Abstract

This paper describes very simple optical logic gates consisting of liquid crystal optical switches. This technique was used to implement all possible 2-operand Boolean functions. The importance of these systems in making optical computers is discussed in terms of a binary half-adder and a flip-flop. A new algebra governing the function of these systems is also proposed.

© 1987 Optical Society of America

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References

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  1. M. T. Fatehi, K. C. Wasmundt, S. A. Collins, “Optical Logic Gates Using Liquid Crystal Light Valve: Implementations and Application Example,” Appl. Opt. 20, 2250 (1981).
    [CrossRef] [PubMed]
  2. M. T. Fatehi, K. C. Wasmundt, S. A. Collins, “Optical Flip-Flops and Sequential Logic Circuits Using a Liquid Crystal Light Valve,” Appl. Opt. 23, 2163 (1984).
    [CrossRef] [PubMed]
  3. B. H. Soffer et al., “Optical Computing with Variable Grating Mode Liquid Crystal Devices,” Proc. Soc. Photo-Opt. Instrum. Eng. 232, 128 (1980).
  4. C. A. Boyer, A. H. Khan, M. R. Murphy, G. A. Solomon, “Liquid Crystal Optical Switch,” in IEEE 1985 Student Papers, 24 (1986).
  5. J. What, S. C. Jain, “Bistable Electro-Optic Switching of a Ferroelectric Liquid Crystal (HOBACPC),” Ferroelectrics (GB) 59, 481 (1984).
  6. J. Markus, Modern Electronic Circuits Reference Manual (McGraw-Hill, New York, 1980).
  7. H. Taub, D. Schilling, Digital Integrated Electronics (McGraw-Hill, New York, 1977).

1986 (1)

C. A. Boyer, A. H. Khan, M. R. Murphy, G. A. Solomon, “Liquid Crystal Optical Switch,” in IEEE 1985 Student Papers, 24 (1986).

1984 (2)

J. What, S. C. Jain, “Bistable Electro-Optic Switching of a Ferroelectric Liquid Crystal (HOBACPC),” Ferroelectrics (GB) 59, 481 (1984).

M. T. Fatehi, K. C. Wasmundt, S. A. Collins, “Optical Flip-Flops and Sequential Logic Circuits Using a Liquid Crystal Light Valve,” Appl. Opt. 23, 2163 (1984).
[CrossRef] [PubMed]

1981 (1)

1980 (1)

B. H. Soffer et al., “Optical Computing with Variable Grating Mode Liquid Crystal Devices,” Proc. Soc. Photo-Opt. Instrum. Eng. 232, 128 (1980).

Boyer, C. A.

C. A. Boyer, A. H. Khan, M. R. Murphy, G. A. Solomon, “Liquid Crystal Optical Switch,” in IEEE 1985 Student Papers, 24 (1986).

Collins, S. A.

Fatehi, M. T.

Jain, S. C.

J. What, S. C. Jain, “Bistable Electro-Optic Switching of a Ferroelectric Liquid Crystal (HOBACPC),” Ferroelectrics (GB) 59, 481 (1984).

Khan, A. H.

C. A. Boyer, A. H. Khan, M. R. Murphy, G. A. Solomon, “Liquid Crystal Optical Switch,” in IEEE 1985 Student Papers, 24 (1986).

Markus, J.

J. Markus, Modern Electronic Circuits Reference Manual (McGraw-Hill, New York, 1980).

Murphy, M. R.

C. A. Boyer, A. H. Khan, M. R. Murphy, G. A. Solomon, “Liquid Crystal Optical Switch,” in IEEE 1985 Student Papers, 24 (1986).

Schilling, D.

H. Taub, D. Schilling, Digital Integrated Electronics (McGraw-Hill, New York, 1977).

Soffer, B. H.

B. H. Soffer et al., “Optical Computing with Variable Grating Mode Liquid Crystal Devices,” Proc. Soc. Photo-Opt. Instrum. Eng. 232, 128 (1980).

Solomon, G. A.

C. A. Boyer, A. H. Khan, M. R. Murphy, G. A. Solomon, “Liquid Crystal Optical Switch,” in IEEE 1985 Student Papers, 24 (1986).

Taub, H.

H. Taub, D. Schilling, Digital Integrated Electronics (McGraw-Hill, New York, 1977).

Wasmundt, K. C.

What, J.

J. What, S. C. Jain, “Bistable Electro-Optic Switching of a Ferroelectric Liquid Crystal (HOBACPC),” Ferroelectrics (GB) 59, 481 (1984).

Appl. Opt. (2)

Ferroelectrics (GB) (1)

J. What, S. C. Jain, “Bistable Electro-Optic Switching of a Ferroelectric Liquid Crystal (HOBACPC),” Ferroelectrics (GB) 59, 481 (1984).

IEEE 1985 Student Papers (1)

C. A. Boyer, A. H. Khan, M. R. Murphy, G. A. Solomon, “Liquid Crystal Optical Switch,” in IEEE 1985 Student Papers, 24 (1986).

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

B. H. Soffer et al., “Optical Computing with Variable Grating Mode Liquid Crystal Devices,” Proc. Soc. Photo-Opt. Instrum. Eng. 232, 128 (1980).

Other (2)

J. Markus, Modern Electronic Circuits Reference Manual (McGraw-Hill, New York, 1980).

H. Taub, D. Schilling, Digital Integrated Electronics (McGraw-Hill, New York, 1977).

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Figures (8)

Fig. 1
Fig. 1

Liquid crystal electrooptic switch.

Fig. 2
Fig. 2

LEG realization of a buffer and an inverter.

Fig. 3
Fig. 3

LEG realization of xnor and xor functions.

Fig. 4
Fig. 4

Rest of the serial LEG configurations.

Fig. 5
Fig. 5

Parallel LEG configurations.

Fig. 6
Fig. 6

LEG realization of a 2-bit full adder.

Fig. 7
Fig. 7

Simplified 2-bit adder.

Fig. 8
Fig. 8

LEG realization of a flip-flop.

Tables (4)

Tables Icon

Table I Functions of Two Independent Binary Variables7

Tables Icon

Table II Truth Table for the 2-Bit Full Adder In Fig. 6

Tables Icon

Table III Truth Table for the Flip-Flop in Fig. 5

Tables Icon

Table IV Angle (·) and Magnitude (+) Operator Truth Table

Equations (8)

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( 1 ) = 1 ,             ( 1 ) = 1 ,             ( 0 ) = 0 .
L ( 0 ) = 1 ,             L ( 1 ) = 1 .
( 1 ) ( λ ) = λ , ( 2 a ) λ · λ = 1 , ( 2 b ) λ + λ = λ , ( 3 a ) λ · λ = 1 , ( 3 b ) λ + λ = 0 , ( 4 a ) 0 · λ = 0 , ( 4 b ) 0 + λ = 0 , ( 5 ) 1 · λ = λ , ( 6 ) 1 · λ = λ , ( 7 ) λ 1 · λ 2 = λ 2 · λ 1 , ( 7 b ) λ 1 + λ 2 = λ 2 + λ 1 , ( 8 a ) λ 1 · ( λ 2 · λ 3 ) = ( λ 1 · λ 2 ) · λ 3 ( 8 b ) λ 1 + ( λ 2 + λ 3 ) = ( λ 1 + λ 2 ) + λ 3 , ( 9 ) λ 1 · ( λ 2 + λ 3 ) = ( λ 1 · λ 2 ) + ( λ 1 · λ 3 )
B ( 1 ) = 1 ,             B ( 1 ) = 1 ,             B ( 0 ) = 0.
[ [ [ 1 · L ( A ) ] + 1 ] · L ( B ) ] + 1 = Z .
[ [ L ( A ) + 1 ] · L ( B ) ] + 1 = Z ( identity # 5 ) , [ [ L ( A ) · L ( B ) ] + [ 1 · L ( B ) ] ] + 1 = Z ( identity # 9 ) , [ [ L ( A ) · L ( B ) ] + L ( B ) ] + 1 = Z ( identity # 6 ) .
[ [ L ( A ) · L ( Q ) ] + L ( Q ) ] + 1 = Q ,
[ [ L ( B ) · L ( Q ) ] + L ( Q ) ] + 1 = Q .

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