Numerical modeling of Dy<sup>3+</sup>-doped aluminosilicate fiber lasers for yellow light emission

Jinho Lee; Yan Ososkov; Stuart D. Jackson

doi:10.1364/AO.516066

Applied Optics
Vol. 63,
Issue 14,
pp. D1-D6
(2024)
•https://doi.org/10.1364/AO.516066

Numerical modeling of Dy³⁺-doped aluminosilicate fiber lasers for yellow light emission

Jinho Lee, Yan Ososkov, and Stuart D. Jackson

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Jinho Lee, Yan Ososkov, and Stuart D. Jackson, "Numerical modeling of Dy³⁺-doped aluminosilicate fiber lasers for yellow light emission," Appl. Opt. 63, D1-D6 (2024)

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Abstract

Numerical simulations of ${{\rm Dy}^{3 +}}$-doped aluminosilicate fiber lasers for yellow light emission are presented. The $^4{{\rm F}_{9/2}}\;{\to ^6}{{\rm H}_{13/2}}$ laser transition emitting at approximately 580 nm has been developed experimentally with 445 nm diode pumping and shows promise for higher output power in both silicate and in particular fluoride glass hosts. In this report, we focus on accumulating the published spectroscopic data in order to quantify cross relaxation (CR) in each of these hosts and use it to estimate its role in the laser dynamics. The model involves calculation of the branching ratios, and radiative and nonradiative decay rates and compares well with reported experimental results. We show the important role of the background losses on previous laser performance and the relatively strong increase in the laser threshold as a result of CR despite the moderately low ${{\rm Dy}^{3 +}}$ concentrations that have been experimentally tested.

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Data availability

The data that supports the findings of this study is available from the corresponding author upon reasonable request.

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Fig. 1. Variation of the measured fluorescence lifetimes of the

$^4{{\rm F}_{9/2}}$

level with increasing

${{\rm Dy}^{3 +}}$

ion concentration in silicate glasses (black, [7,8,15–19]) and ZBLAN glasses (red, [20–22]).

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Fig. 2. Energy level diagram of

${{\rm Dy}^{3 +}}$

ions showing excitation, emission transitions, nonradiative decay, and cross-relaxation (CR) channels in silicate glass.

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Fig. 3. Measured experimental upper laser level lifetimes [7,8,15–19] and the deduced CR energy transfer rates in an assortment of

${{\rm Dy}^{3 +}}$

-doped (high) silicate glasses with changing

${{\rm Dy}^{3 +}}$

concentration.

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Fig. 4. (a) Absorption cross-section and (b) emission cross-section of

${{\rm Dy}^{3 +}}$

ions in silicate and ZBLAN glasses.

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Fig. 5. Laser schematic for the numerical simulation.

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Fig. 6. Measured experimental upper laser level lifetimes [20–22] and the deduced CR decay rates in an assortment of

${{\rm Dy}^{3 +}}$

-doped ZBLAN glasses with changing

${{\rm Dy}^{3 +}}$

concentration.

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Fig. 7. Calculated output power versus the launched pump power into the core of two

${{\rm Dy}^{3 +}}$

-doped silicate fibers (

${{P}_{\rm{th}}}$

: threshold pump power,

$\eta$

: efficiency). Included with the calculations are the published experimental results for (a) aluminosilicate glass [7] with

${L} = {0.27}\;{\rm m}$

${\rm Con}. = 1.3 \times \;{10^{20}}\;{\rm ions/cc}$

${\rm HR} = {99}\%$

${\rm OC} = {11}\%$

${\alpha _{\rm{pump}}} = {7}\;{\rm dB/m}$

${\alpha _{\rm{laser}}} = {0.7}\;{\rm dB/m}$

and (b) germano-aluminosilicate glass [8] with

${L} = {0.685}\;{\rm m}$

${\rm Con}. = 0.373 \times {10^{20}}\;{\rm ions/cc}$

${\rm HR} = {99.2}\%$

${\rm LR} = {94.1}\%$

${\alpha _{\rm{pump}}}= {0.14}\;{\rm dB/m}$

${\alpha _{\rm{laser}}}= {0.05}\;{\rm dB/m}$

. (

$\alpha$

represents the background loss).

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Tables (2)

Table 1. Used Parameters in This Simulation

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Table 2. Calculations for Yellow Light Emission from Silicate Fiber Lasers Showing the Influence of CR

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Equations (12)

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W_{N R} = B {n (T) + 1}^{p} e x p (- α Δ E),

n (T) = \frac{1}{e x p (ℏ ω / k T) - 1},

\frac{1}{τ_{e x p}} = \frac{1}{τ_{r a d}} + W_{N R} + W_{C R},

W_{C R} = \frac{1}{τ_{e x p}} - \frac{1}{τ_{r a d}} - W_{N R} .

\frac{d N}{d t} = LN + W,

L = [\begin{matrix} - \sum_{i = 0}^{m - 1} R_{0 i} & . . . & R_{(m - 1) 0} \\ . . . & . . . \\ R_{0 (m - 1)} & - \sum_{i = 0}^{m - 1} R_{(m - 1) i} \end{matrix}],

R_{ij} = \frac{β_{ij}}{τ_{i}} + W_{ij}^{N R} + \sum_{γ} σ_{ij} (λ) \frac{P (λ) Γ (λ)}{(A_{c o r e} \times h c / λ)},

\begin{aligned} \frac{d P^{\pm} (λ, z)}{d z} & = \pm (P^{\pm} (λ, z) (Γ (λ) [\sum_{i, j} σ_{ij} (λ) N_{i} (z) \\ - σ_{ji} (λ) N_{j} (z)] - l (λ)) + P_{s p o n} (λ)), \end{aligned}

P^{-} (z = L, λ) = R_{e n d} (λ) P^{+} (z = L, λ),

\begin{aligned} P^{+} (z = L, λ) \\ = R_{f r o n t} (λ) P^{-} (z = 0, λ) + (1 - R_{f r o n t} (λ)) P_{i n, f r o n t} (λ), \end{aligned}

P_{o u t p u t} (λ) = (1 - R_{e n d} (λ) P^{+} (z = L, λ) .

C_{D X} = \frac{3 c}{8 π^{4} n^{2}} \int σ_{e m}^{D} (λ) σ_{a b}^{X} (λ) d λ,

Parameters	Values	Sources
$σ_{a b s}$ (445 nm)	$5 \times 10^{- 26} m^{2}$	Fig. 4(a)
$σ_{e m i}$ (580 nm)	$1.2 \times 10^{- 25} m^{2}$	Fig. 4(b)
$β_{10 \to 1}$	0.5852	Calculated
$β_{10 \to 0}$	0.2224	Calculated
$τ_{10, r}$	1.496 ms	Calculated
$W_{10 \to 9}^{N R}$	$1.08 \times 10^{- 4} s^{- 1}$	Calculated
$R_{f r o n t}$ at 580 nm	0.99	–
$R_{e n d}$ at 580 nm	0.95	–
Length	0.5 m	–

	Efficiency (%)	Threshold (mW)
Without CR	$\sim 1.0$	$\sim 477$
With CR	$\sim 0.98$	$\sim 612$

Parameters	Values	Sources
$σ_{a b s}$ (445 nm)	$5 \times 10^{- 26} m^{2}$	Fig. 4(a)
$σ_{e m i}$ (580 nm)	$1.2 \times 10^{- 25} m^{2}$	Fig. 4(b)
$β_{10 \to 1}$	0.5852	Calculated
$β_{10 \to 0}$	0.2224	Calculated
$τ_{10, r}$	1.496 ms	Calculated
$W_{10 \to 9}^{N R}$	$1.08 \times 10^{- 4} s^{- 1}$	Calculated
$R_{f r o n t}$ at 580 nm	0.99	–
$R_{e n d}$ at 580 nm	0.95	–
Length	0.5 m	–

	Efficiency (%)	Threshold (mW)
Without CR	$\sim 1.0$	$\sim 477$
With CR	$\sim 0.98$	$\sim 612$

Abstract

Data availability

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Figures (7)

Tables (2)

Equations (12)

Applied Optics