Phase-preserving NALM regenerator with lower input power by optimizing
the nonreciprocal phase shifter

Shouqi Zhang; Baojian Wu; Feng Wen

doi:10.1364/AO.412775

Applied Optics
Vol. 60,
Issue 3,
pp. 492-498
(2021)
•https://doi.org/10.1364/AO.412775

Phase-preserving NALM regenerator with lower input power by optimizing the nonreciprocal phase shifter

Shouqi Zhang, Baojian Wu, and Feng Wen

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Shouqi Zhang, Baojian Wu, and Feng Wen, "Phase-preserving NALM regenerator with lower input power by optimizing the nonreciprocal phase shifter," Appl. Opt. 60, 492-498 (2021)

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- Fiber Optics, Fiber Sensors, and Optical Communications
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About this Article
History
- Original Manuscript: October 19, 2020
- Revised Manuscript: December 16, 2020
- Manuscript Accepted: December 16, 2020
- Published: January 11, 2021

Abstract

We propose a new nonlinear amplifying loop mirror (NALM)-based phase-preserving amplitude regenerator (so-called NP-NALM) by introducing a nonreciprocal phase shifter to further improve the regeneration performance. The theoretical model of the NP-NALM structure and the amplitude regeneration and phase-preserving conditions are presented. It is shown that the optimal working point power reduces with the increase of the nonreciprocal phase shift in the available range and the first working point power can be as low as 115 mW by optimizing the nonreciprocal phase shifter. We also investigate the cascaded NP-NALM transmission system for quadrature phase-shift keying signals with amplified spontaneous emission noise and the output error vector magnitude (EVM) can reduce to 23% from the EVM limit of 30%, corresponding to bit error ratio of ${10^{- 3}}$ for the cascaded system without regeneration.

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Clockwise Optical Fields		Counterclockwise Optical Fields
VOA and NPS	$E_{+}^{(2)} = \sqrt{1 - ρ} \sqrt{Γ} e^{i φ_{+}} E_{i n}$	Bi-EDFA	$E_{-}^{(2)} = i \sqrt{ρ} \sqrt{G} E_{i n}$
HNLF	$\begin{array}{l} E_{+}^{(3)} = \sqrt{1 - ρ} e^{- α L / 2} \sqrt{Γ} \times \\ \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} e^{i (φ_{+} + γ L_{e f f} (1 - ρ) Γ \| A_{i n} \|^{2})} E_{i n} \end{array}$	HNLF	$\begin{array}{l} E_{-}^{(3)} = i \sqrt{ρ} e^{- α L / 2} \sqrt{G} \times \\ \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} e^{i (γ L_{e f f} ρ G \| A_{i n} \|^{2})} E_{i n} \end{array}$
Bi-EDFA	$\begin{array}{l} E_{+}^{(4)} = \sqrt{1 - ρ} e^{- α L / 2} \sqrt{Γ G} \times \\ \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} e^{i (φ_{1 +} + γ L_{e f f} (1 - ρ) Γ \| A_{i n} \|^{2})} E_{i n} \end{array}$	VOA and NPS	$\begin{array}{l} E_{-}^{(4)} = i \sqrt{ρ} e^{- α L / 2} \sqrt{Γ G} \times \\ \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} e^{i (φ_{-} + γ L_{e f f} ρ G \| A_{i n} \|^{2})} E_{i n} \end{array}$

$θ_{n p s}$	$ρ$	$p_{i n, 1}^{o p t}$	$γ_{N P S}$	$P_{f, 1}^{o p t}$ /W	$P_{f, 1}^{o p t} / ρ$
0	0.09	0.81	35.25	0.52	5.78
$0.5 π$	0.1218	0.58	19.45	0.38	3.12
$π$	0.1804	0.36	8.79	0.26	1.44
$1.5 π$	0.2978	0.17	3.23	0.15	0.50
$1.8 π$	0.4101	0.0675	1.62	0.11	0.27

Clockwise Optical Fields		Counterclockwise Optical Fields
VOA and NPS	$E_{+}^{(2)} = \sqrt{1 - ρ} \sqrt{Γ} e^{i φ_{+}} E_{i n}$	Bi-EDFA	$E_{-}^{(2)} = i \sqrt{ρ} \sqrt{G} E_{i n}$
HNLF	$\begin{array}{l} E_{+}^{(3)} = \sqrt{1 - ρ} e^{- α L / 2} \sqrt{Γ} \times \\ \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} e^{i (φ_{+} + γ L_{e f f} (1 - ρ) Γ \| A_{i n} \|^{2})} E_{i n} \end{array}$	HNLF	$\begin{array}{l} E_{-}^{(3)} = i \sqrt{ρ} e^{- α L / 2} \sqrt{G} \times \\ \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} e^{i (γ L_{e f f} ρ G \| A_{i n} \|^{2})} E_{i n} \end{array}$
Bi-EDFA	$\begin{array}{l} E_{+}^{(4)} = \sqrt{1 - ρ} e^{- α L / 2} \sqrt{Γ G} \times \\ \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} e^{i (φ_{1 +} + γ L_{e f f} (1 - ρ) Γ \| A_{i n} \|^{2})} E_{i n} \end{array}$	VOA and NPS	$\begin{array}{l} E_{-}^{(4)} = i \sqrt{ρ} e^{- α L / 2} \sqrt{Γ G} \times \\ \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} \begin{matrix} \end{matrix} e^{i (φ_{-} + γ L_{e f f} ρ G \| A_{i n} \|^{2})} E_{i n} \end{array}$

$θ_{n p s}$	$ρ$	$p_{i n, 1}^{o p t}$	$γ_{N P S}$	$P_{f, 1}^{o p t}$ /W	$P_{f, 1}^{o p t} / ρ$
0	0.09	0.81	35.25	0.52	5.78
$0.5 π$	0.1218	0.58	19.45	0.38	3.12
$π$	0.1804	0.36	8.79	0.26	1.44
$1.5 π$	0.2978	0.17	3.23	0.15	0.50
$1.8 π$	0.4101	0.0675	1.62	0.11	0.27

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Applied Optics