Abstract

We present a complete all-optical-processing polarization-based binary-logic system, by which any logic gate or processor can be implemented. Following the new polarization-based logic presented in [Opt. Express 14, 7253 (2006)], we develop a new parallel processing technique that allows for the creation of all-optical-processing gates that produce a unique output either logic 1 or 0 only once in a truth table, and those that do not. This representation allows for the implementation of simple unforced OR, AND, XOR, XNOR, inverter, and more importantly NAND and NOR gates that can be used independently to represent any Boolean expression or function. In addition, the concept of a generalized gate is presented which opens the door for reconfigurable optical processors and programmable optical logic gates. Furthermore, the new design is completely compatible with the old one presented in [Opt. Express 14, 7253 (2006)], and with current semiconductor based devices. The gates can be cascaded, where the information is always on the laser beam. The polarization of the beam, and not its intensity, carries the information. The new methodology allows for the creation of multiple-input-multiple-output processors that implement, by itself, any Boolean function, such as specialized or non-specialized microprocessors. Three all-optical architectures are presented: orthoparallel optical logic architecture for all known and unknown binary gates, single-branch architecture for only XOR and XNOR gates, and the railroad (RR) architecture for polarization optical processors (POP). All the control inputs are applied simultaneously leading to a single time lag which leads to a very-fast and glitch-immune POP. A simple and easy-to-follow step-by-step algorithm is provided for the POP, and design reduction methodologies are briefly discussed. The algorithm lends itself systematically to software programming and computer-assisted design. As examples, designs of all binary gates, multiple-input gates, and sequential and non-sequential Boolean expressions are presented and discussed. The operation of each design is simply understood by a bullet train traveling at the speed of light on a railroad system preconditioned by the crossover states predetermined by the control inputs. The presented designs allow for optical processing of the information eliminating the need to convert it, back and forth, to an electronic signal for processing purposes. All gates with a truth table, including for example Fredkin, Toffoli, testable reversible logic, and threshold logic gates, can be designed and implemented using the railroad architecture. That includes any future gates not known today. Those designs and the quantum gates are not discussed in this paper. * Patent Pending

©2006 Optical Society of America

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References

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  1. Y. A. Zaghloul and A. R. M. Zaghloul, “Unforced polarization-based optical implementation of binary logic,” Opt. Express 14, 7253–7269 (2006). Patent Pending.
    [Crossref]
  2. M. M. Mano and C. R. Kime, Logic and computer design fundamentals, 2nd ed. (Prentice Hall, New Jersey, 2001).
  3. D. S. Kliger, J. W. Lewis, and C. E. Randall, Polarized light in optics and spectroscopy (Academic, Boston, 1990).
  4. R. M. A. Azzam, A. R. M. Zaghloul, and N. M. Bashara, “Ellipsometric function of a film-substrate system: Applications to the design of reflection-type optical devices and to ellipsometry,” J. Opt. Soc. Am.65, 252–260 (1975). Also in A. R. M. Zaghloul, “Ellipsometric function of a film-substrate system: Applications to the design of reflection-type optical devices and to ellipsometry,” Ph. D. dissertation, University of Nebraska-Lincoln, 1975.
    [Crossref]
  5. A. R. M. Zaghloul, R. M. A. Azzam, and N. M. Bashara, “Design of film-substrate single-reflection retarders,” J. Opt. Soc. Am. 65, 1043–1049 (1975).
    [Crossref]
  6. A. R. M. Zaghloul, R. M. A. Azzam, and N. M. Bashara, “An angle-of-incidence tunable, SiO2-Si (film-substrate) reflection retarder for the UV mercury line λ=2537 Å,” Opt. Commun. 14, 260–262 (1975).
    [Crossref]
  7. A. R. M. Zaghloul, M. Elshazly-Zaghloul, W. A. Berzett, and D. A. Keeling, “Thin film coatings: A transmission ellipsometric function (TEF) approach I. Non-negative transmission systems, polarization devices, coatings, and closed-form design formulae,” Appl. Opt., In Press.
    [PubMed]
  8. A. R. M. Zaghloul and M. Elshazly-Zaghloul, “Transmission polarization devices using an unsupported film/pellicle: Closed-form design formulae,” SPIE Proceedings of the 2006 Defense and Security Symposium, Orlando, Florida, 17–21 April, 2006.
  9. R. M. A. Azzam, “Simultaneous reflection and refraction of light without change of polarization by a single-layer-coated dielectric surface,” Opt. Lett. 10, 107–109 (1985).
    [Crossref] [PubMed]
  10. A. R. M. Zaghloul, D. A. Keeling, W. A. Berzett, and J. S. Mason, “Design of reflection retarders by use of nonnegative film-substrate systems,” J. Opt. Soc. Am. A 22, 1637–1645 (2005).
    [Crossref]
  11. M. A. Karim and A. A. S. Awwal, Optical computing: An introduction (Wiley, New York, 1992).
  12. E. Fredkin and T. Toffoli, “Conservative logic,” Int. J. Theor. Phys. 21, 219–22 (1982).
    [Crossref]
  13. D. P. Vasudevan, P. K. Lala, J. Di, and J. P. Parkerson, “Reversible-logic design with online testability,” IEEE Trans. Instrum. Meas. 55, 406–414 (2006).
    [Crossref]

2006 (2)

Y. A. Zaghloul and A. R. M. Zaghloul, “Unforced polarization-based optical implementation of binary logic,” Opt. Express 14, 7253–7269 (2006). Patent Pending.
[Crossref]

D. P. Vasudevan, P. K. Lala, J. Di, and J. P. Parkerson, “Reversible-logic design with online testability,” IEEE Trans. Instrum. Meas. 55, 406–414 (2006).
[Crossref]

2005 (1)

1985 (1)

1982 (1)

E. Fredkin and T. Toffoli, “Conservative logic,” Int. J. Theor. Phys. 21, 219–22 (1982).
[Crossref]

1975 (2)

A. R. M. Zaghloul, R. M. A. Azzam, and N. M. Bashara, “Design of film-substrate single-reflection retarders,” J. Opt. Soc. Am. 65, 1043–1049 (1975).
[Crossref]

A. R. M. Zaghloul, R. M. A. Azzam, and N. M. Bashara, “An angle-of-incidence tunable, SiO2-Si (film-substrate) reflection retarder for the UV mercury line λ=2537 Å,” Opt. Commun. 14, 260–262 (1975).
[Crossref]

Awwal, A. A. S.

M. A. Karim and A. A. S. Awwal, Optical computing: An introduction (Wiley, New York, 1992).

Azzam, R. M. A.

R. M. A. Azzam, “Simultaneous reflection and refraction of light without change of polarization by a single-layer-coated dielectric surface,” Opt. Lett. 10, 107–109 (1985).
[Crossref] [PubMed]

A. R. M. Zaghloul, R. M. A. Azzam, and N. M. Bashara, “An angle-of-incidence tunable, SiO2-Si (film-substrate) reflection retarder for the UV mercury line λ=2537 Å,” Opt. Commun. 14, 260–262 (1975).
[Crossref]

A. R. M. Zaghloul, R. M. A. Azzam, and N. M. Bashara, “Design of film-substrate single-reflection retarders,” J. Opt. Soc. Am. 65, 1043–1049 (1975).
[Crossref]

R. M. A. Azzam, A. R. M. Zaghloul, and N. M. Bashara, “Ellipsometric function of a film-substrate system: Applications to the design of reflection-type optical devices and to ellipsometry,” J. Opt. Soc. Am.65, 252–260 (1975). Also in A. R. M. Zaghloul, “Ellipsometric function of a film-substrate system: Applications to the design of reflection-type optical devices and to ellipsometry,” Ph. D. dissertation, University of Nebraska-Lincoln, 1975.
[Crossref]

Bashara, N. M.

A. R. M. Zaghloul, R. M. A. Azzam, and N. M. Bashara, “An angle-of-incidence tunable, SiO2-Si (film-substrate) reflection retarder for the UV mercury line λ=2537 Å,” Opt. Commun. 14, 260–262 (1975).
[Crossref]

A. R. M. Zaghloul, R. M. A. Azzam, and N. M. Bashara, “Design of film-substrate single-reflection retarders,” J. Opt. Soc. Am. 65, 1043–1049 (1975).
[Crossref]

R. M. A. Azzam, A. R. M. Zaghloul, and N. M. Bashara, “Ellipsometric function of a film-substrate system: Applications to the design of reflection-type optical devices and to ellipsometry,” J. Opt. Soc. Am.65, 252–260 (1975). Also in A. R. M. Zaghloul, “Ellipsometric function of a film-substrate system: Applications to the design of reflection-type optical devices and to ellipsometry,” Ph. D. dissertation, University of Nebraska-Lincoln, 1975.
[Crossref]

Berzett, W. A.

A. R. M. Zaghloul, D. A. Keeling, W. A. Berzett, and J. S. Mason, “Design of reflection retarders by use of nonnegative film-substrate systems,” J. Opt. Soc. Am. A 22, 1637–1645 (2005).
[Crossref]

A. R. M. Zaghloul, M. Elshazly-Zaghloul, W. A. Berzett, and D. A. Keeling, “Thin film coatings: A transmission ellipsometric function (TEF) approach I. Non-negative transmission systems, polarization devices, coatings, and closed-form design formulae,” Appl. Opt., In Press.
[PubMed]

Di, J.

D. P. Vasudevan, P. K. Lala, J. Di, and J. P. Parkerson, “Reversible-logic design with online testability,” IEEE Trans. Instrum. Meas. 55, 406–414 (2006).
[Crossref]

Elshazly-Zaghloul, M.

A. R. M. Zaghloul and M. Elshazly-Zaghloul, “Transmission polarization devices using an unsupported film/pellicle: Closed-form design formulae,” SPIE Proceedings of the 2006 Defense and Security Symposium, Orlando, Florida, 17–21 April, 2006.

A. R. M. Zaghloul, M. Elshazly-Zaghloul, W. A. Berzett, and D. A. Keeling, “Thin film coatings: A transmission ellipsometric function (TEF) approach I. Non-negative transmission systems, polarization devices, coatings, and closed-form design formulae,” Appl. Opt., In Press.
[PubMed]

Fredkin, E.

E. Fredkin and T. Toffoli, “Conservative logic,” Int. J. Theor. Phys. 21, 219–22 (1982).
[Crossref]

Karim, M. A.

M. A. Karim and A. A. S. Awwal, Optical computing: An introduction (Wiley, New York, 1992).

Keeling, D. A.

A. R. M. Zaghloul, D. A. Keeling, W. A. Berzett, and J. S. Mason, “Design of reflection retarders by use of nonnegative film-substrate systems,” J. Opt. Soc. Am. A 22, 1637–1645 (2005).
[Crossref]

A. R. M. Zaghloul, M. Elshazly-Zaghloul, W. A. Berzett, and D. A. Keeling, “Thin film coatings: A transmission ellipsometric function (TEF) approach I. Non-negative transmission systems, polarization devices, coatings, and closed-form design formulae,” Appl. Opt., In Press.
[PubMed]

Kime, C. R.

M. M. Mano and C. R. Kime, Logic and computer design fundamentals, 2nd ed. (Prentice Hall, New Jersey, 2001).

Kliger, D. S.

D. S. Kliger, J. W. Lewis, and C. E. Randall, Polarized light in optics and spectroscopy (Academic, Boston, 1990).

Lala, P. K.

D. P. Vasudevan, P. K. Lala, J. Di, and J. P. Parkerson, “Reversible-logic design with online testability,” IEEE Trans. Instrum. Meas. 55, 406–414 (2006).
[Crossref]

Lewis, J. W.

D. S. Kliger, J. W. Lewis, and C. E. Randall, Polarized light in optics and spectroscopy (Academic, Boston, 1990).

Mano, M. M.

M. M. Mano and C. R. Kime, Logic and computer design fundamentals, 2nd ed. (Prentice Hall, New Jersey, 2001).

Mason, J. S.

Parkerson, J. P.

D. P. Vasudevan, P. K. Lala, J. Di, and J. P. Parkerson, “Reversible-logic design with online testability,” IEEE Trans. Instrum. Meas. 55, 406–414 (2006).
[Crossref]

Randall, C. E.

D. S. Kliger, J. W. Lewis, and C. E. Randall, Polarized light in optics and spectroscopy (Academic, Boston, 1990).

Toffoli, T.

E. Fredkin and T. Toffoli, “Conservative logic,” Int. J. Theor. Phys. 21, 219–22 (1982).
[Crossref]

Vasudevan, D. P.

D. P. Vasudevan, P. K. Lala, J. Di, and J. P. Parkerson, “Reversible-logic design with online testability,” IEEE Trans. Instrum. Meas. 55, 406–414 (2006).
[Crossref]

Zaghloul, A. R. M.

Y. A. Zaghloul and A. R. M. Zaghloul, “Unforced polarization-based optical implementation of binary logic,” Opt. Express 14, 7253–7269 (2006). Patent Pending.
[Crossref]

A. R. M. Zaghloul, D. A. Keeling, W. A. Berzett, and J. S. Mason, “Design of reflection retarders by use of nonnegative film-substrate systems,” J. Opt. Soc. Am. A 22, 1637–1645 (2005).
[Crossref]

A. R. M. Zaghloul, R. M. A. Azzam, and N. M. Bashara, “An angle-of-incidence tunable, SiO2-Si (film-substrate) reflection retarder for the UV mercury line λ=2537 Å,” Opt. Commun. 14, 260–262 (1975).
[Crossref]

A. R. M. Zaghloul, R. M. A. Azzam, and N. M. Bashara, “Design of film-substrate single-reflection retarders,” J. Opt. Soc. Am. 65, 1043–1049 (1975).
[Crossref]

A. R. M. Zaghloul, M. Elshazly-Zaghloul, W. A. Berzett, and D. A. Keeling, “Thin film coatings: A transmission ellipsometric function (TEF) approach I. Non-negative transmission systems, polarization devices, coatings, and closed-form design formulae,” Appl. Opt., In Press.
[PubMed]

R. M. A. Azzam, A. R. M. Zaghloul, and N. M. Bashara, “Ellipsometric function of a film-substrate system: Applications to the design of reflection-type optical devices and to ellipsometry,” J. Opt. Soc. Am.65, 252–260 (1975). Also in A. R. M. Zaghloul, “Ellipsometric function of a film-substrate system: Applications to the design of reflection-type optical devices and to ellipsometry,” Ph. D. dissertation, University of Nebraska-Lincoln, 1975.
[Crossref]

R. M. A. Azzam, A. R. M. Zaghloul, and N. M. Bashara, “Ellipsometric function of a film-substrate system: Applications to the design of reflection-type optical devices and to ellipsometry,” J. Opt. Soc. Am.65, 252–260 (1975). Also in A. R. M. Zaghloul, “Ellipsometric function of a film-substrate system: Applications to the design of reflection-type optical devices and to ellipsometry,” Ph. D. dissertation, University of Nebraska-Lincoln, 1975.
[Crossref]

A. R. M. Zaghloul and M. Elshazly-Zaghloul, “Transmission polarization devices using an unsupported film/pellicle: Closed-form design formulae,” SPIE Proceedings of the 2006 Defense and Security Symposium, Orlando, Florida, 17–21 April, 2006.

Zaghloul, Y. A.

Y. A. Zaghloul and A. R. M. Zaghloul, “Unforced polarization-based optical implementation of binary logic,” Opt. Express 14, 7253–7269 (2006). Patent Pending.
[Crossref]

IEEE Trans. Instrum. Meas. (1)

D. P. Vasudevan, P. K. Lala, J. Di, and J. P. Parkerson, “Reversible-logic design with online testability,” IEEE Trans. Instrum. Meas. 55, 406–414 (2006).
[Crossref]

Int. J. Theor. Phys. (1)

E. Fredkin and T. Toffoli, “Conservative logic,” Int. J. Theor. Phys. 21, 219–22 (1982).
[Crossref]

J. Opt. Soc. Am. (1)

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

Opt. Commun. (1)

A. R. M. Zaghloul, R. M. A. Azzam, and N. M. Bashara, “An angle-of-incidence tunable, SiO2-Si (film-substrate) reflection retarder for the UV mercury line λ=2537 Å,” Opt. Commun. 14, 260–262 (1975).
[Crossref]

Opt. Express (1)

Y. A. Zaghloul and A. R. M. Zaghloul, “Unforced polarization-based optical implementation of binary logic,” Opt. Express 14, 7253–7269 (2006). Patent Pending.
[Crossref]

Opt. Lett. (1)

Other (6)

M. M. Mano and C. R. Kime, Logic and computer design fundamentals, 2nd ed. (Prentice Hall, New Jersey, 2001).

D. S. Kliger, J. W. Lewis, and C. E. Randall, Polarized light in optics and spectroscopy (Academic, Boston, 1990).

R. M. A. Azzam, A. R. M. Zaghloul, and N. M. Bashara, “Ellipsometric function of a film-substrate system: Applications to the design of reflection-type optical devices and to ellipsometry,” J. Opt. Soc. Am.65, 252–260 (1975). Also in A. R. M. Zaghloul, “Ellipsometric function of a film-substrate system: Applications to the design of reflection-type optical devices and to ellipsometry,” Ph. D. dissertation, University of Nebraska-Lincoln, 1975.
[Crossref]

A. R. M. Zaghloul, M. Elshazly-Zaghloul, W. A. Berzett, and D. A. Keeling, “Thin film coatings: A transmission ellipsometric function (TEF) approach I. Non-negative transmission systems, polarization devices, coatings, and closed-form design formulae,” Appl. Opt., In Press.
[PubMed]

A. R. M. Zaghloul and M. Elshazly-Zaghloul, “Transmission polarization devices using an unsupported film/pellicle: Closed-form design formulae,” SPIE Proceedings of the 2006 Defense and Security Symposium, Orlando, Florida, 17–21 April, 2006.

M. A. Karim and A. A. S. Awwal, Optical computing: An introduction (Wiley, New York, 1992).

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Figures (15)

Fig. 1.
Fig. 1. Orthoparallel Logic OPL architecture of an AND gate., where BS: beam splitter, P: polarizer, 180/0: retarder producing 180°/0 phase shift in the complex ρ plane, LZB: logic zero branch, and LOB: logic one branch. The BS/-45° P/M/+45° P device combination can be replaced by a single properly designed spatial mask or by an appropriate birefringent polarizer. The 180°/0 retarder can be replaced by a 90° polarization rotation electro-optic device such as a liquid crystal. Only one beam leaves the gate by simple steering.

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Fig. 2.
Fig. 2. Same as in Fig. 1, but for a NAND gate.

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Fig. 3.
Fig. 3. Same as in Fig. 1, but for an OR gate.

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Fig. 4.
Fig. 4. Same as in Fig. 1, but for a NOR gate.

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Fig. 5.
Fig. 5. Same as in Fig. 1, but for an XOR gate.

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Fig. 6.
Fig. 6. Same as in fig. 1, but for an XNOR gate.

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Fig. 7.
Fig. 7. Single-branch architecture of an XOR gate.

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Fig. 8.
Fig. 8. Single-branch architecture of an XNOR gate.

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Fig. 9.
Fig. 9. General OPL architecture of an AND gate.

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Fig. 10.
Fig. 10. Railroad-architecture polarization optical processor, RR-architecture POP, design of a three-input AND gate.

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Fig. 11.
Fig. 11. Reduced design of Fig. 10.

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Fig. 12.
Fig. 12. Digital circuit design of the sequential Boolean expression ABC + D.

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Fig. 14.
Fig. 14. Digital circuit design of the non-sequential Boolean expression AB+CD.

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Fig. 13.
Fig. 13. RR-architecture POP design of the sequential Boolean expression ABC+D.

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Fig. 15.
Fig. 15. RR-architecture POP design of the nonsequential Boolean expression AB+CD.

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Tables (12)

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Table 1. AND gate

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Table 2. NAND gate

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Table 3. OR gate

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Table 4. NOR gate

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Table 5. XOR gate

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Table 6. XNOR gate

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Table 7. Collective table of the control retarder (R) for all gates, Figs. 1–6. LZB is the logic zero branch, top branch, LOB is the logic one branch, lower branch, and L0/L1 are the two states of the control R corresponding to the logic zero L0 and logic one L1 states.

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Table 8. Truth table of a three-input AND gate

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Table 9. Extended truth table for the threeinput AND gate

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Table 10. The lower half of the extended truth table of the three-input AND gate, inverting @ B=0

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Table 11. Extended truth table for the sequential Boolean expression ABC+D

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Table 12. Extended truth table for the non-sequential Boolean expression AB+CD

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