Optical parallel logic gate using spatial light modulators with the Pockels effect

Takumi Minemoto; Kazuhiro Okamoto; Kei Miyamoto

doi:10.1364/AO.24.002055

Applied Optics
Vol. 24,
Issue 14,
pp. 2055-2062
(1985)
•https://doi.org/10.1364/AO.24.002055

Optical parallel logic gate using spatial light modulators with the Pockels effect

Takumi Minemoto, Kazuhiro Okamoto, and Kei Miyamoto

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Takumi Minemoto, Kazuhiro Okamoto, and Kei Miyamoto, "Optical parallel logic gate using spatial light modulators with the Pockels effect," Appl. Opt. 24, 2055-2062 (1985)

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Abstract

This paper describes a new optical gate for logical processing in parallel. The gate consists of two spatial light modulators which spatially modulate a lightwave by the longitudinal electrooptic or Pockels effect. The gate can perform in parallel all sixteen logic functions of two binary variables in both the bright-true logic and the dark-true logic. The gate has the capability of operating on large arrays of binary variables.

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	Operation mode of the PROM device
	Negative mode		Positive mode
Input A	a_x	a_y	a_x	a_y
0	$exp (i \frac{π}{2} \frac{V_{1}}{V_{h}})$	$exp (- i \frac{π}{2} \frac{V_{1}}{V_{h}})$	0	0
1	0	0	$exp (- i \frac{π}{2} \frac{V_{1}}{V_{h}})$	$exp (i \frac{π}{2} \frac{V_{1}}{V_{h}})$

	Operation mode of the PROM device
	Negative mode		Positive mode
Input B	b_x	b_y	b_x	b_y
0	$a_{x} exp (i \frac{π}{2} \frac{k V_{2}}{V_{h}})$	$a_{y} exp (- i \frac{π}{2} \frac{k V_{2}}{V_{h}})$	0	0
1	0	0	$a_{x} exp (- i \frac{π}{2} \frac{k V_{2}}{V_{h}})$	$a_{y} exp (i \frac{π}{2} \frac{k V_{2}}{V_{h}})$

Cases	(Arrangement S) (Arrangement R)		Case 1: S-1 and Case 2: R-2	Case 2: S-2 and Case 1: R-1
Operation modes	(Device 1)	(Device 2)
	Negative	Negative	+1	−1
	Negative	Positive	−1	+1
	Positive	Negative	−1	+1
	Positive	Positive	+1	−1

Input		Device operation		Voltage drop		V₁+kV₂	Output	Function
A	B	1	2	1	2	V₁+kV₂	Output	Bright-true logic	Dark-true logic
0	0			V₁	V₂	V₁ + V₂	b
0	1			V₁	0	V₁	b
1	0	Neg	Neg	0	V₂	V₂	b	nand	nor
1	1			0	0	0	d
0	0			V₁	0	V₁	b
0	1			V₁	V₂	V₁−V₂	0
1	0	Neg	Pos	0	0	0	d	xnor	xor
1	1			0	V₁	V₂	b
0	0			0	V₂	V₂	b
0	1			0	0	0	d
1	0	Pos	Neg	V₁	V₂	V₁−V₂	d	xnor	xor
1	1			V₁	0	V₁	b
0	0			0	0	0	d
0	1			0	V₂	V₂	b
1	0	Pos	Pos	V₁	0	V₁	b	or	and
1	1			V₁	V₂	V₁ + V₂	b
0	0			V₁	0	V₁	b
0	1			V₁	0	V₁	b
1	0	Neg	V_e = 0	0	0	0	d	(Ā)	(Ā)
1	1			0	0	0	d
0	0			0	0	0	d
0	1			0	0	0	d
1	0	Pos	V_e = 0	V₁	0	V₁	b	A	A
1	I			V₁	0	V₁	b
0	0			0	V₂	V₂	b
0	1			0	0	0	d
1	0	V_e = 0	Neg	0	V₂	V₂	b	$\bar{B}$	$\bar{B}$
1	1			0	0	0	d
0	0			0	0	0	d
0	1			0	V₂	V₂	b
1	0	V_e = 0	Pos	0	0	0	d	B	B
1	1			0	V₂	V₂	b

Input		Device Operation		Voltage drop				Funtion
A	B	1	2	1	2	V₁ + kV₂	Output	Bright-true logic	Dark-true logic
0	0	Neg	Neg	V₁	V₂	V₁ − V₂	d	xor	xnor
0	1			V₁	0	V₁	b
1	0			0	V₂	V₂	b
1	1			0	0	0	d
0	0	Neg	Pos	V₁	0	V₁	b	Ā + B	Ā · B
0	1			V₁	V₂	V₁ + V₂	b
1	0			0	0	0	d
1	1			0	V₂	V₂	b
0	0	Pos	Neg	0	V₂	V₂	b	$A + \bar{B}$	$A \cdot \bar{B}$
0	1			0	0	0	d
1	0			V₁	V₂	V₁ + V₂	b
1	1			V₁	0	V₂	b
0	0	Pos	Pos	0	0	0	d	xor	xnor
0	1			0	V₂	V₂	b
1	0			V₁	0	V₁	b
1	1			V₁	V₂	V₁ − V₂	d
0	0	Neg	V_e = 0	V₁	0	V₁	b	Ā	Ā
0	1			V₁	0	V₁	b
1	0			0	0	0	d
1	1			0	0	0	d
0	0	Pos	V_e = 0	0	0	0	d	A	A
0	1			0	0	0	d
1	0			V₁	0	V₁	b
1	1			V₁	0	V₁	b
0	0	V_e = 0	Neg	0	V₂	V₂	b	$\bar{B}$	$\bar{B}$
0	1			0	0	0	d
1	0			0	V₂	V₂	b
I	1			0	0	0	d
0	0	V_e = 0	Pos	0	0	0	d	B	B
0	1			0	V₂	V₂	b
1	0			0	0	0	d
1	1			0	V₂	V₂	b

Function		Function name
		Bright-true logic	Dark-true logic	Arrangement or case	PROM device operation
		Bright-true logic	Dark-true logic	Arrangement or case	Device 1	Device 2
Input
A	0011
B	0101
Output
F₀	0000	F	T	S,R,U	V_e = 0	V_e = 0
F₁	0001	and	or	U	Pos	Pos
F₂	0010	$A \cdot \bar{B}$	$A + \bar{B}$	U	Pos	Neg
F₃	0011	A	A	S,R	Pos	V_e = 0
				U	Neg	No exp
F₄	0100	Ā · B	Ā + B	U	Neg	Pos
F₅	0101	B	B	S,R	V_e = 0	Pos
				U	No exp	Pos
F₆	0110	xor	xnor	S-2,R-1	Neg	Neg
				S-2,R-1	Pos	Pos
F₇	0111	or	and	S-1,R-2	Pos	Pos
F₈	1000	nor	nand	U	Neg	Neg
F₉	1001	xnor	xor	S-1,R-2	Neg	Pos
				S-1,R-2	Pos	Neg
F₁₀	1010	$\bar{B}$	$\bar{B}$	S,R	V_e = 0	Neg
				U	No exp	Neg
F₁₁	1011	$A + \bar{B}$	$A \cdot \bar{B}$	S-2,R-1	Pos	Neg
F₁₂	1100	Ā	Ā	S,R	Neg	V_e = 0
				U	Neg	No exp
F₁₃	1101	Ā + B	Ā · B	S-2,R-1	Neg	Pos
F₁₄	1110	nand	nor	S-l,R-2	Neg	Neg
F₁₅	1111	T	F	S,R,U	No exp	No exp

Abstract

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Figures (6)

Tables (7)

Equations (32)

Applied Optics