Single Mach–Zehnder interferometer based optical Boolean logic gates

Cláudia Reis; Tanay Chattopadhyay; Paulo André; António Teixeira

doi:10.1364/AO.51.008693

Single Mach–Zehnder interferometer based optical Boolean logic gates

Cláudia Reis, Tanay Chattopadhyay, Paulo André, and António Teixeira

Applied Optics
Vol. 51,
Issue 36,
pp. 8693-8701
(2012)
•doi: 10.1364/AO.51.008693

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Cláudia Reis, Tanay Chattopadhyay, Paulo André, and António Teixeira, "Single Mach–Zehnder interferometer based optical Boolean logic gates," Appl. Opt. 51, 8693-8701 (2012)

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Abstract

In this paper, we demonstrate different optical logic gates using a single Mach–Zehnder interferometer with controlled phase modulators in each arm. The operational conditions to obtain 16 optical logic circuits, using the same design, are investigated and are a result of a constructive or destructive interference process. The proposed configuration presents significant low complexity and high scalability, and its feasibility is evaluated through numerical simulations.

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$X$	$Y$	$θ_{1}$ (deg)	$θ_{2}$ (deg)	$Δ θ$ (deg)	$P_{I}$	$P_{J}$
0	0	0	0	0	0	1
0	1	0	60	$- 60$	0.25 $P_{A}$	0.75 $P_{A}$
1	0	300	0	300	0.25 $P_{A}$	0.75 $P_{A}$
1	1	300	60	240	0.75 $P_{A}$	0.25 $P_{A}$

				Output Power When Input Signal $X : Y$
Logic Gate	$θ_{1}$ (deg)	$θ_{2}$ (deg)	Output Port	$0 ∶ 0$	$0 ∶ 1$	$1 ∶ 0$	$1 ∶ 1$
$X Y (AND)$	300	60	Port I	0	0.25	0.25	0.75
$\bar{X} + \bar{Y} (NAND)$	300	60	Port J	1	0.75	0.75	0.25
$X \bar{Y}$	120	60	Port I	0	0.25	0.75	0.25
$\bar{X} + Y$	120	60	Port J	1	0.75	0.25	0.75
$\bar{X} Y$	60	120	Port I	0	0.75	0.25	0.25
$X + \bar{Y}$	60	120	Port J	1	0.25	0.75	0.75
$X \oplus Y (XOR)$	180	180	Port I	0	1	1	0
$\bar{X \oplus Y} (XNOR)$	180	180	Port J	1	0	0	1
0(False)	60	60	Port I	0	0.25	0.25	0
1(True)	60	60	Port J	1	0.75	0.75	1
$X$	240	60	Port I	0	0.25	0.75	1
$\bar{X}$	240	60	Port J	1	0.75	0.25	0
$Y$	60	240	Port I	0	0.75	0.25	1
$\bar{Y}$	60	240	Port J	1	0.25	0.75	0
$X + Y (OR)$	240	120	Port I	0	0.75	0.75	0.75
$\bar{X} \bar{Y} (NOR)$	240	120	Port J	1	0.25	0.25	0.25

Logic Functions (I/J)	Before Thresholder (dB)		After Thresholder (dB)
Logic Functions (I/J)	I	J	I	J
$X Y (AND) / \bar{X} + \bar{Y} (NAND)$	4.23	4.68	15	15.3
$X \bar{Y} / \bar{X} + Y$	3.75	4.24	14	15.1
$\bar{X} Y / X + \bar{Y}$	4.03	3.98	14.4	14.2
$X \oplus Y (XOR) / \bar{X \oplus Y} (XNOR)$	16.99	16.99	14.9	14.9
0(False)/1(True)	11.3	13.85	9.7	14.6
$X / \bar{X}$	4.24	4.36	15	15
$Y / \bar{Y}$	4.29	4.27	15.1	15.1
$\bar{X} \bar{Y} (NOR) / X + Y (OR)$	13.22	7.12	14.9	14.1

MZI-A				MZI-B				MZI-C
$x$	$y$	$θ_{1}$ (deg)	$θ_{2}$ (deg)	$a$	$b$	$θ_{1}$ (deg)	$θ_{2}$ (deg)	$a$	$b$	$θ_{1}$ (deg)	$θ_{2}$ (deg)	Port 1	Port 2	Port 3	Port 4
{0011}	{0101}	300	60	{1110}	{1000}	300	60	{1110}	{1000}	300	60	{0000}	{0001}	{1000}	{0110}
		300	60			120	60			120	60	{0000}	{0001}	{0110}	{1000}
		120	60			180	180			180	180	{0010}	{0000}	{0100}	{1001}

$X$	$Y$	$θ_{1}$ (deg)	$θ_{2}$ (deg)	$Δ θ$ (deg)	$P_{I}$	$P_{J}$
0	0	0	0	0	0	1
0	1	0	60	$- 60$	0.25 $P_{A}$	0.75 $P_{A}$
1	0	300	0	300	0.25 $P_{A}$	0.75 $P_{A}$
1	1	300	60	240	0.75 $P_{A}$	0.25 $P_{A}$

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