Researching | Modeling of three-dimensional exciplex pumped fluid Cs vapor laser with transverse and longitudinal gas flow

Journals >High Power Laser Science and Engineering >Volume 9 >Issue 2 >Page 02000e26 > Article

High Power Laser Science and Engineering
Vol. 9, Issue 2, 02000e26 (2021)

Modeling of three-dimensional exciplex pumped fluid Cs vapor laser with transverse and longitudinal gas flow

Chenyi Su¹, Xingqi Xu^1,2, Jinghua Huang¹, and Bailiang Pan^1,*

Author Affiliations

¹Department of Physics, Zhejiang University, Hangzhou310027, China

²Interdisciplinary Center for Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Department of Physics, Zhejiang University, Hangzhou310027, China

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DOI: 10.1017/hpl.2021.8 Cite this Article Set citation alerts

Chenyi Su, Xingqi Xu, Jinghua Huang, Bailiang Pan, "Modeling of three-dimensional exciplex pumped fluid Cs vapor laser with transverse and longitudinal gas flow," High Power Laser Sci. Eng. 9, 02000e26 (2021) Copy Citation Text

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Abstract

Considering the thermodynamical fluid mechanics in the gain medium and laser kinetic processes, a three-dimensional theoretical model of an exciplex-pumped Cs vapor laser with longitudinal and transverse gas flow is established. The slope efficiency of laser calculated by the model shows good agreement with the experimental data. The comprehensive three-dimensional distribution of temperature and particle density of Cs is depicted. The influence of pump intensity, wall temperature, and fluid velocity on the laser output performance is also simulated and analyzed in detail, suggesting that a higher wall temperature can guarantee a higher output laser power while causing a more significant heat accumulation in the cell. Compared with longitudinal gas flow, the transverse flow can improve the output laser power by effectively removing the generated heat accumulation and alleviating the temperature gradient in the cell.

Keywords

excimer lasers gas flow simulation theoretical model

\begin{aligned} \frac{d n_{1} (x, y, z)}{d t} & = k_{01} n_{0} (x, y, z) [Ar] - k_{10} n_{1} (x, y, z) - P_{12} (x, y, z), \end{aligned}

((1))

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\begin{aligned} \frac{d n_{2} (x, y, z)}{d t} & = P_{12} (x, y, z) - k_{23} n_{2} (x, y, z) \\ + k_{32} n_{3} (x, y, z) [Ar], \end{aligned}

((2))

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\begin{aligned} \frac{d n_{3} (x, y, z)}{d t} & = - L_{30} (x, y, z) + k_{23} n_{2} (x, y, z) \\ - k_{32} n_{3} (x, y, z) [Ar] + A_{43} (x, y, z) \\ - A_{30} (x, y, z) - {E p}_{34} (x, y, z) - {P h e}_{34} (x, y, z) \\ - P e n (x, y, z), \end{aligned}

((3))

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\begin{aligned} \frac{d n_{4} (x, y, z)}{d t} & = E p_{34} (x, y, z) - P e n (x, y, z) - A_{43} (x, y, z) \\ + R_{2} (x, y, z) - P h i_{45} (x, y, z) + P h e_{34} (x, y, z), \end{aligned}

((4))

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\begin{aligned} \frac{d n_{5} (x, y, z)}{d t} & = P h i_{45} (x, y, z) + P e n (x, y, z) - R_{1} (x, y, z), \end{aligned}

((5))

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\begin{aligned} \frac{d n_{6} (x, y, z)}{d t} & = R_{1} (x, y, z) - R_{2} (x, y, z), \end{aligned}

((6))

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\begin{aligned} \frac{d n_{0} (x, y, z)}{d t} & = N_{Cs} (x, y, z) - \sum_{i = 1}^{i = 6} n_{i} (x, y, z), \end{aligned}

((7))

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\begin{aligned} L_{30} (x, y, z) & = [n_{3} (x, y, z) - 2 n_{0} (x, y, z)] σ_{D 1} \\ \cdot \frac{f_{l} (x, y, z) [P_{l}^{+} (x, y, z) + P_{l}^{-} (x, y, z)]}{h ν_{l}}, \end{aligned}

((8))

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\begin{aligned} P_{12} (x, y, z) & = [n_{1} (x, y, z) - n_{2} (x, y, z)] \\ \cdot \int \frac{σ_{D 2} (ν) f_{p} (x, y, z) P_{p} (x, y, z, ν)}{h ν_{p}} d ν, \end{aligned}

((9))

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\begin{array}{r} P_{p} (x, y, 0, ν) = P_{p, 0} \frac{2}{ν_{p}} \sqrt{\frac{\ln 2}{π}} \exp [- 4 \ln 2 \frac{{(ν - ν_{p})}^{2}}{Δ {ν_{p}}^{2}}], \end{array}

((10))

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\begin{array}{r} f_{p, l} (x, y, z) = \frac{\sqrt{2}}{π w_{p, l} {(z)}^{2}} \exp {- \sqrt{2} [\frac{x^{2} + y^{2}}{w_{p, l} {(z)}^{2}}]}, \end{array}

((11))

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\begin{array}{r} w_{p, l} (z) = w_{0, p, l} \sqrt{{[\frac{(z - z_{0, p, l}) λ_{p, l}}{π w_{0, p, l}}]}^{2} + 1}, \end{array}

((12))

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\begin{aligned} P_{p} (x, y, z + Δ z) = P_{p} (x, y, z) \cdot \sum_{S} f_{p} (x, y, z) \\ \cdot \exp {- [n_{1} (x, y, z) - n_{2} (x, y, z)] σ_{D 2} (ν) Δ z} Δ x Δ y, \end{aligned}

((13))

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\begin{aligned} P_{l}^{\pm} (x, y, z + Δ z) = P_{l}^{\pm} (x, y, z) \cdot \sum_{S} f_{l} (x, y, z) \\ \cdot \exp {\pm [n_{3} (x, y, z) - 2 n_{0} (x, y, z)] σ_{D 1} Δ z} Δ x Δ y, \end{aligned}

((14))

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\begin{aligned} P_{l}^{-} (0) & = \frac{P_{l}}{T_{l} (1 - R_{oc})}, \end{aligned}

((15))

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\begin{aligned} P_{l}^{+} (0) & = \frac{P_{l} T_{l} R_{oc}}{1 - R_{oc}} . \end{aligned}

((16))

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\begin{aligned} Ω (x, y, z) & = Δ x Δ y Δ z {[k_{01} n_{0} (x, y, z) [Ar] - k_{10} n_{1} (x, y, z)] \\ \cdot Δ E_{10} + [- k_{32} n_{3} (x, y, z) [Ar] + k_{23} n_{2} (x, y, z)] \\ \cdot Δ E_{23} + R_{2} (x, y, z) E_{io}}, \end{aligned}

((17))

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\begin{array}{r} H_{c} (x, y, z) = 2 π Δ z \frac{k_{e} [T (x, y, z) - T_{w}]}{\ln (R / \sqrt{x^{2} + y^{2}})}, \end{array}

((18))

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\begin{aligned} F_{L} (x, y, z) & = {\begin{matrix} \frac{u Δ x Δ y n_{t} (x, y, z)}{N_{A}} \int_{T_{w}}^{T (x, y, z)} C_{p} (T^{'}) d T^{'}, z = 0, \\ \frac{u Δ x Δ y n_{t} (x, y, z)}{N_{A}} \int_{T (x, y, z - Δ z)}^{T (x, y, z)} C_{p} (T^{'}) d T^{'}, z > 0, \end{matrix} \end{aligned}

((19))

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\begin{aligned} F_{T} (x, y, z) & = {\begin{matrix} \frac{u Δ z Δ y n_{t} (x, y, z)}{N_{A}} \int_{T_{w}}^{T (x, y, z)} C_{p} (T^{'}) d T^{'}, x = 0, \\ \frac{u Δ z Δ y n_{t} (x, y, z)}{N_{A}} \int_{T (x - Δ x, y, z)}^{T (x, y, z)} C_{p} (T^{'}) d T^{'}, x > 0, \end{matrix} \end{aligned}

((20))

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\begin{aligned} Φ (x, y, z) & = K (x, y, z) N u (x, y, z) \\ \cdot {\frac{Δ x Δ y}{Δ z} {[T (x, y, z + Δ z) - T (x, y, z)] \\ - [T (x, y, z) - T (x, y, z - Δ z)]} \\ + \frac{Δ y Δ z}{Δ x} {[T (x + Δ x, y, z) - T (x, y, z)] \\ - [T (x, y, z) - T (x - Δ x, y, z)]} \\ + \frac{Δ z Δ x}{Δ y} {[T (x, y + Δ y, z) - T (x, y, z)] \\ - [T (x, y, z) - T (x, y - Δ y, z)]}}, \end{aligned}

((21))

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\begin{array}{r} Ω (x, y, z) = F_{L, T} (x, y, z) + Φ (x, y, z) . \end{array}

((22))

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Chenyi Su, Xingqi Xu, Jinghua Huang, Bailiang Pan, "Modeling of three-dimensional exciplex pumped fluid Cs vapor laser with transverse and longitudinal gas flow," High Power Laser Sci. Eng. 9, 02000e26 (2021)

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