Integrable all-optical NOT gate using nonlinear photonic crystal MZI for photonic integrated circuit

Shatrughna Kumar; Mrinal Sen

doi:10.1364/JOSAB.380351

Journal of the Optical Society of America B
Vol. 37,
Issue 2,
pp. 359-369
(2020)
•https://doi.org/10.1364/JOSAB.380351

Integrable all-optical NOT gate using nonlinear photonic crystal MZI for photonic integrated circuit

Shatrughna Kumar and Mrinal Sen

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Shatrughna Kumar and Mrinal Sen, "Integrable all-optical NOT gate using nonlinear photonic crystal MZI for photonic integrated circuit," J. Opt. Soc. Am. B 37, 359-369 (2020)

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Abstract

A silicon photonic crystal (PhC)-based nonlinear Mach–Zehnder interferometer (NMZI) is used to design a new model for an all-optical NOT gate. The nonlinear arm of the NMZI is considered to be made of a slotted-PhC waveguide, where the slot is filled with silicon nanocrystal ($ {\rm SiNC}/{{\rm SiO}_2} $) material. The high nonlinearity of the $ {\rm SiNC}/{{\rm SiO}_2} $ and low group velocity of the PhC make it possible to attain a significant phase shift in low-power high-frequency pulses traveling through the nonlinear arm. A control wave is utilized to increase the phase shift by the cross-phase modulation phenomenon. A complete study on the phase variation is performed by varying various parameters such as powers and pulse widths of the probe and control signal. The study is used to determine the length of the nonlinear arm to calculate the transfer characteristic of the device. The transfer characteristic shows a successful inversion operation in the power range of 28–60 mW for a pulse width of 3 ps. The overall dimension of the device is found as $ \approx {112} \times {7}\,\,\unicode{x00B5}{\rm m^2} $. Tolerances of the device performance under fabrication imperfections are analyzed by allowing random variations in the positions and the radii of the holes. This study reveals that the inversion characteristic is sustained, even for the significant fabrication imperfections.

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Parameters	Nonlinear Arm Section C1		Linear Arm Section C2		Source
Signal	Probe	Control	Probe	Control	Cal/Refs.
$β_{1} (\times 10^{- 8} s / m)$	9.87	5.11	5.75	4.96	Cal.
$β_{2} (\times \frac{10^{- 21} s^{2}}{m})$	−2.8	−5.43	−3.42	−1.17	Cal.
$β_{3} (\times \frac{10^{- 33} s^{3}}{m})$	0.13	1.6	1.21	0.314	Cal.
$β_{4} (\times \frac{10^{- 46} s^{4}}{m})$	−0.96	−8.18	−4.53	−0.37	Cal.
Group index ( $n_{g}$ )	29.62	15.34	17.3	14.9	Cal.
$a_{e f f}$ ( $µ m^{2}$ ) (SPM)	0.123	0.12	0.07	0.075	Cal. [Eq. (A3)]
$a_{e f f}$ ( $µ m^{2}$ ) (XPM)	0.125		0.0725		Cal. [Eq. (A3)]
$α_{l} (d b / c m)$	10		10		[31]
Kerr coeff. ( $n_{2}) m^{2} / W$	$2 \times 10^{- 16}$		$2 \times 10^{- 18}$		[13,14]
TPA ( $β_{T P A}$ ) m/W	$50 \times 10^{- 11}$		$50 \times 10^{- 12}$		[13,14]

Probe Signal			Control Signal			NSPCW
Power (mW)	Wavelength (nm)	Pulse Width (ps)	Power (mW)	Wavelength (nm)	Pulse Width (ps)	Length (µm)
5	1550	3	—	—	—	145
10✓	1550	3	—	—	—	129
15	1550	3	—	—	—	109
20	1550	3	—	—	—	95
10✓	1550	3	1	1545	3	121
10	1550	3	2	1545	3	114
10	1550	3	3	1545	3	107
10	1550	3	4	1545	3	100
10	1550	3	4	1540	3	106
10	1550	3	4	1535	3	109
10	1550	3	4	1530	3	111
10	1550	3	2	1545	3	129
10	1550	4	2	1545	4	145
10	1550	5	2	1545	5	191

Parameters	Nonlinear Arm Section C1		Linear Arm Section C2		Source
Signal	Probe	Control	Probe	Control	Cal/Refs.
$β_{1} (\times 10^{- 8} s / m)$	9.87	5.11	5.75	4.96	Cal.
$β_{2} (\times \frac{10^{- 21} s^{2}}{m})$	−2.8	−5.43	−3.42	−1.17	Cal.
$β_{3} (\times \frac{10^{- 33} s^{3}}{m})$	0.13	1.6	1.21	0.314	Cal.
$β_{4} (\times \frac{10^{- 46} s^{4}}{m})$	−0.96	−8.18	−4.53	−0.37	Cal.
Group index ( $n_{g}$ )	29.62	15.34	17.3	14.9	Cal.
$a_{e f f}$ ( $µ m^{2}$ ) (SPM)	0.123	0.12	0.07	0.075	Cal. [Eq. (A3)]
$a_{e f f}$ ( $µ m^{2}$ ) (XPM)	0.125		0.0725		Cal. [Eq. (A3)]
$α_{l} (d b / c m)$	10		10		[31]
Kerr coeff. ( $n_{2}) m^{2} / W$	$2 \times 10^{- 16}$		$2 \times 10^{- 18}$		[13,14]
TPA ( $β_{T P A}$ ) m/W	$50 \times 10^{- 11}$		$50 \times 10^{- 12}$		[13,14]

Probe Signal			Control Signal			NSPCW
Power (mW)	Wavelength (nm)	Pulse Width (ps)	Power (mW)	Wavelength (nm)	Pulse Width (ps)	Length (µm)
5	1550	3	—	—	—	145
10✓	1550	3	—	—	—	129
15	1550	3	—	—	—	109
20	1550	3	—	—	—	95
10✓	1550	3	1	1545	3	121
10	1550	3	2	1545	3	114
10	1550	3	3	1545	3	107
10	1550	3	4	1545	3	100
10	1550	3	4	1540	3	106
10	1550	3	4	1535	3	109
10	1550	3	4	1530	3	111
10	1550	3	2	1545	3	129
10	1550	4	2	1545	4	145
10	1550	5	2	1545	5	191

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Journal of the Optical Society of America B