Analysis of free carrier effects on modulational instability in silicon-on-insulator nano-waveguides

Deepa Chaturvedi; Akhilesh Kumar Mishra; Ajit Kumar

doi:10.1364/JOSAB.34.001060

Journal of the Optical Society of America B
Vol. 34,
Issue 5,
pp. 1060-1069
(2017)
•https://doi.org/10.1364/JOSAB.34.001060

Analysis of free carrier effects on modulational instability in silicon-on-insulator nano-waveguides

Deepa Chaturvedi, Akhilesh Kumar Mishra, and Ajit Kumar

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Deepa Chaturvedi, Akhilesh Kumar Mishra, and Ajit Kumar, "Analysis of free carrier effects on modulational instability in silicon-on-insulator nano-waveguides," J. Opt. Soc. Am. B 34, 1060-1069 (2017)

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Table of Contents Category
- Nonlinear Optics
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About this Article
History
- Original Manuscript: January 13, 2017
- Revised Manuscript: April 10, 2017
- Manuscript Accepted: April 11, 2017
- Published: May 1, 2017

Abstract

We present a comprehensive theoretical study on the effects of two-photon absorption, free-carrier-induced loss, and high-order dispersion on the modulational instability (MI) at low-input powers in silicon-on-insulator nano-waveguides. The MI analysis is carried out in both the normal and anomalous dispersion regimes at telecommunication wavelength. To realize these two different kinds of dispersion, two different waveguide structures have been considered. Further, the effects of carrier lifetime and power dependence on MI gain spectra have also been delineated.

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	Distance of Propagation $z$	$y_{1}$	$y_{2}$	Carrier Density $N_{0} (m^{- 3})$	Interaction Term (IT) $sgn (β_{2}) \| β_{2} \| y_{2}$
$TPA = 0$ , $FCA = 0$ , $FCD = 0$	1 mm	0	$3.3 \times 10^{2}$	0	$- 3.15 \times 10^{- 21}$
$TPA = 0$ , $FCA = 0$ , $FCD = 0$	5 mm	0	$3.3 \times 10^{2}$	0	$- 3.15 \times 10^{- 21}$
$TPA \neq 0$ , $FCA = 0$ , $FCD = 0$	1 mm	−16.22	$3.25 \times 10^{2}$	0	$- 3.1 \times 10^{- 21}$
$TPA \neq 0$ , $FCA = 0$ , $FCD = 0$	5 mm	−15.24	$3.05 \times 10^{2}$	0	$- 2.91 \times 10^{- 21}$
$TPA = 0$ , $FCA \neq 0$ , $FCD = 0$	1 mm	−64.50	$3.1 \times 10^{2}$	$3.21 \times 10^{22}$	$- 2.95 \times 10^{- 21}$
$TPA = 0$ , $FCA \neq 0$ , $FCD = 0$	5 mm	−46.28	$2.62 \times 10^{2}$	$2.31 \times 10^{22}$	$- 2.50 \times 10^{- 21}$
$TPA = 0$ , $FCA = 0$ , $FCD \neq 0$	1 mm	0	$- 1.39 \times 10^{3}$	$3.65 \times 10^{22}$	$1.32 \times 10^{- 20}$
$TPA = 0$ , $FCA = 0$ , $FCD \neq 0$	5 mm	0	$- 1.39 \times 10^{3}$	$3.65 \times 10^{22}$	$1.32 \times 10^{- 20}$
$TPA \neq 0$ , $FCA \neq 0$ , $FCD \neq 0$	1 mm	−77.98	$- 1.2 \times 10^{3}$	$3.13 \times 10^{22}$	$1.15 \times 10^{- 20}$
$TPA \neq 0$ , $FCA \neq 0$ , $FCD \neq 0$	5 mm	−54.49	$- 8.27 \times 10^{2}$	$2.09 \times 10^{22}$	$7.89 \times 10^{- 21}$

	Distance of Propagation $z$	$y_{1}$	$y_{2}$	Carrier Density $N_{0} (m^{- 3})$	Interaction Term (IT) $sgn (β_{2}) \| β_{2} \| y_{2}$
$TPA = 0$ , $FCA = 0$ , $FCD = 0$	1 mm	0	$1.11 \times 10^{2}$	0	$9.74 \times 10^{- 24}$
$TPA = 0$ , $FCA = 0$ , $FCD = 0$	5 mm	0	$1.11 \times 10^{2}$	0	$9.74 \times 10^{- 24}$
$TPA \neq 0$ , $FCA = 0$ , $FCD = 0$	1 mm	−5.51	$1.1 \times 10^{2}$	0	$9.69 \times 10^{- 24}$
$TPA \neq 0$ , $FCA = 0$ , $FCD = 0$	5 mm	−5.39	$1.08 \times 10^{2}$	0	$9.48 \times 10^{- 24}$
$TPA = 0$ , $FCA \neq 0$ , $FCD = 0$	1 mm	−9.8	$1.09 \times 10^{2}$	$6.02 \times 10^{21}$	$9.64 \times 10^{- 24}$
$TPA = 0$ , $FCA \neq 0$ , $FCD = 0$	5 mm	−9.13	$1.06 \times 10^{2}$	$5.6 \times 10^{21}$	$9.3 \times 10^{- 24}$
$TPA = 0$ , $FCA = 0$ , $FCD \neq 0$	1 mm	0	$- 2.03 \times 10^{2}$	$6.13 \times 10^{21}$	$- 1.78 \times 10^{- 23}$
$TPA = 0$ , $FCA = 0$ , $FCD \neq 0$	5 mm	0	$- 2.03 \times 10^{2}$	$6.13 \times 10^{21}$	$- 1.78 \times 10^{- 23}$
$TPA \neq 0$ , $FCA \neq 0$ , $FCD \neq 0$	1 mm	−15.15	$- 1.97 \times 10^{2}$	$5.95 \times 10^{21}$	$- 1.72 \times 10^{- 23}$
$TPA \neq 0$ , $FCA \neq 0$ , $FCD \neq 0$	5 mm	−13.86	$- 1.76 \times 10^{2}$	$5.34 \times 10^{21}$	$- 1.54 \times 10^{- 23}$

Year	Loss (dB/cm)	Wavelengths (nm)	Reference
2001	0.8	1540	[37]
2004	3.6	1500	[40]
2005	2.8	1500	[41]
2009	0.3	1520	[38]
2010	0.27	1530–1560	[39]

	Distance of Propagation $z$	$y_{1}$	$y_{2}$	Carrier Density $N_{0} (m^{- 3})$	Interaction Term (IT) $sgn (β_{2}) \| β_{2} \| y_{2}$
$TPA = 0$ , $FCA = 0$ , $FCD = 0$	1 mm	0	$3.3 \times 10^{2}$	0	$- 3.15 \times 10^{- 21}$
$TPA = 0$ , $FCA = 0$ , $FCD = 0$	5 mm	0	$3.3 \times 10^{2}$	0	$- 3.15 \times 10^{- 21}$
$TPA \neq 0$ , $FCA = 0$ , $FCD = 0$	1 mm	−16.22	$3.25 \times 10^{2}$	0	$- 3.1 \times 10^{- 21}$
$TPA \neq 0$ , $FCA = 0$ , $FCD = 0$	5 mm	−15.24	$3.05 \times 10^{2}$	0	$- 2.91 \times 10^{- 21}$
$TPA = 0$ , $FCA \neq 0$ , $FCD = 0$	1 mm	−64.50	$3.1 \times 10^{2}$	$3.21 \times 10^{22}$	$- 2.95 \times 10^{- 21}$
$TPA = 0$ , $FCA \neq 0$ , $FCD = 0$	5 mm	−46.28	$2.62 \times 10^{2}$	$2.31 \times 10^{22}$	$- 2.50 \times 10^{- 21}$
$TPA = 0$ , $FCA = 0$ , $FCD \neq 0$	1 mm	0	$- 1.39 \times 10^{3}$	$3.65 \times 10^{22}$	$1.32 \times 10^{- 20}$
$TPA = 0$ , $FCA = 0$ , $FCD \neq 0$	5 mm	0	$- 1.39 \times 10^{3}$	$3.65 \times 10^{22}$	$1.32 \times 10^{- 20}$
$TPA \neq 0$ , $FCA \neq 0$ , $FCD \neq 0$	1 mm	−77.98	$- 1.2 \times 10^{3}$	$3.13 \times 10^{22}$	$1.15 \times 10^{- 20}$
$TPA \neq 0$ , $FCA \neq 0$ , $FCD \neq 0$	5 mm	−54.49	$- 8.27 \times 10^{2}$	$2.09 \times 10^{22}$	$7.89 \times 10^{- 21}$

	Distance of Propagation $z$	$y_{1}$	$y_{2}$	Carrier Density $N_{0} (m^{- 3})$	Interaction Term (IT) $sgn (β_{2}) \| β_{2} \| y_{2}$
$TPA = 0$ , $FCA = 0$ , $FCD = 0$	1 mm	0	$1.11 \times 10^{2}$	0	$9.74 \times 10^{- 24}$
$TPA = 0$ , $FCA = 0$ , $FCD = 0$	5 mm	0	$1.11 \times 10^{2}$	0	$9.74 \times 10^{- 24}$
$TPA \neq 0$ , $FCA = 0$ , $FCD = 0$	1 mm	−5.51	$1.1 \times 10^{2}$	0	$9.69 \times 10^{- 24}$
$TPA \neq 0$ , $FCA = 0$ , $FCD = 0$	5 mm	−5.39	$1.08 \times 10^{2}$	0	$9.48 \times 10^{- 24}$
$TPA = 0$ , $FCA \neq 0$ , $FCD = 0$	1 mm	−9.8	$1.09 \times 10^{2}$	$6.02 \times 10^{21}$	$9.64 \times 10^{- 24}$
$TPA = 0$ , $FCA \neq 0$ , $FCD = 0$	5 mm	−9.13	$1.06 \times 10^{2}$	$5.6 \times 10^{21}$	$9.3 \times 10^{- 24}$
$TPA = 0$ , $FCA = 0$ , $FCD \neq 0$	1 mm	0	$- 2.03 \times 10^{2}$	$6.13 \times 10^{21}$	$- 1.78 \times 10^{- 23}$
$TPA = 0$ , $FCA = 0$ , $FCD \neq 0$	5 mm	0	$- 2.03 \times 10^{2}$	$6.13 \times 10^{21}$	$- 1.78 \times 10^{- 23}$
$TPA \neq 0$ , $FCA \neq 0$ , $FCD \neq 0$	1 mm	−15.15	$- 1.97 \times 10^{2}$	$5.95 \times 10^{21}$	$- 1.72 \times 10^{- 23}$
$TPA \neq 0$ , $FCA \neq 0$ , $FCD \neq 0$	5 mm	−13.86	$- 1.76 \times 10^{2}$	$5.34 \times 10^{21}$	$- 1.54 \times 10^{- 23}$

Abstract

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Figures (8)

Tables (3)

Equations (38)

Journal of the Optical Society of America B