Simulation and analysis of the time evolution of laser power and temperature in static pulsed XPALs 
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Department of Physics, Zhejiang University, Hangzhou 310027, China
Figures & Tables
Fig. 1. Schematic diagram of the XPAL configuration.
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Fig. 2. Four-level system of XPAL.
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Fig. 3. Flow diagram of iterative operation.
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Fig. 4. Temperature and output laser power as functions of time in an XPAL under single long-time pulse pumping.
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Fig. 5. Schematic diagram of the temperature distribution in the cell after the pump light is turned on for 8 ms.
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Fig. 6. (a) Relationship between the output laser power and time under different initial temperature conditions; (b) peak optical–optical efficiency of laser at different initial temperatures.
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Fig. 7. Power and temperature as functions of time in a multi-pulse XPAL with a rectangular shape pump light. (a) Turn on the pump light again when the temperature rise drops to $1/3$ of its maximum; (b) turn on the pump light again when the temperature rise drops to $1/2.5$ of its maximum; (c) turn on the pump light again when the temperature rise drops to $1/2$ of its maximum.
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Fig. 8. Graphical representation of the data in Table 2.
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Fig. 9. Power and temperature as functions of time in a multi-pulse XPAL with different initial temperatures. All the pump light is turned on again when the temperature rise drops to $1/2$ of its maximum. (a) $T_{0}=410$ K; (b) $T_{0}=420$ K; (c) $T_{0}=430$ K; (d) $T_{0}=440$ K.
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Fig. 10. Graphical representation of the data in Table 3.
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Table1. Parameters in the simulation.
| Parameter | Description | Value |
|---|
| $L$ | Length of the cell | 2 cm | | $R$ | Radius of the cell | 1.2 cm | | $[\text{Ar}]$ | Concentration of Ar | $2.5\times 10^{25}~\text{m}^{-3}$ | | $P_{\text{Cs}}$ | Pressure of Cs vapor at a temperature of $T_{0}$ | $10^{9.171{-}3830/T_{0}}$ | | $\unicode[STIX]{x1D70F}_{D1}$ | Lifetime of a particle at the $\text{B}^{2}\unicode[STIX]{x03A3}_{1/2}^{+}$ state | 30.5 ns | | $\unicode[STIX]{x1D70E}_{D2}$ | Stimulated emission cross-section of the D2 line | $5.54\times 10^{-17}~\text{m}^{2}$ | | $\unicode[STIX]{x1D708}_{\text{abs}}$ | Central frequency of the absorption line | $3.5830\times 10^{14}~\text{Hz}$ | | $\unicode[STIX]{x0394}\unicode[STIX]{x1D708}_{\text{abs}}$ | Linewidth of the absorption line | ${\sim}2$ nm | | $\unicode[STIX]{x1D708}_{p}$ | Central frequency of the pump line | $3.5830\times 10^{14}~\text{Hz}$ | | $\unicode[STIX]{x0394}E_{10}$ | Energy gap between the states 1 and 0 | $10~\text{cm}^{-1}$ | | $\unicode[STIX]{x0394}E_{23}$ | Energy gap between the states 2 and 3 | $249~\text{cm}^{-1}$ | | $R_{0}$ | Internuclear distance | $4.5\times 10^{-10}~\text{m}$ | | $\unicode[STIX]{x0394}R$ | Range of the internuclear distance | $1\times 10^{-10}~\text{m}$ | | $k_{ij}$ | Equilibrium constant between the energy levels | [10] | | $k_{\text{abs}}$ | Reduced absorption coefficient | $1.3\times 10^{-36}~\text{cm}^{5}$ | | $R_{oc}$ | Reflectivity of the output coupler | 0.75 | | $R_{p}$ | Reflectivity of the back reflector | 0.98 | | $T_{l}$ | Single-pass cell window transmission | 0.98 | | $T_{s}$ | Intra-cavity single-pass losses | 0.9 | | $w_{0,p}$ | Waist of the pump beam | $5\times 10^{-4}~\text{m}$ | | $w_{0,l}$ | Waist of the laser beam | $4\times 10^{-4}~\text{m}$ |
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Table2. Data for the multi-pulse XPAL at $T_{0}=410$ K in Figure 7.
| Parameter | (a) | (b) | (c) |
|---|
| Thermal relaxation time (ms) | 3.88 | 2.53 | 1.65 | | Recovery coefficient | 0.77 | 0.73 | 0.68 | | Temporal linewidth of the laser (except the first pulse) (ms) | 0.95 | 0.83 | 0.68 | | Average power of the laser for a single pulse (except the first pulse) (W) | 13.30 | 12.91 | 12.38 | | Number of pulses in 12 ms | 3 | 4 | 5 | | Total energy of the laser in 12 ms (mJ) | 54.35 | 61.70 | 63.17 |
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Table3. Data for the multi-pulse XPAL with different $T_{0}$ in Figure 9.
| Parameter | (a) | (b) | (c) | (d) |
|---|
| Initial temperature (K) | 410 | 420 | 430 | 440 | | Maximum temperature rise (K) | 170.3 | 195.8 | 206.4 | 229.5 | | Thermal relaxation time (ms) | 1.88 | 1.38 | 1.18 | 1.08 | | Maximum optical–optical efficiency (%) | 0.085 | 0.135 | 0.208 | 0.315 | | Recovery coefficient | 0.68 | 0.65 | 0.64 | 0.63 | | Temporal linewidth of the laser (except the first pulse) (ms) | 0.68 | 0.43 | 0.28 | 0.18 | | Average power of the laser for a single pulse (except the first pulse) (W) | 12.38 | 18.72 | 28.61 | 42.38 | | Number of pulses in 7 ms | 3 | 4 | 5 | 6 | | Total energy of the laser in 7 ms (mJ) | 46.46 | 51.64 | 57.16 | 62.37 |
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Chenyi Su, Binglin Shen, Xingqi Xu, Chunsheng Xia, Bailiang Pan. Simulation and analysis of the time evolution of laser power and temperature in static pulsed XPALs[J]. High Power Laser Science and Engineering, 2019, 7(3): 03000e44.
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