean xor gate with semiconductor optical amplifier-assisted Sagnac interferometer,” Opt. Commun. 258, 114-134 (2006).
[CrossRef]

Opt. Eng. (3)

T. Houbavlis and K. E. Zoiros, “Ultrafast pattern-operated all-optical Boolean xor with semiconductor optical amplifier-assisted Sagnac switch,” Opt. Eng. 42, 3415-3416 (2003).

T. Houbavlis and K. E. Zoiros, “Numerical simulation of semiconductor optical amplifier assisted Sagnac gate and investigation of its switching characteristics,” Opt. Eng. 43, 1622-1627 (2004).

C. S. Vikram and H. J. Caulfield, “Position-sensing detector for logical operations using incoherent light,” Opt. Eng. 44, 115201 (2005).

Opt. Express (2)

Opt. Laser Technol. (1)

T. Chattopadhyay and J. N. Roy, “All-optical conversion scheme: binary to quaternary and quaternary to binary number,” Opt. Laser Technol. 41, 289-294 (2009).

Opt. Lett. (1)

Opt. Quantum Electron. (2)

T. Houbavlis and K. E. Zoiros, “SOA-assisted Sagnac switch and investigation of its roadmap from 10 to 40 GHz,” Opt. Quantum Electron. 35, 1175-1203 (2003).
[CrossRef]

K. E. Zoiros, T. Houbavlis, and M. Kalyvas, “Ultra-high speed all-optical shift registers and their applications in OTDM networks,” Opt. Quantum Electron. 36 (11), 1005-1053 (2004).
[CrossRef]

Optik (Jena) (3)

K. E. Zoiros, R. Chasioti, C. S. Koukourlis, and T. Houbavlis, “On the output characteristics of a semiconductor optical amplifier driven by an ultrafast optical time division multiplexing pulse train,” Optik (Jena) 118, 134-146 (2007).
[CrossRef]

T. Chattopadhyay and J. N. Roy, “Polarization encoded TOAD based all-optical quaternary Literals,” Optik (Jena) [doi: 10.1016/j.ijleo.2008.09.014]
[CrossRef]

T. Chattopadhyay and J. N. Roy, “Polarization encoded all-optical quaternary multiplexer and demultiplexer -a proposal,” Optik (Jena) , doi:10.1016/j.ijleo.2008.03.030 [In press].
[CrossRef]

Phys. Scr. (1)

J. Yi, H. He, and Y. Lu, “Ternary optical computer architecture,” Phys. Scr. T118, 98-101 (2005).

Proc. of SPIE (1)

Y. J. Jung, S. Lee, and N. Park, “All-optical 4-bit gray code to binary coded decimal converter,” Proc. of SPIE 6890, 68900S (2008).
[CrossRef]

Other (5)

G. P. Agrawal, Applications of Nonlinear Fibre Optics (Academic , India [an imprint of Elsevier, 2001]).

T. Yang, C. Shu, and C. Lin, “Depolarization technique for wavelength conversion using four-wave mixing in a dispersion-flattened photonic crystal fiber,” Opt. Express 13, 5409-5415 (2005).

M. H. A. Khan and M. A. Perkowski, “GF(4) based synthesis of quaternary reversible/ quantum logic circuits,” in Proceedings of the International Symposia on Multiple-Valued Logic (IEEE Computer Society, 2007).

N. A. Khader and P. Siy, “Inversion/division in Galois field using multiple-valued logic,” in Proceedings of the International Symposia on Multiple-Valued Logic (IEEE Computer Society, 2007)

M. H. A. Khan, N. K. Siddika, and M. A. Perkowski, “Minimization of quaternary Galois field sum of products expression for multi-output quaternary logic function using quaternary Galois field decision diagram,” in Proceedings of the International Symposia on Multiple-Valued Logic (IEEE Computer Society, 2008), pp. 125-130.
[CrossRef]

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 (12)

Fig. 1
Fig. 1

TOAD-based optical switch.

Fig. 2
Fig. 2

All-optical circuit for binary xor with the TOAD optical tree. BS, beam splitter; HPLS, horizontally polarized pulsed light source; M, position of HPLS; ( N , O , P ) are the nodes of the tree, where the TOAD switches are placed.

Fig. 3
Fig. 3

All-optical GF (4) adder circuit: ▹: EDFA, BC, beam combiner; PC, polarization controller; bxor, binary xor gate.

Fig. 4
Fig. 4

Simulated waveform for input (X and Y) and output (O).

Fig. 5
Fig. 5

Gain variation of SOA (in decibels) of TOAD S 1 , S 2 , and S 3 in OTA-1 and OTA-2.

Fig. 6
Fig. 6

Variation of CR with CP energy ( E c ).

Fig. 7
Fig. 7

Variation of CR with eccentricity of loop (T) of the TOAD.

Fig. 8
Fig. 8

Variation of CR with FWHM of CP (σ) in picoseconds.

Fig. 9
Fig. 9

Variation of BER with CP energy ( E c ).

Fig. 10
Fig. 10

All-optical quaternary inverter circuit. \rot270⨹ , all-optical GF(4) adder circuit.

Fig. 11
Fig. 11

All-optical quaternary successor circuit.

Fig. 12
Fig. 12

All-optical quaternary cw cycle and ccw cycle circuit; Suc, quaternary successor circuit.

Tables (4)

Tables Icon

Table 1 Truth Table of the Quaternary Galois Field Addition [ GF ( 4 ) + ]

Tables Icon

Table 2 Different State of Light Present in Different Paths in an All-Optical GF(4) Adder Circuit

Tables Icon

Table 3 Parameters Used in the Simulation

Tables Icon

Table 4 Truth Table of Quaternary Inverter, Successor, Clockwise, and Counterclockwise Cycles

Equations (21)

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

P X , Y ( t ) = n , m [ a | E c p | 2 σ π exp { ( t n ξ ) 2 σ 2 } y ^ + b | E c p | 2 σ π exp { ( t m ξ ) 2 σ 2 } x ^ ] ,
P A 1 = P B 1 = | M λ / 2 ( θ ) · M y · J input | 2 = | E x | 2 , P A 2 = P B 2 = | M x · J input | 2 = | E y | 2 .
[ P port 1 ( t ) ] S 1 = P VPLS ( t ) 4 { G c w ( t ) + G c c w ( t ) 2 G c w ( t ) · G c c w ( t ) cos ( Δ φ ) } ,
[ P port 2 ( t ) ] S 1 = P VPLS ( t ) 4 { G c w ( t ) + G c c w ( t ) + 2 G c w ( t ) · G c c w ( t ) cos ( Δ φ ) } ,
G ( t ) = 1 1 ( 1 1 G 0 ) exp ( E cp ( t ) E sat ) ,
E cp ( t ) = t P cp ( t ) d t
G ( t ) = G 0 [ G ( t s ) G 0 ] exp [ ( t t s ) / τ e ] ; t t s ,
G ( t ) = { 1 ( 1 1 / G l ) exp [ E c p ( t ) / E sat ] } 1 .
E cp ( t ) = E c 2 [ 1 + erf ( t σ ) ] ,
G f = G ( t s ) = G l G l ( G l 1 ) exp ( E c / E sat ) .
G l = G ( ξ ) = G 0 [ G f G 0 ] exp { ( ξ T FWHM ) / τ e } .
G c c w G c w = [ G f G 0 ] { exp [ ( t + T t s ) / τ e ] exp [ ( t t s ) / τ e ] } ,
[ P port 2 ( t ) ] S 2 = [ P port 1 ( t ) ] S 1 4 { G c w ( t ) + G c c w ( t ) + 2 G c w ( t ) G c c w ( t ) cos ( Δ φ ) } ,
[ P port 1 ( t ) ] S 3 = [ P port 2 ( t ) ] S 1 4 { G c w ( t ) + G c c w ( t ) 2 G c w ( t ) G c c w ( t ) cos ( Δ φ ) } .
P O = [ ( P port 2 ( t ) ) S 2 + ( P port 1 ( t ) ) S 3 ] BXOR 1 x ^ + [ ( P port 2 ( t ) ) S 2 + ( P port 1 ( t ) ) S 3 ] BXOR 2 y ^ .
C R ( d B ) = 10 log ( P Min H P Max 0 ) .
Q = P 1 P 0 σ 1 + σ 0 .
BER = 1 2 erfc ( Q 2 ) ,
f ( x 1 , x 2 , , x n ) = c 0 c 1 x ˙ 1 c 2 x ˙ 2 c n x ˙ n c n + 1 x ˙ 1 x ˙ n c 2 n 1 x ˙ 1 x ˙ 2 x ˙ n ,
X ^ b = ( x + b ) mod 4 ,
X ^ b c = ( x b ) mod 4 ,

Metrics