Optimization of an all-optical three-input universal logic gate with an enhanced contrast ratio by exploiting a T-shaped photonic crystal waveguide

Maddala Rachana; Sandip Swarnakar; Mallavarapu Rajan Babu; Paradesi Mary Swetha; Yagateela Pandu Rangaiah; Sabbi Vamshi Krishna; Santosh Kumar; Santosh Kumar

doi:10.1364/AO.463845

Applied Optics
Vol. 61,
Issue 28,
pp. 8162-8171
(2022)
•https://doi.org/10.1364/AO.463845

Optimization of an all-optical three-input universal logic gate with an enhanced contrast ratio by exploiting a T-shaped photonic crystal waveguide

Maddala Rachana, Sandip Swarnakar, Mallavarapu Rajan Babu, Paradesi Mary Swetha, Yagateela Pandu Rangaiah, Sabbi Vamshi Krishna, and Santosh Kumar

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Maddala Rachana, Sandip Swarnakar, Mallavarapu Rajan Babu, Paradesi Mary Swetha, Yagateela Pandu Rangaiah, Sabbi Vamshi Krishna, and Santosh Kumar, "Optimization of an all-optical three-input universal logic gate with an enhanced contrast ratio by exploiting a T-shaped photonic crystal waveguide," Appl. Opt. 61, 8162-8171 (2022)

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Abstract

Universal gates (NAND and NOR) are used for any electronic circuit that is affordable and straightforward to build all logic gates (LoG). In this work, the T-shaped 2D photonic crystal (PhC) is exploited to design a three-input universal LoG premised on the beam-interference principle. The design criteria of pitch ($a$), rod radius ($r$), and refractive index ($n$) are employed to obtain a high impact output. The methodologies of plane wave expansion and finite-difference time-domain are employed for examining the framework of universal LoG at 1550 nm wavelengths ($\lambda$). The suggested universal LoG design has a compact size of ${8.4}\;{\unicode{x00B5}{\rm m}} \times {4.8}\;{\unicode{x00B5}{\rm m}}$. Additionally, the structure yields a high contrast ratio (CR) of 20.37 dB for the NAND LoG and 28.45 dB for the NOR LoG, and maximum transmission efficiency of 50.6% and 70% for the NAND and NOR gates; correspondingly, the best and worst three-input NAND gate response times are 19.5 ps and 21.4 ps. Similarly, the response time of the three-input NOR gate is 26 ps. The proposed universal gate’s primary goal is to offer a high CR and a compact structure while being compatible with any other logic gate.

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Input Logic					Phase Orientations (NAND)
$P$	$Q$	$R$	$C 1$	$C 2$	$P$	$Q$	$R$	$C 1$	$C 2$
Disable	Disable	Disable	Enable	Enable	–	–	–	0º	180º
Disable	Disable	Enable	Enable	Enable	–	–	0º	180º	180º
Disable	Enable	Disable	Enable	Enable	–	180º	–	180º	180º
Disable	Enable	Enable	Enable	Enable	–	0º	180º	0º	0º
Enable	Disable	Disable	Enable	Enable	0º	–	–	180º	180º
Enable	Disable	Enable	Enable	Enable	180º	–	180º	0º	0º
Enable	Enable	Disable	Enable	Enable	180º	0º	–	0º	0º
Enable	Enable	Enable	Enable	Enable	0º	0º	0º	0º	0º

Input Logic					Phase Orientations (NOR)
$P$	$Q$	$R$	$C 1$	$C 2$	$P$	$Q$	$R$	$C 1$	$C 2$
Disable	Disable	Disable	Enable	Enable	–	–	–	180º	0º
Disable	Disable	Enable	Enable	Enable	–	–	0º	0º	180º
Disable	Enable	Disable	Enable	Enable	–	180º	–	0º	180º
Disable	Enable	Enable	Enable	Enable	–	0º	0º	0º	180º
Enable	Disable	Disable	Enable	Enable	180º	–	–	180º	0º
Enable	Disable	Enable	Enable	Enable	180º	–	0º	0º	180º
Enable	Enable	Disable	Enable	Enable	180º	180º	–	0º	180º
Enable	Enable	Enable	Enable	Enable	0º	0º	0º	180º	0º

Input Combinations							Normalized Power Intensities of
$P$	$Q$	$R$	$C 1$	$C 2$	Result	Output Power	Three-Input NAND Gate
Disable	Disable	Disable	Enable	Enable	Enable	0.506	0.46
Disable	Disable	Enable	Enable	Enable	Enable	0.77	0.7
Disable	Enable	Disable	Enable	Enable	Enable	0.64	0.58
Disable	Enable	Enable	Enable	Enable	Enable	0.93	0.84
Enable	Disable	Disable	Enable	Enable	Enable	0.82	0.74
Enable	Disable	Enable	Enable	Enable	Enable	1.098	1
Enable	Enable	Disable	Enable	Enable	Enable	0.58	0.52
Enable	Enable	Enable	Enable	Enable	Disable	0.0185	0.01

			Intensities of Output Power for Various Refractive Index Values
Input Configurations			3.36	3.38	3.4	3.42	3.44
$P$	$Q$	$R$	$W$	$W$	$W$	$W$	$W$
Disable	Disable	Disable	0.76	0.72	0.82	0.73	0.74
Disable	Disable	Enable	0.84	0.85	0.88	0.87	0.86
Disable	Enable	Disable	0.76	0.76	0.84	0.78	0.82
Disable	Enable	Enable	0.87	0.88	0.98	0.94	0.95
Enable	Disable	Disable	0.77	0.69	0.80	0.68	0.78
Enable	Disable	Enable	0.84	0.80	0.94	0.81	0.90
Enable	Enable	Disable	0.71	0.72	0.89	0.73	0.84
Enable	Enable	Enable	0.088	0.04	0.04	0.08	0.066

Input Configurations			Photonic Crystal Rods of Various Radii
$P$	$Q$	$R$	$0.20 a$	$0.21 a$	$0.22 a$	$0.23 a$	$0.24 a$
Disable	Disable	Disable	0.82	0.71	0.506	0.32	0.166
Disable	Disable	Enable	0.88	0.94	0.77	0.59	0.41
Disable	Enable	Disable	0.84	0.85	0.64	0.33	0.153
Disable	Enable	Enable	0.98	1.107	0.93	0.59	0.38
Enable	Disable	Disable	0.80	0.69	0.82	0.43	0.07
Enable	Disable	Enable	0.94	0.92	1.098	0.75	0.47
Enable	Enable	Disable	0.89	0.82	0.58	0.41	0.166
Enable	Enable	Enable	0.04	0.045	0.0185	0.055	0.160

Input Configurations			Photonic Crystal Rods of Various Radii
$P$	$Q$	$R$	$0.18 a$	$0.19 a$	$0.20 a$	$0.21 a$	$0.22 a$
Disable	Disable	Disable	0.56	0.65	0.82	0.70	0.67
Disable	Disable	Enable	0.52	0.042	0.07	0.010	0.037
Disable	Enable	Disable	0.051	0.042	0.13	0.039	0.001
Disable	Enable	Enable	0.045	0.036	0.07	0.013	0.025
Enable	Disable	Disable	0.043	0.037	0.08	0.008	0.010
Enable	Disable	Enable	0.035	0.029	0.04	0.004	0.042
Enable	Enable	Disable	0.040	0.034	0.08	0.011	0.0018
Enable	Enable	Enable	0.031	0.024	0.04	0.001	0.032

Sl. No.	Parameters	Three-Input NAND [1]	Two-Input NAND Gate using Triangular [19]	Two-Input Nonlinear Ring Resonator [20]	Two-Input Kerr-Effect [21]	Two-Input NAND Gate [6]	NAND Gate using Two Ring Resonators [2]	Three-Input Ring Resonator [22]	Two-Input NAND Hexagonal Ring Resonator [39]	Two-Input NAND Gate [40]	Two-Input NAND Gate [41]	Present Three-Input T-Shaped NAND Gate
1.	Applied material	Si	Si	n.r.^a	n.r.^a	Si	Si	Si	Chalcogenide	n.r.^a	n.r.^a	Si
2.	Total no. of inputs	Three-input	Two- input	Two-input	Two- input	Two-input	Two ring resonators	Two-input	Two-input	Two-input	Two-input	Three-input
3.	Rod radii	124 nm	0.3a	0.265a	0.1188	0.2 a	0.2a	0.3a	0.2a	n.r.^a	n.r.^a	0.21a
4.	Device size	$12.5 µ m \times 12 µ m$	$15.84 µ m \times 15.84 µ m$	$45.375 µ m \times 16.5 µ m$	$19 µ m \times 16.64 µ m$	$12.6 µ m \times 18.6 µ m$	$17.2 µ m \times 12.555 µ m$	n.r.^a	$9.6 µ m \times 9.6 µ m$	$37.50 µ m \times 18.91 µ m$	$27 µ m \times 17 µ m$	$8.4 µ m \times 4.8 µ m$
5.	Wavelength ( $λ$ )	1.55 µm	n.r.^a	1.55 µm	1.55 µm	1.55 µm	1.55 µm	1.55 µm	1.55 µm	1.55 µm	n.r.^a	1.55 µm
6.	Pitchconstant ( $a$ )	0.616 µm	0.352 µm	0.825 µm	0.5943µm	0.6 µm	0.465 µm	0.352 µm	0.6 µm	n.r.^a	n.r.^a	0.6 µm
7.	Refractive index ( $n$ )	3.46	3.5	3.1	3.1 and 3.6	3.46	3.5	3.5	3.1	n.r.^a	n.r.^a	3.4
8.	Contrast ratio (dB)	8.47 dB	n.r.	n.r.^a	n.r.^a	5.18 dB	n.r.^a	n.r.^a	22.6 dB	5.74 dB	18.66 dB	20.37 dB (Best case) $14.436 d B$ (Worst case)
9.	Response time	n.r.^a	6.48 ps	n.r.^a	n.r.^a	n.r.^a	n.r.^a	2.168 ps	n.r.^a	80 ps	n.r.^a	$B e s t = 19.5 p s;$ $W o r s t = 21.4 p s$
10.	Bit rate	n.r.^a	0.154 Tbps	n.r.^a	n.r.^a	7.485 Tbps	n.r.^a	0.461 Tbps	n.r.^a	n.r.^a	n.r.^a	51.28 Tbps
11.	Transmission efficiency	n.r.^a	n.r.^a	n.r.^a	n.r.^a	n.r.^a	n.r.^a	n.r.^a	n.r.^a	n.r.^a	n.r.^a	109 %
12.	Insertion loss	n.r.^a	n.r.^a	n.r.^a	n.r.^a	n.r.^a	n.r.^a	n.r.^a	n.r.^a	n.r.^a	n.r.^a	0.37 dB

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Applied Optics