Dual-pump few-mode fiber optical parametric amplification: analytical model and optimization strategy

Xiaoshan Huang; Meng Xiang; Songnian Fu; Jianping Li; Yuwen Qin

doi:10.1364/JOSAB.472044

Journal of the Optical Society of America B
Vol. 39,
Issue 11,
pp. 3088-3099
(2022)
•https://doi.org/10.1364/JOSAB.472044

Dual-pump few-mode fiber optical parametric amplification: analytical model and optimization strategy

Xiaoshan Huang, Meng Xiang, Songnian Fu, Jianping Li, and Yuwen Qin

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Xiaoshan Huang, Meng Xiang, Songnian Fu, Jianping Li, and Yuwen Qin, "Dual-pump few-mode fiber optical parametric amplification: analytical model and optimization strategy," J. Opt. Soc. Am. B 39, 3088-3099 (2022)

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Table of Contents Category
- Fiber Optics
Optics & Photonics Topics
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About this Article
History
- Original Manuscript: August 1, 2022
- Revised Manuscript: September 19, 2022
- Manuscript Accepted: October 1, 2022
- Published: October 31, 2022

Abstract

The realization of long-haul mode-division multiplexing (MDM) transmission requires a matched optical amplifier with similar gain profiles among all guided modes. The fiber optical parametric amplifier (FOPA) has several attractive characteristics, including wideband, high gain, and fast transient response. Here, we demonstrate an analytical model for the dual-pump few-mode FOPA (FM-FOPA), by taking all types of intramodal and intermodal four-wave mixing (FWM) interactions arising in a highly nonlinear few-mode fiber (HN-FMF) into account. Meanwhile, we provide a detailed description of corresponding phase-matching conditions, including the effect of high-order dispersion coefficients up to the fourth order. Equipped with this tool, we outline the optimization strategy of the dual-pump FM-FOPA. Next, we design a graded-index HN-FMF to satisfy the dispersion requirements of the dual-pump FM-FOPA. Under the optimal HN-FMF design, the dual-pump FM-FOPA can simultaneously amplify two modes with the simultaneous features of wide bandwidth (${\sim}{35}\;{\rm nm}$), high gain (${\gt}{56.29}\;{\rm dB}$), low differential mode gain (DMG) (${\lt}{0.59}\;{\rm dB}$), and low wavelength-dependent gain ripple (WDGR) (${\lt}{1.92}\;{\rm dB}$).

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Type of FWM	Type of Process	FWM Process^a
Intramodal MI	Main process	$2 p_{1}^{m / n} \to s^{m / n} + i_{1}^{m / n}$
Intramodal MI	Cascaded process	$2 p_{2}^{m / n} \to i_{2}^{m / n} + i_{3}^{m / n}$
Intramodal PC	Main process	$p_{1}^{m / n} + p_{2}^{m / n} \to s^{m / n} + i_{3}^{m / n}$
Intramodal PC	Cascaded process	$p_{1}^{m / n} + p_{2}^{m / n} \to i_{1}^{m / n} + i_{2}^{m / n}$
Intramodal BS	Main process	$s^{m / n} + p_{2}^{m / n} \to p_{1}^{m / n} + i_{2}^{m / n}$
Intramodal BS	Cascaded process	$i_{3}^{m / n} + p_{1}^{m / n} \to p_{2}^{m / n} + i_{1}^{m / n}$
Intermodal PC	Main process	$p_{1}^{m / n} + p_{1}^{n / m} \to s^{m / n} + i_{1}^{n / m}$
Intermodal PC	Cascaded process	$p_{2}^{m / n} + p_{2}^{n / m} \to i_{2}^{m / n} + i_{3}^{n / m}$
Intermodal BS	Main process	$s^{m / n} + p_{1}^{n / m} \to s^{n / m} + p_{1}^{m / n}$
Intermodal BS	Cascaded process	$i_{3}^{n / m} + p_{2}^{m / n} \to p_{2}^{n / m} + i_{3}^{m / n}$

Type of FWM	Type of Process	FWM Process^a
Intermodal BS	Pump & pump	$p_{1}^{n / m} + p_{2}^{m / n} \to p_{1}^{m / n} + p_{2}^{n / m}$
	Signal & pump 2	$p_{2}^{m / n} + s^{n / m} \to p_{2}^{n / m} + s^{m / n}$
	Primary idler & pump 1	$p_{1}^{m / n} + i_{3}^{n / m} \to p_{1}^{n / m} + i_{3}^{m / n}$
	Secondary idlers & pumps	$i_{1 / 2}^{n / m} + p_{1 / 2}^{m / n} \to p_{1 / 2}^{n / m} + i_{1 / 2}^{m / n}$
Intermodal PC	Pump & pump	$p_{1 / 2}^{n / m} + p_{1 / 2}^{m / n} \to p_{2 / 1}^{m / n} + i_{6 / 7}^{n / m}$
	Signal & pump 2	$p_{2}^{n / m} + p_{2}^{m / n} \to s^{n / m} + i_{5}^{m / n}$
	Primary idler & pump 1	$p_{1}^{n / m} + p_{1}^{m / n} \to i_{3}^{n / m} + i_{4}^{m / n}$
	Secondary idlers & pumps	$i_{1}^{n / m} + p_{1}^{m / n} \to p_{1}^{n / m} + s^{m / n}$ $i_{2}^{n / m} + p_{2}^{m / n} \to p_{2}^{n / m} + i_{3}^{m / n}$

$β_{4}$	Avg. Gain	DMG	WDGR
Ignored for $β_{4}$	32.10 dB	${L P}_{01}$	$< 0.36 d B$
Ignored for $< 1.28 d B$	32.10 dB	${L P}_{01}$	${L P}_{11 a}$
$< 1.38 d B$ for $2.0 \times 10^{- 55} (s^{4} / m)$	33.87 dB	${L P}_{01}$	$< 0.83 d B$
$< 0.85 d B$ for $3.0 \times 10^{- 55} (s^{4} / m)$	33.87 dB	${L P}_{01}$	${L P}_{11 a}$
$< 0.28 d B$ for $4.0 \times 10^{- 55} (s^{4} / m)$	33.56 dB	${L P}_{01}$	$< 1.27 d B$
$< 1.03 d B$ for $5.0 \times 10^{- 55} (s^{4} / m)$	33.56 dB	${L P}_{01}$	${L P}_{11 a}$
$< 2.13 d B$ for $- 2.0 \times 10^{- 55} (s^{4} / m)$	28.40 dB	${L P}_{01}$	$< 1.37 d B$
$< 0.91 d B$ for $- 3.0 \times 10^{- 55} (s^{4} / m)$	28.40 dB	${L P}_{01}$	${L P}_{11 a}$
$< 2.17 d B$ for $- 4.0 \times 10^{- 55} (s^{4} / m)$	21.43 dB	${L P}_{01}$	$< 1.06 d B$
$< 3.24 d B$ for $- 5.0 \times 10^{- 55} (s^{4} / m)$	21.43 dB	${L P}_{01}$	${L P}_{11 a}$

Type of FWM	Type of Process	FWM Process^a
Intramodal MI	Main process	$2 p_{1}^{m / n} \to s^{m / n} + i_{1}^{m / n}$
Intramodal MI	Cascaded process	$2 p_{2}^{m / n} \to i_{2}^{m / n} + i_{3}^{m / n}$
Intramodal PC	Main process	$p_{1}^{m / n} + p_{2}^{m / n} \to s^{m / n} + i_{3}^{m / n}$
Intramodal PC	Cascaded process	$p_{1}^{m / n} + p_{2}^{m / n} \to i_{1}^{m / n} + i_{2}^{m / n}$
Intramodal BS	Main process	$s^{m / n} + p_{2}^{m / n} \to p_{1}^{m / n} + i_{2}^{m / n}$
Intramodal BS	Cascaded process	$i_{3}^{m / n} + p_{1}^{m / n} \to p_{2}^{m / n} + i_{1}^{m / n}$
Intermodal PC	Main process	$p_{1}^{m / n} + p_{1}^{n / m} \to s^{m / n} + i_{1}^{n / m}$
Intermodal PC	Cascaded process	$p_{2}^{m / n} + p_{2}^{n / m} \to i_{2}^{m / n} + i_{3}^{n / m}$
Intermodal BS	Main process	$s^{m / n} + p_{1}^{n / m} \to s^{n / m} + p_{1}^{m / n}$
Intermodal BS	Cascaded process	$i_{3}^{n / m} + p_{2}^{m / n} \to p_{2}^{n / m} + i_{3}^{m / n}$

Type of FWM	Type of Process	FWM Process^a
Intermodal BS	Pump & pump	$p_{1}^{n / m} + p_{2}^{m / n} \to p_{1}^{m / n} + p_{2}^{n / m}$
	Signal & pump 2	$p_{2}^{m / n} + s^{n / m} \to p_{2}^{n / m} + s^{m / n}$
	Primary idler & pump 1	$p_{1}^{m / n} + i_{3}^{n / m} \to p_{1}^{n / m} + i_{3}^{m / n}$
	Secondary idlers & pumps	$i_{1 / 2}^{n / m} + p_{1 / 2}^{m / n} \to p_{1 / 2}^{n / m} + i_{1 / 2}^{m / n}$
Intermodal PC	Pump & pump	$p_{1 / 2}^{n / m} + p_{1 / 2}^{m / n} \to p_{2 / 1}^{m / n} + i_{6 / 7}^{n / m}$
	Signal & pump 2	$p_{2}^{n / m} + p_{2}^{m / n} \to s^{n / m} + i_{5}^{m / n}$
	Primary idler & pump 1	$p_{1}^{n / m} + p_{1}^{m / n} \to i_{3}^{n / m} + i_{4}^{m / n}$
	Secondary idlers & pumps	$i_{1}^{n / m} + p_{1}^{m / n} \to p_{1}^{n / m} + s^{m / n}$ $i_{2}^{n / m} + p_{2}^{m / n} \to p_{2}^{n / m} + i_{3}^{m / n}$

Abstract

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Equations (14)

Journal of the Optical Society of America B