Simple and efficient method of lines based algorithm for modeling of erbium doped Q-switched fluoride fiber lasers

Slawomir Sujecki

doi:10.1364/JOSAB.33.002288

Journal of the Optical Society of America B
Vol. 33,
Issue 11,
pp. 2288-2295
(2016)
•https://doi.org/10.1364/JOSAB.33.002288

Simple and efficient method of lines based algorithm for modeling of erbium doped Q-switched fluoride fiber lasers

Slawomir Sujecki

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Slawomir Sujecki, "Simple and efficient method of lines based algorithm for modeling of erbium doped Q-switched fluoride fiber lasers," J. Opt. Soc. Am. B 33, 2288-2295 (2016)

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Abstract

An improved algorithm based on the method of lines for modeling of $Q$ -switched fluoride glass based erbium doped fiber lasers is presented. The algorithm uses the finite difference method to reduce partial differential equations to a set of ordinary differential equations. Unlike the method of characteristics, the ratio of the temporal and spatial step is not fixed. Thus computationally efficient algorithms with an adaptive step control for the solution of a set of ordinary differential equations can be directly applied. The performance of the improved algorithm against the standard one is compared. The results obtained show that the improved algorithm is significantly more computationally efficient.

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Equations (31)

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Parameter	Unit	Value
$b_{1} / b_{2}$		$0.1 / 0.16$
$W_{11}$	$m^{3} / s$	$1 \times 10^{- 24}$
$W_{22}$	$m^{3} / s$	$0.3 \times 10^{- 24}$
$λ_{p}$	m	$976 \times 10^{- 9}$
$λ_{s}$	m	$2.8 \times 10^{- 6}$
$σ_{GSA}$	$m^{2}$	$2.1 \times 10^{- 25}$
$σ_{SE}$	$m^{2}$	$4.5 \times 10^{- 25}$
$N_{Er}$	$1 / m^{3}$	$9.6 \times 10^{26}$
$L$	m	2.5
$Γ_{p}$		0.009
$Γ_{s}$		1.0
$α_{p}$	1/m	$23 \times 10^{- 3}$
$α_{s}$	1/m	$3.0 \times 10^{- 3}$
$R_{p} (z = 0)$		0
$R_{p} (z = L)$		0.04
$R_{s} (z = 0)$		0.96
$R_{s} (z = L)$		0.04
$A_{eff}$	$m^{2}$	$314 \times 10^{- 12}$

Parameter	Unit	Value
$τ_{1}$	ms	9.0
$τ_{2}$	ms	6.9
$τ_{3}$	μs	10
$τ_{4}$	μs	120
$β_{21}, β_{20}$		0.37, 0.63
$β_{32}, β_{31}, β_{30}$		0.99, 0.0, 0.01
$β_{43}, β_{42}, β_{41}, β_{40}$		0.85, 0.006, 0.004, 0.14

Pump Power $(z = 0) / W$	Output Power $(z = L_{fib}) / W$	CPU Time/s
5	1.39527600015	78.76
10	3.11902141885	85.94
15	4.85305182935	86.19
20	6.55663433930	84.27

Pump Power/W	First Order	Second Order
5	0.996	1.973
10	0.997	1.998
15	0.997	2.026
20	0.995	2.044

Parameter	Unit	Value
$b_{1} / b_{2}$		$0.1 / 0.16$
$W_{11}$	$m^{3} / s$	$1 \times 10^{- 24}$
$W_{22}$	$m^{3} / s$	$0.3 \times 10^{- 24}$
$λ_{p}$	m	$976 \times 10^{- 9}$
$λ_{s}$	m	$2.8 \times 10^{- 6}$
$σ_{GSA}$	$m^{2}$	$2.1 \times 10^{- 25}$
$σ_{SE}$	$m^{2}$	$4.5 \times 10^{- 25}$
$N_{Er}$	$1 / m^{3}$	$9.6 \times 10^{26}$
$L$	m	2.5
$Γ_{p}$		0.009
$Γ_{s}$		1.0
$α_{p}$	1/m	$23 \times 10^{- 3}$
$α_{s}$	1/m	$3.0 \times 10^{- 3}$
$R_{p} (z = 0)$		0
$R_{p} (z = L)$		0.04
$R_{s} (z = 0)$		0.96
$R_{s} (z = L)$		0.04
$A_{eff}$	$m^{2}$	$314 \times 10^{- 12}$

Abstract

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Equations (31)

Journal of the Optical Society of America B