Ultrafast convergent power-balance model for Raman random fiber laser with half-open cavity

Shengtao Lin; Zinan Wang; Hugo A. Araújo; Ernesto P. Raposo; Ernesto P. Raposo; Ernesto P. Raposo; Anderson S. L. Gomes; Han Wu; Mengqiu Fan; Yunjiang Rao

doi:10.1364/OE.398386

Optics Express
Vol. 28,
Issue 15,
pp. 22500-22510
(2020)
•https://doi.org/10.1364/OE.398386

Ultrafast convergent power-balance model for Raman random fiber laser with half-open cavity

Shengtao Lin, Zinan Wang, Hugo A. Araújo, Ernesto P. Raposo, Anderson S. L. Gomes, Han Wu, Mengqiu Fan, and Yunjiang Rao

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Shengtao Lin, Zinan Wang, Hugo A. Araújo, Ernesto P. Raposo, Anderson S. L. Gomes, Han Wu, Mengqiu Fan, and Yunjiang Rao, "Ultrafast convergent power-balance model for Raman random fiber laser with half-open cavity," Opt. Express 28, 22500-22510 (2020)

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Abstract

The power-relevant features of Raman random fiber laser (RRFL), such as lasing threshold, slope efficiency, and power distribution, are among the most critical parameters to characterize its operation status. In this work, focusing on the power features of the half-open cavity RRFL, an ultrafast convergent power-balance model is proposed, which highlights the physical essence of the most common RRFL type and sharply reduces the computation workload. By transforming the time-consuming serial calculation to a parallel one, the calculation efficiency can be improved by more than 100 times. Particularly, for different point-mirror reflectivities and different fiber lengths, the input-output power curves and power distribution curves calculated by the present model match nicely with those of the conventional model, as well as with the experimental data. Moreover, through the present model the relationship between point-mirror reflectivity and laser threshold is analytically derived, and the way for improving RRFL’s slope efficiency is also provided with a lucid theoretical explanation.

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Fig. 1. The schematic diagram of the simplified RRFL.

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Fig. 2. The iterative block diagram for solving Eqs. (5) and (6).

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Fig. 3. Methods for solving the systems of differential equations of the RRFL: (a) traditional Euler method; (b) the method for solving UCM used in "loop body one".

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Fig. 4. The power distribution for (a) forward pump wave; (b) backward Stokes wave under 20 km backward-pumped structure with initial value

$P_{p}^{+}\left ( 0 \right )=2$

W and

$P_{s}^{-}\left ( 0 \right )=0.2$

W. After cycle once: Time

$T_3$

in Fig. 3(b).

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Fig. 5. Output power vs. pump power for some typical half-open cavity RRFL structure. UCM: ultrafast convergent power-balance model.

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Fig. 6. Comparison between the conventional model and the UCM for the half-open cavity RRFL. (a-c) backward-pumped RRFL; (d-f) forward-pumped RRFL. (a) and (d) Raman output power vs. pump power with different reflectivity values; (b) and (e) power distribution with 25% reflective mirror at 2 W pump power; (c) and (f) the threshold of RRFL as a function of point-mirror reflectivity.

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Fig. 7. Comparison between the conventional model and the UCM with different fiber length: (a) backward-pumped RRFL; (b) forward-pumped RRFL.

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Tables (1)

Table 1. Parameters for the numerical calculation

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Equations (18)

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\frac{d P_{p}^{\pm}}{d x} \pm α_{p} P_{p}^{\pm} = \mp (\frac{ν_{p}}{ν_{s}}) g_{R} P_{p}^{\pm} (P_{s}^{+} + P_{s}^{-}) \pm ε_{p} P_{p}^{\mp},

\pm \frac{d P_{s}^{\pm}}{d x} + α_{s} P_{s}^{\pm} = g_{R} P_{s}^{\pm} (P_{p}^{+} + P_{p}^{-}) + ε_{s} P_{s}^{\mp},

P_{s}^{-} (0) P_{s}^{+} (0) = P_{s}^{+} (x) P_{s}^{-} (x) = P_{s}^{+} (L) P_{s}^{-} (L) .

\frac{P_{A}}{P_{B}} = \frac{1 - R_{A}}{1 - R_{B}} \sqrt{\frac{R_{B}}{R_{A}}} .

\frac{d P_{p}^{+}}{d x} + α_{p} P_{p}^{+} = - \frac{1}{ν_{s}} g P_{p}^{+} P_{s}^{-},

- \frac{d P_{s}^{-}}{d x} + α_{s} P_{s}^{-} = \frac{1}{v_{p}} g P_{s}^{-} P_{p}^{+},

P_{p}^{+} (0) = P_{i n},

P_{s}^{-} (L) = \sqrt{R_{e f f}} \sqrt{R} P_{s}^{-} (0),

\frac{d P_{s}^{+}}{d x} + α_{s} P_{s}^{+} = \frac{1}{v_{p}} g P_{s}^{+} P_{p}^{+},

P_{s}^{+} (0) = \sqrt{R_{e f f}} \sqrt{R} P_{s}^{+} (L) .

\sqrt{R_{e f f}} = \frac{1}{\sqrt{R}} \exp (- g_{R} P_{t h} L_{e f f} + α_{s} L),

P_{t h} (R) = - \frac{1}{G} \ln (R) + κ,

P_{p}^{+} (x) = P_{p}^{+} (0) e^{- α_{p} x} \exp [- \frac{g}{ν_{s}} \int_{0}^{x} P_{s}^{-} (x) d x],

P_{s}^{-} (x) = P_{s}^{-} (0) e^{α_{s} x} \exp (- \frac{g}{ν_{p}} \int_{0}^{x} P_{p}^{+} (x) d x),

\sqrt{R_{e f f}} \sqrt{R} = e^{α_{s} L} \exp (- \frac{g}{ν_{p}} \int_{0}^{L} P_{p}^{+} (x) d x) .

P_{s}^{-} (x) = P_{s}^{-} (0) e^{α_{s} x} \exp (- \frac{g}{ν_{p}} P_{p}^{+} (0) x) .

P_{p}^{+} (x) = P_{p}^{+} (0) \exp {- α_{p} x - \frac{g ν_{p} P_{s}^{-} (0)}{ν_{s} [α_{s} ν_{p} - g P_{p}^{+} (0)]} [e^{(α_{s} - \frac{g}{ν_{p}} P_{p}^{+} (0)) x} - 1]} .

P_{s}^{+} (x) = P_{s}^{+} (0) e^{- α_{s} x} \exp (\frac{g}{ν_{p}} \int_{0}^{x} P_{p}^{+} (x) d x) .

Wavelength (nm)	$α$ (dB/km)	$ε$ ( $k m^{- 1}$ )	$g_{R}$ ( $W^{- 1} k m^{- 1}$ )
1365	0.31	$1 \times 10^{- 4}$	0.53
1455	0.24	$6 \times 10^{- 5}$	-

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Tables (1)

Equations (18)

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