Static analysis of gain control for a few-mode erbium-doped fiber amplifier employing pump power adjustment

Hirotaka Ono; Makoto Yamada

doi:10.1364/AO.488413

Applied Optics
Vol. 62,
Issue 16,
pp. 4180-4186
(2023)
•https://doi.org/10.1364/AO.488413

Static analysis of gain control for a few-mode erbium-doped fiber amplifier employing pump power adjustment

Hirotaka Ono and Makoto Yamada

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Hirotaka Ono and Makoto Yamada, "Static analysis of gain control for a few-mode erbium-doped fiber amplifier employing pump power adjustment," Appl. Opt. 62, 4180-4186 (2023)

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Table of Contents Category
- Lasers, Optical Amplifiers, and Laser Optics
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About this Article
History
- Original Manuscript: February 23, 2023
- Revised Manuscript: April 28, 2023
- Manuscript Accepted: May 1, 2023
- Published: May 22, 2023

Abstract

In mode-division multiplexing (MDM) optical transmission systems and MDM networks, the gain must be kept nearly constant even when the input signal power of the few-mode (FM), erbium-doped fiber amplifier (EDFA) changes. This paper investigates controllability of the gain in a 4-LP mode EDFA, whose EDF has signal modes of ${{\rm LP}_{01}}$, ${{\rm LP}_{11}}$, ${{\rm LP}_{21}}$, and ${{\rm LP}_{02}}$ or ${{\rm LP}_{01}}$, ${{\rm LP}_{11}}$, ${{\rm LP}_{21}}$, and ${{\rm LP}_{31}}$, by using analytical and full models. The results of calculation using the analytical model and a gain simulation using the full model show that the gain can be kept almost constant with an error less than 0.25 dB simply by adjusting the ${{\rm LP}_{01}}$ pump power of the EDFA with signal modes of ${{\rm LP}_{01}}$, ${{\rm LP}_{11}}$, ${{\rm LP}_{21}}$, and ${{\rm LP}_{31}}$. This result suggests that it is possible to control the gain simply by adjusting the pump power in FM-EDFAs where all signal modes have a radial mode number of one.

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Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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	Circular-Core EDF	Ring-Core EDF-1	Ring-Core EDF-2
Core radius (µm)	6.0	Inner 0.8	Inner 4.3
		Outer 6.0	Outer 6.9
$Δ$ (%)	1.0
Erbium ion	$1.0 \times 10^{25}$
concentration ( $m^{- 3}$ )
Signal mode	${L P}_{01}$ , ${L P}_{11}$ , ${L P}_{21}$ , ${L P}_{02}$		${L P}_{01}$ , ${L P}_{11}$ , ${L P}_{21}$ , ${L P}_{31}$

	${L P}_{01} - {L P}_{11}$	${L P}_{01} - {L P}_{21}$	${L P}_{01} - {L P}_{02} / {L P}_{31}$	${L P}_{11} - {L P}_{21}$	${L P}_{11} - {L P}_{02} / {L P}_{31}$	${L P}_{21} - {L P}_{02} / {L P}_{31}$
Circular-core EDF	0.790	0.580	0.746	0.927	0.450	0.435
Ring-core EDF-1	0.872	0.676	0.709	0.929	0.482	0.444
Ring-core EDF-2	0.998	0.986	0.954	0.994	0.969	0.989

		Signal Mode
(a) Ring-core EDF-1		${L P}_{01}$	${L P}_{11}$	${L P}_{21}$	${L P}_{02}$
Pump mode	${L P}_{01}$	0.82	−0.48	−1.97	−1.64
	${L P}_{11}$	0.06	−0.01	−0.06	−1.77
	${L P}_{21}$	−0.78	0.38	0.52	−2.17
	${L P}_{02}$	0.49	−0.27	−0.39	3.65
		Signal Mode
(b) Ring-core EDF-2		${LP}_{01}$	${LP}_{11}$	${LP}_{21}$	${LP}_{31}$
Pump mode	${L P}_{01}$	0.03	0.01	−0.07	−0.19
	${L P}_{11}$	0.04	0.02	−0.05	−0.17
	${L P}_{21}$	0.03	0.02	−0.03	−0.13
	${L P}_{02}$	0.09	0.01	−0.11	−0.12

		Signal Mode Change
(a) Ring-core EDF-1		${L P}_{01} - {L P}_{11}$	${L P}_{01} - {L P}_{21}$	${L P}_{01} - {L P}_{02}$	${L P}_{11} - {L P}_{21}$	${L P}_{11} - {L P}_{02}$	${L P}_{21} - {L P}_{02}$
Pump mode	${L P}_{01}$	0.02	$> 5$	$> 5$	4.8	$> 5$	$> 5$
	${L P}_{11}$	0.01	$> 5$	$> 5$	3.2	$> 5$	$> 5$
	${L P}_{21}$	0.01	$> 5$	$> 5$	3.2	$> 5$	$> 5$
	${L P}_{02}$	0.01	$> 5$	$> 5$	3.1	$> 5$	$> 5$
		Signal Mode Change
(b) Ring-core EDF-2		${LP}_{01} - {LP}_{11}$	${LP}_{01} - {LP}_{21}$	${LP}_{01} - {LP}_{31}$	${LP}_{11} - {LP}_{21}$	${LP}_{11} - {LP}_{31}$	${LP}_{21} - {LP}_{31}$
Pump mode	${L P}_{01}$	0.01	0.01	0.29	0.03	0.28	0.17
	${L P}_{11}$	0.02	0.01	0.29	0.03	0.28	0.17
	${L P}_{21}$	0.03	0.06	0.29	0.03	0.26	0.16
	${L P}_{02}$	0.04	0.12	0.43	0.09	0.45	0.27

	Circular-Core EDF	Ring-Core EDF-1	Ring-Core EDF-2
Core radius (µm)	6.0	Inner 0.8	Inner 4.3
		Outer 6.0	Outer 6.9
$Δ$ (%)	1.0
Erbium ion	$1.0 \times 10^{25}$
concentration ( $m^{- 3}$ )
Signal mode	${L P}_{01}$ , ${L P}_{11}$ , ${L P}_{21}$ , ${L P}_{02}$		${L P}_{01}$ , ${L P}_{11}$ , ${L P}_{21}$ , ${L P}_{31}$

Abstract

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Equations (24)

Applied Optics