Chinese Journal of Chemical Physics  2018, Vol. 31 Issue (6): 741-748

The article information

Shan He, Jun-zhi Chu, Dong Liu, Xue-yang Li, Jing-wei Guo, Jin-bo Liu, Shu Hu, Hui Li, Peng-yuan Wang, Ying Chen, Feng-ting Sang, Yu-qi Jin
何山, 褚俊植, 刘栋, 李学杨, 郭敬为, 刘金波, 胡墅, 李慧, 王鹏远, 陈莹, 桑凤亭, 金玉奇
Energy-Transfer Processes of Xe (6p[1/2]$_\textbf{0}$, 6p[3/2]$_\textbf{2}$, and 6p[5/2]$_\textbf{2}$) Atoms under the Condition of Ultrahigh Pumped Power
超高泵浦功率下的Xe(6p[1/2]$_\bf{0}$,6p[3/2]$_\bf{2}$和6p[5/2]$_\bf{2}$)原子的能量转移过程
Chinese Journal of Chemical Physics, 2018, 31(6): 741-748
化学物理学报, 2018, 31(6): 741-748
http://dx.doi.org/10.1063/1674-0068/31/cjcp1806142

Article history

Received on: June 15, 2018
Accepted on: August 22, 2018
Energy-Transfer Processes of Xe (6p[1/2]$_\textbf{0}$, 6p[3/2]$_\textbf{2}$, and 6p[5/2]$_\textbf{2}$) Atoms under the Condition of Ultrahigh Pumped Power
Shan Hea,b, Jun-zhi Chua,b, Dong Liua, Xue-yang Lia,b, Jing-wei Guoa, Jin-bo Liua, Shu Hua, Hui Lia, Peng-yuan Wanga, Ying Chena, Feng-ting Sanga, Yu-qi Jina     
Dated: Received on June 15, 2018; Accepted on August 22, 2018
a. Key Laboratory of Chemical Lasers, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, China;
b. University of Chinese Academy of Sciences, Beijing 100049, China
*Author to whom correspondence should be addressed. Jing-wei Guo, E-mail:jingweiguo@dicp.ac.cn
Abstract: The kinetic processes of Xe (6p[1/2]$_0$, 6p[3/2]$_2$, and 6p[5/2]$_2$) atoms under the focused condition were investigated. The atomic density of the laser prepared state significantly increases. Therefore, the probability of the energy-pooling between two high-lying atoms increases. There are three major types of the energy-pooling collisions. The first type is the energy-pooling ionization. Once the excitation laser is focused, the obvious ionization can be observed from the side window whenever the laser prepared state is 6p[1/2]$_0$, 6p[3/2]$_2$, or 6p[5/2]$_2$ state. Ionization of Xe is attributed to the energy-pooling ionization or a Xe$^*$ atom reabsorbing another excitation photon. The second type is energy-pooling with big energy difference. When the 6p[1/2]$_0$ state is the laser prepared state, the energy-pooling collision between two 6p[1/2]$_0$ atoms can produce one 5d[3/2]$_1$ atom and one 6s$'$[1/2]$_0$ atom. The third type is energy-pooling with small energy difference. The intensities of fluorescence lines are much stronger that five secondary 6p states act as the upper states, and the rising edges of these fluorescence lines are much steeper. The primary mechanism of generating the secondary 6p atoms is energy-pooling collision instead of collision relaxation. Based on the collision probability, the rate of energy-pooling between two 6p[1/2]$_0$ atoms is deduced (6.39$\times$10$^8$ s$^{-1}$). In addition, the 6s atoms also increase under the focused condition. Therefore, all the fluorescence lines are serious trailing by radiation trapping.
Key words: Energy-pooling    Kinetics    Xe    Ultrahigh pumped power    
Ⅰ. INTRODUCTION

Recently, diode-pumped metastable rare gas laser is a promising subject for its unique advantages including mild working conditions and inert chemical property etc. So many groups pay their attentions to this subject [1-9]. Heaven and co-workers have demonstrated a CW diode-pumped Ar$^*$ laser providing 4 W [9]. It is a great progress in the regime of diode-pumped rare gas laser.

The study about diode-pumped metastable Xe laser is sparse. In comparison with the lighter rare gas atoms, the metastable Xe atoms are easier to produce. However, the kinetics between the high-lying Xe states is very complex because the energy differences between the high-lying Xe states are relatively low. The energy-transfer processes between the high-lying Xe states have been studied [10, 11], but the power of the excitation laser is relatively low. However, the laser system usually requires high power pumped sources. Consequently, it is important to study the energy-transfer processes between the high-lying Xe states under the high power pumped condition.

Energy-pooling collisions can be produced in diode-pumped alkali lasers (DPAL) under the strong pumping condition [12]. Energy pooling is a kinetic process in which two excited atoms collide to produce one atom in a higher state and the other one in a lower state. This process has been widely studied in alkali metals [13, 14] and alkaline earth metals [15, 16]. However, studies about energy-pooling collision between the high-lying Xe states are sparse. The high-lying states of the rare gas atoms are more abundant. The type of energy-pooling collisions between the rare gas atoms probably is more abundant.

Previously, we have studied kinetics of the 6p[1/2]$_0$ state under the condition of strong excitation laser, and found that the high power of the excitation laser can trigger the ASE of 3408 nm (6p[1/2]$_0$-6s$'$[1/2]$_1$) [17]. We have also systematically studied the kinetics of 6p[1/2]$_0$ atoms in buffer gases and found that the Kr, Ar, and Ne buffer gases can accelerate the transfers of 6p[1/2]$_0$$\rightarrow$5d[1/2]$_1$ [18]. However, the energy-pooling collision has never been observed. Although the power of the excitation laser we used was relatively high, the energy-pooling collision may need even higher power.

In this work, the time-resolved fluorescence and ASE spectra were detected under the focused condition. Only when the excitation laser is resonant and focused, can ionization phenomenon be observed. The ionization should be produced by energy-pooling collision or the high-lying atoms reabsorbing excitation photons. When the laser prepared state is 6p[1/2]$_0$ state, two new ASE lines at 1732 nm (5d[3/2]$_1$-6p[5/2]$_2$) and 2026 nm (5d[3/2]$_1$-6p[3/2]$_1$) appear. The substantial 5d[3/2]$_1$ atoms are produced by energy-pooling collision between two 6p[1/2]$_0$ atoms. By virtue of the unique arrangements near the 5d[3/2]$_1$ and 6s$'$[1/2]$_0$ states, the probability of self-pooling can be pretty high. Besides, all the intensities of fluorescence lines with the higher states being secondary 6p states become stronger, and the rising edges of those lines are much steeper under the focused condition. Therefore, the primary mechanism of producing the secondary 6p atoms should be the energy-pooling collision instead of collision relaxation.

Ⅱ. EXPERIMENTS

The experimental apparatus has been described in detail previously [17, 18]. Only a brief description was given here. The excitation laser was obtained from the second harmonic of dye laser (Sirah CBST-LG-18-EG). The Xe (6p[1/2]$_0$, 6p[3/2]$_2$, and 6p[5/2]$_2$) atoms were prepared by two-photon excitation at wavelengths about 249.5, 252.4, and 255.9 nm, respectively. The dye laser was pumped by the third harmonic of a Nd:YAG laser (Beamtech SGR-10). A quartz lens ($f$=200 mm) was used to focus the excitation laser. A stainless-steel sample cell was used to contain the gases. It has four windows. One window is made of sapphire to ensure the MIR pass through. The rest three windows are made of fused quartz. An uncoated Si plate was placed between the sapphire window of the cell and the slit of the MIR monochromator (HORIBA micro HR MHRA-2A-MS). It can absorb the excitation laser and transmit the MIR ASE.

A series of lenses were placed along the axis perpendicular to the axis of excitation laser to collect the fluorescence. The focal point of the excitation laser and that of the fluorescence collection lens systems nearly overlapped. The fluorescence was separated by a monochromator (Princeton Instrument SpectraPro 2500i) with a 1200 g/mm grating. A single spontaneous emission line was measured by an APD and recorded by a 2 GHz oscilloscope (LeCroy waverunner 620zi). The schematic diagram is shown in FIG. 1.

FIG. 1 Schematic diagram of the experimental apparatus.

All the gases used in this experiment were ultrahigh purity: Xe (99.999%), Kr (99.999%), Ar (99.999%).

Ⅲ. RESULTS AND DISCUSSION

FIG. 2 shows the phenomena directly observed from the side window. Evidently, strong visible emissions are produced under the resonant and focused condition. The wavelengths of emissions with the upper states being six 6p states are all longer than 800 nm. So there is no visible emission under the resonant and unfocused condition. As a result, the upper states of these visible emissions are not the six 6p states. There must be some new processes happening under the resonant and focused condition. To probe the new process, the fluorescence spectrum is observed under the resonant and focused condition, as shown in FIG. 3. Firstly, the typical fluorescence lines of 6p-6s such as 828 nm (6p[1/2]$_0$-6s[3/2]$_1$), 823 nm (6p[3/2]$_2$-6s[3/2]$_2$), and 882 nm (6p[5/2]$_3$-6s[3/2]$_2$) are observed.Secondly, the continuous spectrum from 400-700 nm is obviously produced by ionization. The Xe atoms are ionized under the resonant and focused condition and these two factors are both indispensable. The ionization processes should occur as follows (Xe$^*$ is the laser prepared state including the 6p[1/2]$_0$, 6p[3/2]$_2$, and 6p[5/2]$_2$ states):

$ \textrm{Xe}^* + \textrm{Xe}^* \frac{\textrm{collision}}{}\hspace{-0.3cm}\rightarrow \textrm{Xe}_2{^ +} + \textrm{e} \rightarrow \textrm{Xe}^ + + \textrm{Xe} + \textrm{e} $ (1)
$ \textrm{Xe}^* + h\gamma \rightarrow \textrm{Xe}^ + $ (2)
FIG. 2 The phenomena directly observed from the side window. The experimental conditions from top to bottom are resonant and unfocused, non-resonant and focused, and resonant and focused, respectively. The excitation state is 6p[1/2]$_0$, 6p[3/2]$_2$, or 6p[5/2]$_2$. The pressure of Xe is 6.0 Torr. The energy of excitation laser is 2.30 mJ (3.54$\times$10$^{10}$ W/cm$^2$).
FIG. 3 Fluorescence spectrum under the resonant and focused condition. The laser prepared state is the 6p[1/2]$_0$ state. The pressure of Xe is 6.0 Torr. The energy of excitation laser is 2.30 mJ (3.54$\times$10$^{10}$ W/cm$^2$).

The first mechanism (reaction (1)) is the "energy-pooling ionization". Substantial Xe$^*$ atoms are generated near the focal point under the resonant and focused condition. It increases the probability of the effective collision between the two Xe$^*$ atoms. Since the potential energy of Xe$_2$$^+$ is $\sim$90000 cm$^{-1}$ [19], the potential energies of two Xe$^*$ atoms (higher than 154000 cm$^{-1}$) are high enough to trigger the reaction (1).

The second mechanism (reaction (2)) is that a Xe$^*$ atom absorbs another excitation photon. Not only the Xe$^*$ density but also the photon density of excitation laser is very high in the area near the focal point. Thus the probability of reaction (2) can also increase. In addition, the potential energy of Xe$^*$ is bigger than 78000 cm$^{-1}$. The energy of a $\sim$250 nm photon is $\sim$40000 cm$^{-1}$. The energy sum of a Xe$^*$ and an excitation photon is high enough to trigger the ionization. Because no ionization phenomenon appears under the non-resonant and focused condition, the mechanism of a ground state Xe atom absorbing three or more photons is excluded.

Thirdly, the atomic lines in 450-500 nm can be owed to the lines of 6p$'$-6s and 7p-6s, such as 450 nm (6p$'$[1/2]$_0$-6s[3/2]$_2$), 467 nm (7p[5/2]$_3$-6s[3/2]$_2$), 482 nm (7p[3/2]$_1$-6s[3/2]$_1$). The energy differences between the 6p[1/2]$_0$ state and 6p$'$, 7p states are $\sim$9000 cm$^{-1}$. Relaxation normally cannot produce exothermic transfer, let alone the exothermic transfer with such a big energy difference. The following two mechanisms may explain the production of 6p$'$ and 7p atoms. The first mechanism is a Xe$^+$ combining an electron to populate a 6p$'$ or 7p atom. The second mechanism is energy-pooling between two 6p[1/2]$_0$ atoms.

FIG. 4 is the mid-infrared ASE spectra measured in the forward direction along the excitation laser. The laser prepared state is the 6p[1/2]$_0$ state. As shown in FIG. 4(a), the intensity of ASE at 3408 nm (6p[1/2]$_0$-6s$'$[1/2]$_1$) in pure Xe under the focused condition is much stronger than that under the unfocused condition. The density of the 6p[1/2]$_0$ atoms significantly increases in the region near the focal point. It results in the high gain coefficient of the ASE at 3408 nm (6p[1/2]$_0$-6s$'$[1/2]$_1$). So the intensity of ASE at 3408 nm (6p[1/2]$_0$-6s$'$[1/2]$_1$) becomes stronger. Unexpectedly, new peaks at 1732, 2026, 3464, and 4052 nm emerge. The peaks at 1732 nm and 2026 nm should be attributed to the transfers of 5d[3/2]$_1$-6p[5/2]$_2$ and 5d[3/2]$_1$-6p[3/2]$_1$, respectively. And the peaks at 3464 and 4052 nm are the second order diffraction of the peaks at 1732 and 2026 nm, respectively. This phenomenon indicates substantial 5d[3/2]$_1$ atoms are produced. The kinetic process for the generation of 5d[3/2]$_1$ atoms should be energy-pooling collision illustrated as reaction (3). The probability of reaction (3) must be pretty high, because the population inversions can be formed between the 5d[3/2]$_1$ state and the 6p[5/2]$_2$, 6p[3/2]$_1$ states. This can be owed to the following two aspects. Firstly, the energy difference between the 6p[1/2]$_0$ state and the 5d[3/2]$_1$ state is very close to that between the 6p[1/2]$_0$ state and the 6s$'$[1/2]$_0$ state. To some extent, this energy-pooling collision is a near-resonance process. Secondly, the energy level arrangements near the 5d[3/2]$_1$ state and the 6s$'$[1/2]$_0$ state are unique. As shown in FIG. 5, both of these two states have big energy differences from the adjacent states:

$ \begin{eqnarray} &&{E}(7\textrm{s}[3/2]_2)-E(5\textrm{d}[3/2]_1){=1298.8 \hspace{0.15cm}\textrm{cm}^{-1}}, \\ &&{E}(5\textrm{d}[3/2]_1)-{E}(5\textrm{d}[5/2]_3)=1459.8 \hspace{0.15cm} \textrm{cm}^{-1}, \\ &&{E}(6\textrm{s}'[1/2]_1) -{E}(6\textrm{s}'[1/2]_0)=988.2 \hspace{0.15cm}\textrm{cm}^{-1}, \\ &&{E}(6\textrm{s}'[1/2]_0)-{E}(6\textrm{s}[3/2]_1)=8151.6 \hspace{0.15cm}\textrm{cm}^{-1} \end{eqnarray} $
FIG. 4 The mid-infrared ASE spectra in the forward direction along the excitation laser. The laser prepared state is the 6p[1/2]$_0$ state. The energy of excitation laser is 2.30 mJ (3.54$\times$10$^{10}$ W/cm$^2$). For clear comparison, the spectrum under the focused condition is moved upward 0.50 Arb. unit.
FIG. 5 Schematic diagram of the energy levels of Xe$^*$ related to this work. Each state is marked with its energy (in cm$^{-1}$) in reference to the ground state S$_0$.

Once one 6p[1/2]$_0$ atom reaches the 6s$'$[1/2]$_1$ state, another 6p[1/2]$_0$ atom strongly tends to reach the 5d[3/2]$_1$ state.

$ \textrm{ Xe}(6\textrm{p}[1/2]_0 ) + \textrm{Xe}\left( {6\textrm{p}[1/2]_0 } \right)\underrightarrow{{\rm{collision}}} \\ \;\;\;\;\;\;\textrm{Xe}(6\textrm{s}'[1/2]_0 ) + \textrm{Xe}(5\textrm{d}[3/2]_1 ){\kern 1pt} + \Delta E \\ \Delta E=-151.18 \;{\textrm{cm}}^{ - 1} $ (3)

Ar and Kr atoms can accelerate the transfer of 6p[1/2]$_0$$\rightarrow$5d[1/2]$_1$ [10, 11, 18]. Therefore, they can switch ASE channel from 3408 nm (6p[1/2]$_0$-6s$'$[1/2]$_1$) to 3680 nm (5d[1/2]$_1$-6p[1/2]$_1$) by collision [18]. Accordingly, ASE spectra in buffer gas of Ar or Kr have two peaks at 3408 and 3680 nm, as shown in FIG. 4 (b) and (c). The intensity of ASE at 3680 nm decreases and new peaks at 1732, 2026, 3464, and 4052 nm emerge under the focused condition. The probability of collision between one 6p[1/2]$_0$ atom and another atom is described as Eq.(4):

$ \begin{eqnarray} z = \pi d_{\textrm{AB}}^2 \sqrt {\frac{{8RT}}{{\pi \mu }}} n_\textrm{A} n_\textrm{B} \end{eqnarray} $ (4)

where $z$ is the collision probability between A and B, $d_{\textrm{AB}}$ is the sum of radius of A and B, $\mu$ is the reduced mass of A and B, $T$ is the temperature, $n_\textrm{A}$ and $n_\textrm{B}$ are the concentration of A and B, respectively.

Obviously, collision probability between A and B is proportional to the concentration of buffer atoms. Although the density of the 6p[1/2]$_0$ atoms near the focal point is high, it must be much lower than the density of Ar or Kr atoms ($D_{\textrm{Rg}}$=$\sim$2.57$\times$10$^{17}$ cm$^{-3}$). Consequently, the probability of collision between two 6p[1/2]$_0$ atoms is much lower than that between one 6p[1/2]$_0$ atom and one buffer gas atom. However, FIG. 4 (b) and (c) reflect that the primary kinetic process under the focused condition is the energy-pooling collision instead of collision relaxation. It indicates that the collision between two 6p[1/2]$_0$ atoms is more effective than that between a 6p[1/2]$_0$ atom and a buffer gas atom (Ar or Kr), because 6p[1/2]$_0$ atoms are more active than ground state Ar and Kr atoms.

Based on the analysis above, if the density of 6p[1/2]$_0$ atoms holds constant, the rate of energy pooling is constant. Some semi-quantitative deductions are given here. The pressure of Xe and excitation power hold constant. We suppose that the rate of energy-pooling is $V$. Then the Ar is filled into the cell. The probability of collision between Xe$^*$ and Ar increases. The rate of relaxation can be expressed as $\displaystyle{k_{6\textrm{p}[1/2]_0 , T}^{\textrm{Ar}} \times p}$. Ar can switch the ASE channel from 3408 nm (6p[1/2]$_0$-6s$'$[1/2]$_1$) to 3680 nm (5d[1/2]$_1$-6p[1/2]$_1$). It is attributed to the high value of $k_{6\textrm{p}[1/2]_0, 5\textrm{d}[1/2]_1 }^{\textrm{Ar}}$. With the increasing pressure of Ar, the ASE at 3680 nm should gradually increase, the ASE at 3408 and 1732 nm should gradually decrease. As shown in FIG. 6, the actual phenomenon precisely follows this prediction. Then the intensity of 3680 nm is proportional to $\displaystyle{\frac{{k_{6\textrm{p}[1/2]_0, 5\textrm{d}[1/2]_1 }^{\textrm{Ar}} \times p}}{{V + k_{6\textrm{p}[1/2]_0 , T}^{\textrm{Ar}} \times p}}}$ as Eq.(5).

$ \begin{eqnarray} I_{3680} \propto \frac{{k_{6\textrm{p}[1/2]_0, 5\textrm{d}[1/2]_1 }^{\textrm{Ar}} \times p}}{{V + k_{6\textrm{p}[1/2]_0 , T}^{\textrm{Ar}} \times p}} \end{eqnarray} $ (5)
FIG. 6 Plot of ASE at (a) 1732 nm, (b) 3408 nm, and (c) 3680 nm against pressures of Ar. The pressure of Xe is 6.0 Torr. The energy of excitation laser is 2.30 mJ (3.54$\times$10$^{10}$ W/cm$^2$).

Then we can introduce a parameter $\alpha$ to modify the intensity of 3680 nm. Eq.(5) can be rewritten as Eq.(6).

$ \begin{eqnarray} \alpha \times I_{3680} = \frac{{k_{6\textrm{p}[1/2]_0, 5\textrm{d}[1/2]_1 }^{\textrm{Ar}} \times p}}{{V + k_{6\textrm{p}[1/2]_0, T}^{\textrm{Ar}} \times p}} \end{eqnarray} $ (6)

According to this equation, $\displaystyle{\frac{1}{{I_{3680} }}}$ should be linear with $\displaystyle{\frac{1}{p}}$ as Eq.(7).

$ \begin{eqnarray} \frac{1}{{I_{3680} }} = \frac{{\alpha \times V}}{{k_{6\textrm{p}[1/2]_0, 5\textrm{d}[1/2]_1 }^{\textrm{Ar}} \times p}} + \frac{{\alpha \times k_{6\textrm{p}[1/2]_0, T}^{\textrm{Ar}} }}{{k_{6\textrm{p}[1/2]_0, 5\textrm{d}[1/2]_1 }^{\textrm{Ar}} }} \end{eqnarray} $ (7)

Then the slope $\displaystyle{\frac{{\alpha \times V}}{{k_{6\textrm{p}[1/2]_0, 5\textrm{d}[1/2]_1 }^{\textrm{Ar}} }}}$ and intercept $\displaystyle{\frac{{\alpha \times k_{6\textrm{p}[1/2]_0, T}^{\textrm{Ar}} }}{{k_{6\textrm{p}[1/2]_0, 5\textrm{d}[1/2]_1 }^{\textrm{Ar}} }}}$ can be deduced (FIG. 7). The value of $k_{6\textrm{p}[1/2]_0, T}^{\textrm{Ar}}$ and $k_{6\textrm{p}[1/2]_0, 5\textrm{d}[1/2]_1 }^{\textrm{Ar}}$ have been deduced in our previous work [18]. Then the parameter $\alpha$ can be deduced. The values of $\alpha$, $k_{6\textrm{p}[1/2]_0, 5\textrm{d}[1/2]_1 }^{\textrm{Ar}}$, and $\displaystyle{\frac{{\alpha \times V}}{{k_{6\textrm{p}[1/2]_0, 5\textrm{d}[1/2]_1 }^{\textrm{Ar}} }}}$ are all known. As a result, $V$=6.39$\times$10$^8$ s$^{-1}$.

FIG. 7 Plot of 1/$I_{3680}$ against 1/$p$. The pressure of Xe is 6.0 Torr. The buffer gas is Ar. The energy of excitation laser is 2.30 mJ (3.54$\times$10$^{10}$ W/cm$^2$). The line is the result of linear fitting.

When the laser prepared state is the 6p[1/2]$_0$ state, the time-resolved fluorescence lines of 6p-6s are shown in FIG. 8. The intensity of 828 nm under the focused condition is much stronger than that under the unfocused condition. It results from the high density of the 6p[1/2]$_0$ atom under the focused condition. The rest five fluorescence lines can reflect the populations of the five secondary 6p states. Under the unfocused condition, the primary mechanism generating the 6p[3/2]$_2$, 6p[3/2]$_1$, 6p[5/2]$_3$, and 6p[5/2]$_2$ atoms is collisional relaxation. The intensities of these fluorescence lines are weak. Obviously, the intensities of fluorescence lines of 823, 916, 882, and 904 nm are much stronger and their rising edges are much steeper under the focused condition. Therefore, a new mechanism, energy-pooling collision, should emerge under the focused condition described as reaction (8).

$ \textrm{Xe}(6\textrm{p}[1/2]_0 ) + \textrm{Xe}\left( {6\textrm{p}[1/2]_0 } \right) \underrightarrow{\text{collision}} \\ \;\;\;\;\;\textrm{Xe}(6\textrm{p}) + \textrm{Xe}(5\textrm{d}) $ (8)
FIG. 8 Time-resolved fluorescence lines of the six 6p states under the focused and unfocused conditions. The laser prepared state is the 6p[1/2]$_0$ state. The gases contain 6.0 Torr Xe and 8.7 Torr Ar. The energy of excitation laser is 2.30 mJ (3.54 $\times$10$^{10}$ W/cm$^2$). Note: 828 nm (6p[1/2]$_0$-6s[3/2]$_1$), 823 nm (6p[3/2]$_2$-6s[3/2]$_2$), 916 nm (6p[3/2]$_1$-6s[3/2]$_1$), 882 nm (6p[5/2]$_3$-6s[3/2]$_2$), 904 nm (6p[5/2]$_2$-6s[3/2]$_2$), and 980 nm (6p[1/2]$_1$-6s[3/2]$_2$).

Collision of this type between two 6p[1/2]$_0$ atoms can lead to one atom reaching a higher state and the other one reaching a lower state. Besides, the ASE at 1732 nm (5d[3/2]$_1$-6p[5/2]$_2$) and 2026 nm (5d[3/2]$_1$-6p[3/2]$_1$) can also populate the 6p[5/2]$_2$ state and the 6p[3/2]$_1$ state, respectively. This is another reason why the intensities of 916 and 904 nm become stronger. The dominant mechanism of populating 6p[1/2]$_1$ atoms is a series of processes related to the ASE at 3408 nm (6p[1/2]$_0$-6s$'$[1/2]$_1$) and 3680 nm (5d[1/2]$_1$-6p[1/2]$_1$) under the unfocused condition [17, 18]. According to FIG. 4, the intensity of ASE at 3408 nm increases and that at 3680 nm decreases under the focused condition. Thus the population of the 6p[1/2]$_1$ atoms should be mainly owed to the processes related to the ASE at 3408 nm. Another phenomenon shown in FIG. 8 is that all the fluorescence lines are serious trailing under the focused condition. The lifetimes of these states are $\sim$30 ns [10, 11, 17]. However, even at $\sim$1500 ns, all these fluorescence lines are still observed. It means that there still exist some channels populating these 6p atoms even at $\sim$1500 ns. Maybe the channel populating these 6p atoms be radiation trapping. This phenomenon was widely reported in high-lying states of alkali metals [20] and some states of rare gases [21]. The mechanism of this phenomenon is that radiation near a resonance line can be absorbed and emitted many times before escaping. Then, the apparent radiative lifetime of the higher state can be obviously extended by this effect. However, the prerequisite of radiation trapping is that the population density of the lower state is high enough. If the population density of the lower state is relatively low, the radiation cannot be effectively absorbed. Then, the radiation cannot be trapped by absorbing and emitting many times. The lifetimes of alkali metal states and 6s states of Xe are usually affected by this effect [20, 21], since the lower state is the ground state. However, the 6p states of Xe is ever hardly affected for the lower state being the 6s state. The situation may be different in our work. Not only the density of the 6p[1/2]$_0$ state but also those of the 6s states should be very high in the area near the focal point. Then the radiation lines with the higher states being the 6p states can be trapped. The trailing of the fluorescence line is probably due to this reason.

When the laser prepared state is the 6p[3/2]$_2$ state, time-resolved fluorescence lines of 6p-6s under both the focused and unfocused conditions are shown in FIG. 9. Under the unfocused condition, the fluorescence lines of 916, 882, 904, and 980 nm were observed, while that of 828 nm could not be observed. It indicates that the 6p[3/2]$_2$ atoms can reach the lower states including the 6p[3/2]$_1$, 6p[5/2]$_3$, 6p[5/2]$_2$, but the 6p[1/2]$_1$ state cannot reach the higher state (6p[1/2]$_0$). Collision relaxation usually cannot cause endothermic transfer with big energy difference. However, under the focused condition, the fluorescence at 828 nm is observed. The 6p[1/2]$_0$ atoms cannot be produced by collision relaxation. The mechanism is probably an energy-pooling process between two 6p[3/2]$_2$ atoms. Besides, intensities of all the fluorescence lines are much stronger and the rising edges of all the fluorescence lines are much steeper under the focused condition. It should also owe to the energy-pooling collision. Similar to the phenomenon shown in FIG. 8, the fluorescence lines are serious trailing under the focused condition. The reason is attributed to the radiation trapping. When the laser prepared state is the 6p[5/2]$_2$ state, time-resolved fluorescence lines of 6p-6s under the focused and unfocused conditions are shown in FIG. 10. The phenomena are similar to those shown in FIG. 9. The collision relaxation can cause the endothermic transfer of 6p[5/2]$_2$$\rightarrow$6p[5/2]$_3$ for small energy difference, but the endothermic transfers for big energy differences are hard to generate by collision relaxation. Therefore, the primary mechanism for producing the 6p[1/2]$_0$, 6p[3/2]$_2$, 6p[3/2]$_1$, and 6p[5/2]$_3$ atoms is the energy-pooling collision instead of collision relaxation under the focused condition. And the serious trailing is probably owed to the radiation trapping.

FIG. 9 Time-resolved fluorescence lines of the six 6p states under the focused and unfocused conditions. The laser prepared state is the 6p[3/2]$_2$ state. These plots were obtained in pure Xe. And the pressure of Xe is 6.0 Torr. The energy of excitation laser is 2.30 mJ (3.54$\times$10$^{10}$ W/cm$^2$).
FIG. 10 Time-resolved fluorescence lines of the six 6p states under the focused and unfocused conditions. The laser prepared state is the 6p[5/2]$_2$ state. These plots were obtained in pure Xe. And the pressure of Xe is 6.0 Torr. The energy of excitation laser is 1.50 mJ (2.31$\times$10$^{10}$ W/cm$^2$).
Ⅳ. CONCLUSION

The kinetic processes of Xe atoms in the 6p[1/2]$_0$, 6p[3/2]$_2$, and 6p[5/2]$_2$ states were studied under the focused condition. The density of the atoms in the laser prepared state under the focused condition is much higher than that under the unfocused condition. The atoms in the high-lying state are much more active than the atoms in the ground state. Then, the collision between two 6p[1/2]$_0$ atoms is more effective than that between a 6p[1/2]$_0$ atom and a buffer gas atom (Ar or Kr). Therefore, primary mechanism is the energy-pooling collision instead of the collision relaxation under the focused condition. Since the Xe states are more complex than alkali metals states, the energy-pooling collisions are more abundant among high-lying Xe atoms.

The phenomenon observed from the side window is the energy-pooling ionization. The energies of these three laser prepared states are all high enough to trigger the ionization. When the laser prepared state is the 6p[1/2]$_0$ state, two new ASE peaks at 1732 nm (5d[3/2]$_1$-6p[5/2]$_2$) and 2026 nm (5d[3/2]$_1$-6p[3/2]$_1$) appear. Thanks to the unique energy level arrangements near the 5d[3/2]$_1$ state and the 6s$'$[1/2]$_0$ state, two 6p[1/2]$_0$ atoms strongly tend to pool their internal energy to produce one 5d[3/2]$_1$ atom and one 6s$'$[1/2]$_0$ atom. Based on the collision probability, the rate of energy-pooling between two 6p[1/2]$_0$ atoms is deduced (6.39$\times$10$^8$ s$^{-1}$). The intensities of all the fluorescence curves increase and their rising edges are steeper under the focused condition. The atoms in the secondary states are mainly produced by energy-pooling collision. Another phenomenon is that even at $\sim$1500 ns, all these fluorescence lines are still observed, although the lifetimes of these states are $\sim$30 ns. The densities of the 6s states should be very high in the area near the focal point. Radiation near a resonance line can be absorbed and emitted many times before escaping. Then the apparent radiative lifetime of the higher state can be obviously extended. The mechanism is probably due to the radiation trapping.

Ⅴ. ACKNOWLEDGMENTS

This work was supported by the National Natural Science Foundation of China (No.11475177 and No.61505210) and Key Laboratory of Chemical Laser Foundation (KLCL 2017).

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超高泵浦功率下的Xe(6p[1/2]$_\bf{0}$,6p[3/2]$_\bf{2}$和6p[5/2]$_\bf{2}$)原子的能量转移过程
何山a,b, 褚俊植a,b, 刘栋a, 李学杨a,b, 郭敬为a, 刘金波a, 胡墅a, 李慧a, 王鹏远a, 陈莹a, 桑凤亭a, 金玉奇a     
a. 中国科学院化学激光重点实验室,中国科学院大连化学物理研究所,大连 116023;
b. 中国科学院大学,北京 100049
摘要: 本文研究了Xe(6p[1/2]$_0$,6p[3/2]$_2$和6p[5/2]$_2$)原子在聚焦条件下的动力学过程.激发能级的原子密度在聚焦条件下会显著地增加,因此两个高激发态原子之间的energy-pooling碰撞的概率也会增加.这种energy-pooling碰撞主要有三种类型.第一种类型为energy-pooling碰撞导致的电离.一旦将激发激光聚焦,就可以从侧面的窗口观察到非常明显的电离现象,不论激发能级是6p[1/2]$_0$、6p[3/2]$_2$或6p[5/2]$_2$能级.这种电离的产生机理是energy-pooling电离或者一个Xe$^*$原子再吸收一个光子产生电离.第二种类型为跨越较大能极差的energy-pooling碰撞.当激发能级为6p[1/2]$_0$能级的情况下,两个6p[1/2]$_0$原子碰撞会产生一个5d[3/2]$_1$原子和一个6s$'$[1/2]$_0$原子.第三种类型为跨越较小能级差的energy-pooling碰撞.以5个二次产生的6p能级为上能级的荧光强度都变得更强,并且这些荧光的上升沿都变得更陡峭.产生这些6p原子的主要机理是energy-pooling碰撞并非简单的碰撞弛豫.基于理想气体原子之间的碰撞概率公式,推导出两个6p[1/2]$_0$原子的energy-pooling碰撞速率为6.39$\times$10$^8$ s$^{-1}$.此外,6s原子在聚焦条件下的密度也会增加.因此所有的荧光曲线会因为辐射俘获效应而出现非常严重的拖尾.
关键词: 能量池碰撞    动力学        超高激发功率