Modeling of diode pumped metastable rare gas lasers

Zining Yang; Guangqi Yu; Hongyan Wang; Qisheng Lu; Xiaojun Xu

doi:10.1364/OE.23.013823

1. Introduction

Diode pumped alkali vapor lasers (DPALs) provide a possible way for efficient conversion of high power diode laser output into single aperture scaled gas laser output with high beam quality [1–4]. Till now, a Cs DPAL with power of ~1kW and optical conversion efficiency of ~48% has been realized [5]. However, due to the highly reactive nature of alkali metals, there are chemical reaction challenges and engineering difficulties for DPALs. For example, under high intense pumping, the alkali atoms may react with hydrocarbons [6, 7] and window materials [8], which deplete the neutral alkali atoms and contaminate the windows. As vapor rather than gas, the concentration of alkali atoms is highly dependent on the gain cell’s temperature, especially the coldest point of the total gain cell, which enhances the engineering complexity. Solutions are being investigated, including using high pressure helium (~10atm) as the only buffer gas instead of hydrocarbons [9], sapphire windows with AR microstructures (ARMs) [10] etc.

As an alternative, Han and Heaven proposed and demonstrated a new type of optically pumped gas laser in year 2012 — the optically pumped metastable rare gas laser (OPRGL) [11]. OPRGLs are kinetically analogous to DPALs, due to the similarity of energy structures between metastable rare gas atoms (Rg*) and alkali atoms. The electrical discharge produced metastable 1s₅ state (Paschen notation) is used as the common lower pump and laser level. The pump light excites the 1s₅ state into 2p₉ state, and lasing process occurs from 2p₁₀ to 1s₅. The population transfer from 2p₉ to 2p₁₀ is realized through collisional relaxation by adding helium. The pump wavelengths of OPRGLs are within the range of the current high power diode laser wavelengths (811.6nm for Ar*, 811.5nm for Kr* and 882.2nm for Xe*), and the quantum efficiencies are high (89% for Ar*, 91% for Kr* and 98% for Xe*). From the physical point of view, both DPALs and OPRGLs are potential candidates for high power single aperture scaled lasers. A great advantage of OPRGLs is their usage of noble gas only, which makes these lasers inherently chemical inert. So no issues of chemical reaction, materials handling etc. have to be considered. In 2012, Han et al. have firstly demonstrated lasing in optically pumped Ar*, Kr* and Xe* by using pulsed electrical discharge and pulsed laser excitation [11]. In 2013, they realized an Ar* laser by using cw diode pumping source and pulsed electrical discharge [12]. In the same year, Rawlins et al. realized the first cw Ar* laser by using microwave frequency microplasma discharge [13]. Due to the observation of much shorter laser pulse duration than the discharge pulse duration, kinetics of OPRGLs that mainly focused on the influence of an intermediate 1s₄ state have been studied [14]. Demyanov et al. have theoretically modeled the OPRGLs by considering the required discharge power [15].

In this paper, with the aim to get a further understanding of OPRGLs’ kinetics, we have set up a model by considering more complete energy levels that are involved. A comparison with Rawlins et al. experimental results and the influences of important operation parameters are analyzed.

2. Theoretical model of OPRGLs

The energy levels and population transfer channels that are involved in OPRGLs are shown in Fig. 1:

Fig. 1 Energy levels and population transfer channels in OPRGLs.

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The bold red lines represent the pumping and lasing processes, the dotted red lines represent the spontaneous emission processes and the black lines represent the collisional relaxation processes. An excited rare gas atom (except for helium) has four 1s states and ten 2p states. The $1 s_{5}$ and $1 s_{3}$ states are metastable (in this paper we use Paschen notation). The $1 s_{4}$ and $1 s_{2}$ states have strong dipole allowed transitions to the ground state ¹S₀, but are radiative trapped in OPRGL’s conditions. The electrical discharge non-selectively excites population into all the four 1s, ten 2p and other higher energy level states. In OPRGLs, we mainly care about the excited population concentration of the $1 s_{5}$ state. The OPRGLs operate typically in a DPAL-like three-level scheme by pumping ( $1 s_{5} \to 2 p_{9}$ ), collisional transfer ( $2 p_{9} \to 2 p_{10}$ ) and lasing ( $2 p_{10} \to 1 s_{5}$ ) processes. But other processes exist: (1) The upper laser level ( $2 p_{10}$ ) radiates not only to $1 s_{5}$ state, but to all the other three 1s states. The radiative decay to $1 s_{4}$ , $1 s_{3}$ and $1 s_{2}$ accounts for 21.8%, 0.6% and 3.6% of the total decay rate of $2 p_{10}$ . A relatively low collisional relaxation rate of $1 s_{4} \to 1 s_{5}$ may form a bottleneck in the population cycling process [14]. (2) The population in upper pump ( $2 p_{9}$ ) and laser ( $2 p_{10}$ ) levels could be further collisionally relaxed into higher levels by endothermic processes, especially to the $2 p_{8}$ level, which subsequently radiates to the $1 s_{5}$ , $1 s_{4}$ and $1 s_{2}$ states. (3) The $1 s_{5}$ population may deplete by a formation of excimer $A r_{2}^{*}$ . In the model, the trapped radiative decay process of the $1 s_{4}$ state is also considered. Due to the incomplete intermultiplet transfer data in 1s manifold, we ignore the subsequent population transfer from $1 s_{2}$ and $1 s_{3}$ levels, and assume this portion of population as depletion for a conservative estimation. The population transfer to even higher levels such as $2 p_{6}$ and $2 p_{7}$ is also ignored.

We consider a longitudinally pumped double-pass configuration. The rate-equation based model of OPRGLs is set as follows:

\begin{array}{l} \frac{d n_{1}}{d t} = - W_{p u m p} + W_{l a s e r} + k_{21} [n_{2} - \frac{g_{2}}{g_{1}} n_{1} \exp (- \frac{Δ E_{21}}{k T})] + n_{3} (A_{31} + k_{31}) + n_{4} (A_{41} + k_{41}) \\ + n_{5} (A_{51} + k_{51}) - n_{1} k_{A r_{2}^{*}}, \end{array}

\frac{d n_{2}}{d t} = n_{3} A_{32} + n_{5} A_{52} - k_{21} [n_{2} - \frac{g_{2}}{g_{1}} n_{1} \exp (- \frac{Δ E_{21}}{k T})] - n_{2} A_{20}^{e f f},

\begin{array}{l} \frac{d n_{3}}{d t} = - W_{l a s e r} + k_{43} [n_{4} - \frac{g_{4}}{g_{3}} n_{3} \exp (- \frac{Δ E_{43}}{k T})] + k_{53} [n_{5} - \frac{g_{5}}{g_{3}} n_{3} \exp (- \frac{Δ E_{53}}{k T})] \\ - n_{3} (A_{31} + A_{32} + A_{p 10 \to s 2} + A_{p 10 \to s3} + k_{31}), \end{array}

\frac{d n_{4}}{d t} = W_{p u m p} + k_{54} [n_{5} - \frac{g_{5}}{g_{4}} n_{4} \exp (- \frac{Δ E_{54}}{k T})] - k_{43} [n_{4} - \frac{g_{4}}{g_{3}} n_{3} \exp (- \frac{Δ E_{43}}{k T})] - n_{4} (A_{41} + k_{41}),

\begin{array}{l} \frac{d n_{5}}{d t} = - k_{54} [n_{5} - \frac{g_{5}}{g_{4}} n_{4} \exp (- \frac{Δ E_{54}}{k T})] - k_{53} [n_{5} - \frac{g_{5}}{g_{3}} n_{3} \exp (- \frac{Δ E_{53}}{k T})] \\ - n_{5} (A_{51} + A_{52} + A_{p 8 \to s 2} + k_{51}), \end{array}

\frac{d I_{L}}{d t} = \frac{c}{2 l_{c a v i t y}} {R_{L} R_{O C} T_{r}^{2} \exp [2 (n_{3} - \frac{g_{3}}{g_{1}} n_{1}) σ_{31}^{b r o a d e n e d} l_{g a i n}] - 1} \cdot I_{L} .

Equations (1)-(5) describe the population variations and Eq. (6) describes the laser intensity variation.

n_{i} (i = 1, 2, 3, 4, 5)

and

g_{i} (i = 1, 2, 3, 4, 5)

represent the population densities and degenerate degrees of

1 s_{5}

,

1 s_{4}

,

2 p_{10}

,

2 p_{9}

and

2 p_{8}

energy levels.

A_{31}

,

A_{41}

,

A_{51}

,

A_{p 10 \to s 2}

and

A_{p 10 \to s3}

are spontaneous emission rates of transitions

2 p_{10} \to 1 s_{5}

,

2 p_{9} \to 1 s_{5}

,

2 p_{8} \to 1 s_{5}

,

2 p_{10} \to 1 s_{2}

and

2 p_{10} \to 1 s_{3}

[16, 17].

A_{20}^{e f f}

represents the effective radiation rate of the trapped transition from

1 s_{4}

to the ground state

^{1} S_{0}

, and we quote

A_{20}^{e f f} = 5.7 \times 10^{5} s^{- 1}

in the calculation [13].

Δ E_{21}

,

Δ E_{43}

,

Δ E_{53}

and

Δ E_{54}

are energy separations between the corresponding energy levels.

k

is Boltzmann constant,

T

is absolute temperature,

I_{L}

is output laser intensity,

R_{L}

and

R_{O C}

are reflectivities of back reflector and output coupler,

T_{r}

is single pass transmission of the resonator,

l_{c a v i t y}

and

l_{g a i n}

are lengths of the resonator and gain medium,

σ_{31}^{b r o a d e n e d}

is the central atomic cross section of the buffer gas broadened laser transition. The collisional relaxation processes and rates are listed in Table 1:

Table 1. Collisional relaxation processes that involved in the model.

View Table

We have listed the intermultiplet and intramultiplet collisional relaxation rates that induced by helium and argon. The intramultiplet rates ( $k_{31}$ , $k_{41}$ and $k_{51}$ ) are the values that measured from a certain 2p state to the total 1s-manifold. Due to incomplete data of the intermultiplet rates among 1s-manifold, we assume these transfer channels finally to the $1 s_{5}$ state. The rates of the inverse of these collisional relaxation processes are decided by the principle of detailed balance. The process of excimer $k_{A r * 2}$ formation is also considered. The collisional broadening coefficients for 1s₅→2p₉ transition is $2.6 \times$ 10⁻¹⁰cm³s⁻¹ (316K) for Ar [15] and assumed the same value for He; for 1s₅→2p₁₀ transition is $1.5 \times$ 10⁻¹⁰cm³s⁻¹ (300K) for Ar [15] and $7.5 \times$ 10⁻¹⁰cm³s⁻¹ (300K) for He [13]. The pump transition rate is described as [20]:

\begin{matrix} W_{p u m p} = \frac{η_{d e l} η_{\mod e}}{l_{g a i n}} \int d λ \frac{1}{h v_{P}} I_{P} \cdot g_{P} (λ) \cdot {1 - \exp [- (n_{1} - \frac{g_{1}}{g_{4}} n_{4}) σ_{14}^{b r o a d e n e d} (λ) l_{g a i n}]} \\ \cdot {1 + R_{P} T_{r}^{2} \exp [- (n_{1} - \frac{g_{1}}{g_{4}} n_{4}) σ_{14}^{b r o a d e n e d} (λ) l_{g a i n}]}, \end{matrix}

where

η_{d e l}

is pump delivering factor,

η_{\mod e}

is mode overlapping factor,

h v_{P}

is pump photon energy,

I_{P}

is pump intensity,

R_{P}

is reflectivity of the back pump reflector. We use the spectral integral to calculate the pump absorption,

σ_{14}^{b r o a d e n e d} (λ)

is the spectrally resolved pump transition cross section, and

g_{P} (λ)

is the lineshape of the pump light, which is assumed to be in Gaussian distribution. The laser transition rate is described as [20]:

W_{l a s e r} = \frac{1}{l_{g a i n}} \frac{I_{L}}{h ν_{L}} \frac{R_{O C}}{1 - R_{O C}} \cdot (\frac{1}{T_{r} \sqrt{R_{L} R_{O C}}} - 1) \cdot (1 + T_{r} \sqrt{\frac{R_{L}}{R_{O C}}}),

where

h v_{L}

is laser photon energy,

I_{L}

is pump intensity.

An algorithm has been developed to solve for the steady state solution of the equations. When the steady state $n_{i} (i = 1, 2, 3, 4, 5)$ and $I_{L}$ have been solved, the energy conversion channels can be calculated as follows:

P_{l a s e r} = I_{l a s e r} S,

P_{f l u o r e s c e n c e} = V_{g a i n} \cdot (n_{3} A_{31} Δ E_{31} + n_{3} A_{32} Δ E_{32} + n_{4} A_{41} Δ E_{41} + n_{5} A_{51} Δ E_{51} + n_{5} A_{52} Δ E_{52}),

\begin{array}{l} P_{h e a t} = V_{g a i n} \cdot {n_{3} k_{31} Δ E_{31} + n_{4} k_{41} Δ E_{41} + n_{5} k_{51} Δ E_{51} + k_{21} Δ E_{21} [n_{2} - \frac{g_{2}}{g_{1}} n_{1} \exp (- \frac{Δ E_{21}}{k T})] \\ + k_{43} Δ E_{43} [n_{4} - \frac{g_{4}}{g_{3}} n_{3} \exp (- \frac{Δ E_{43}}{k T})] + k_{54} Δ E_{54} [n_{5} - \frac{g_{5}}{g_{4}} n_{4} \exp (- \frac{Δ E_{54}}{k T})] \\ + k_{53} Δ E_{53} [n_{5} - \frac{g_{5}}{g_{3}} n_{3} \exp (- \frac{Δ E_{53}}{k T})]}, \end{array}

P_{s c a t t e r} = P_{l a s e r} \cdot [R_{O C} / (1 - R_{O C}) \cdot 1 / \sqrt{R_{L} R_{O C} T_{r}^{2}}] \cdot [(1 - T_{r}) + T_{r} (1 - R_{L}) + T_{r} R_{L} (1 - T_{r})],

P_{a d d i t i o n a l l o s s} = V_{g a i n} \cdot [n_{2} A_{20} Δ E_{21} + n_{3} (A_{p 10 \to s 2} + A_{p 10 \to s 3}) Δ E_{31} + n_{5} A_{p 8 \to s 2} Δ E_{51}] .

Where

P_{l a s e r}

,

P_{f l u o r e s c e n c e}

,

P_{h e a t}

,

P_{s c a t t e r}

and

P_{a d d i t i o n a l l o s s}

are respectively the output laser power, fluorescence power, waste heat, scattered laser power, and additional loss power.

S

is the cross section area of the laser beam and

V_{g a i n}

is the mode volume.

3. Comparison with Rawlins et al.’s experimental results

To verify the validity of the model, a comparison between model prediction and Rawlins et al.’s experimental results [13] has been made. The model parameters are set as experimental conditions: gain length $l_{g a i n} = 1.9$ cm, total gas pressure 770torr (room temperature) with 98% helium and 2% argon, gas temperature $T$ = 600K, pump intensity $I_{P} = 1.32$ kW/cm², pump linewidth 2GHz, reflectivities of back reflector $R_{L}$ = 99% and output coupler $R_{O C}$ = 85%, single pass transmission is assumed to be 98%. Because the collisional relaxation rates (Table 1) are values in ~300K, we use Arrhenius temperature scaling to modify the rates at temperature of 600K. In literature [13], the concentration of Ar (1s₅) is estimated in a range of (3 to 5) × 10¹²cm⁻³,the absorbed pump power and laser power are 40mW and 22mW, with optical conversion efficiency of 55%. Our calculation gives the results of pump absorption power 73mW, laser power 39mW, efficiency 53% for Ar (1s₅) concentration of 3 × 10¹²cm⁻³, pump absorption power 99mW, laser power 52mW, efficiency 53.2% for Ar (1s₅) concentration of 4 × 10¹²cm⁻³, and pump absorption power 125mW, laser power 66mW, efficiency 53.3% for Ar (1s₅) concentration of 5 × 10¹²cm⁻³. For Ar (1s₅) concentration of 3 × 10¹²cm⁻³, the calculated results agree qualitatively with experimental results. The relatively larger calculated results are mainly due to two reasons: one is the mode overlap factor, which is assumed to be 100% in calculation; the other is the uncertain values of collisional relaxation rates, which has not been experimental confirmed at realistic gas temperature of ~600K.

4. Theoretical study of characteristics of OPRGL

In this section, some main characteristics of DPGRLs are theoretically studied. First we study the influence of $k_{21}$ , the collisional relaxation rate from $1 s_{4}$ to $1 s_{5}$ . Jiande Han et al. found that the relatively low value of $k_{21}$ may form a bottleneck in atomic cycling process, thus decrease the laser efficiency [14]. Our simulation results are shown in Fig. 2. The parameters are set as follows: gain length l_gain = 10cm, helium pressure P_He = 740torr, argon pressure P_Ar = 20torr, back reflector R_L = 99%, output coupler R_OC = 20%, single pass transmission T_r = 98%, pump linewidth 0.1nm (FWHM). Due to the lack of collisional rates at higher temperature (also the reliable temperature scaling laws), the collisional relaxation rates are quoted from Table 1 which are values at room temperature. In realistic conditions, the temperature of the gain medium may be higher due to both electrical and pumping energy deposition. Because properly elevated temperature may be beneficial to laser performance due to faster energy transfer kinetics [13], our calculations (at room temperature) give a conservative estimation:

Fig. 2 Influence of k₂₁ on laser performance. The solid circle dot line and solid diamond dot line represent I_laser vs I_Pump at different Ar 1s₅ concentration at realistic k₂₁ value, while the hollow circle dot line represents the performance at infinite k₂₁ value

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The results show that, at relatively low Ar (1s₅) concentration (3 × 10¹²cm⁻³), the slow relaxation rate k₂₁ dramatically decreases the laser performance, which is mainly due to the limited recycling rate of atoms. But this bottleneck effect could be well compensated by employing much more atoms to work, that is, by increasing the Ar (1s₅) concentration (3 × 10¹³cm⁻³) to realize a linear laser performance.

Then we study the influence of Ar (1s₅) concentration on laser performance at different pump intensities from 1 to 5 kW/cm², see Fig. 3, parameters are set as above.

Fig. 3 Influence of Ar (1s5) concentration on optical conversion efficiency at different pump intensities.

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The results show that, as similar as DPALs, OPRGLs have an optimal concentration of lasing species to get a best balance between pump absorption and non-lasing losses, for example fluorescence or heat etc., thus to obtain a highest optical conversion efficiency. Also as similar as DPALs, the required pump intensity is several kW/cm² and metastable atom concentration is 10¹²-10¹³cm⁻³. To get higher efficiency, higher pump intensity and higher Ar (1s₅) concentration are needed. At 2-5kW/cm² moderate pump intensities, the optical conversion efficiency could reach 50-60%. Figure 4 shows the equivalence between gain length and metastable atom concentration. For the same column concentration of Ar (1s₅), the optical conversion efficiency keeps the same theoretically, so we could design the gain length according to the collimation distance of the pump light (while keeping the required pump intensity) and adjust the metastable atom concentration to optimize the laser performance.

Fig. 4 Influence of Ar (1s5) concentration on optical conversion efficiency at different gain length, pump intensity 5kW/cm².

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A great advantage of OPRGL over DPAL is the ability to use inert buffer gas (helium) only, thus ensure the chemical stability of the lasers. Figure 5 simulates the influence of helium pressure on optical conversion efficiency. For each curve, the Ar (1s₅) concentration is optimized under different pump intensities:

Fig. 5 Influence of helium pressure (with constant Ar partial pressure of 20torr) on optical conversion efficiency at different pump intensity and Ar (1s5) concentration.

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The results shows that, a relatively low helium pressure (<1.5atm) is sufficient for population relaxation from 2p₉ to 2p₁₀, thus to support efficient laser operation. Higher helium pressure will increase the match degree between the atomic absorption linewidth (1s₅→2p₉) and pump spectral linewidth (~0.1nm), thus to increase the pump absorption efficiency. But, due to the collisional broadening of also the laser transition (2p₁₀→1s₅), the decrease of stimulated emission cross section weakens the competitive ability of the lasing process than the non-radiative transition (heat) and spontaneous radiation processes, thus decrease the total laser efficiency (see Fig. 6). In real design, the helium pressure should be optimized by consideration of pump linewidth, laser efficiency and electrical discharge conditions etc.

Fig. 6 Influence of helium pressure (with constant Ar partial pressure of 20torr) on pump absorption efficiency ( $η_{p u m p a b s o r p t i o n}$ ), optical conversion efficiency ( $η_{l a s e r}$ ), optical conversion efficiency relative to absorbed pump power ( $η_{l a s e r - a b s}$ ), fluorescence efficiency relative to absorbed pump power ( $η_{f l u o r e s c e n c e - a b s}$ ) and heat efficiency relative to absorbed pump power ( $η_{h e a t - a b s}$ ).

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As comparison with DPALs, OPRGLs have much more complex energy levels and population relaxation channels. Figure 7 calculated the detailed pump power distribution. Parameters are set as typical values with pump intensity of 3kW/cm² and Ar (1s5) of 2.4 × 10¹³cm³, other parameters are the same as above:

Fig. 7 Absorbed pump power distribution of a diode pumped Ar metastable laser.

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The laser shows a pump absorption fraction of 90.8%, and an optimized optical conversion efficiency of 52.2%. The population fraction for 1s₅, 1s₄, 2p₁₀, 2p₉, 2p₈ are 24%, 48.2%, 14.8%, 9.1% and 3.9% respectively. It can be seen that, due to the slow k₂₁, population accumulates largely at 1s₄ level, and has to be compensated by sufficient metastable atom concentration. Relative to the absorbed pump power, the laser accounts for 57.4%; the fluorescence accounts for 13.9%, including the transitions 2p₈→1s₅ 0.7%, 2p₉→1s₅ 5.9%, 2p₁₀→1s₅ 4.5%, 2p₈→1s₄ 1.5% and 2p₁₀→1s₄ 1.3%; heat accounts for 25.9%, including the transitions 2p₈→1s₅ 3.4%, 2p₈→2p₉ −0.16%, 2p₉→1s₅ 11.6%, 2p₈→2p₁₀ 0.83%, 2p₉→2p₁₀ 7.8%, 2p₁₀→1s₅ 2.3% and 1s₄→1s₅ 0.13%; scattering loss accounts for 2.38%, including mirror and cavity losses; other loss accounts for 0.42%, including the transitions 2p₈→1s₂ 0.14%, 2p₁₀→1s₃ 0.22%, 2p₁₀→1s₂ 0.04%, and 1s₄→¹S₀ 0.02%. It can be seen that, due to the existence of many non-radiative relaxation channels and large non-radiative relaxation rates (e.g. k₄₁ for helium), OPRGLs have much larger waste heat fraction (25.9%) than quantum defect (11%). And efficient convective cooling is required to keep reliable heat management.

5. Conclusions

In this paper, a multi-level rate equation based model of OPRGLs is set up, and the corresponding numerical approach is developed. The simulation result shows a qualitative agreement with Rawlins et al.’s experimental result. The precise collisional relaxation rates at the realistic temperature (600K in Rawlins et al.’s experiment) need to be experimentally established for a further comparison between theoretical and experimental results. The key parameters’ influences and pump distribution characteristics of metastable Ar lasers are theoretically studied. The results show that, the relatively slow relaxation rate from 1s₄ to 1s₅ could be compensated by increasing the metastable atom (1s₅) concentration; at moderate pump intensity of 2-4kW/cm², metastable atom (1s₅) concentration of (1-5) × 10¹³cm⁻³, and helium pressure of 1-2atm, the laser could reach 50-60% optical conversion efficiency. Due to the complex energy levels and population relaxation channels, the waste heat fraction of Ar metastable laser is much higher (20-30%) than the quantum defect (11%) so more efficient convective thermal management needs to be used.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (No. 61308044).

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Processes	Rate constants (cm³atom⁻¹s⁻¹)	Temperature	Reference
Ar(1s₄)→Ar(1s₅)	Ar: k₂₁<1e-13 He: k₂₁ = 1.2e-13	300K 303K	[18]
Ar(2p₉)→Ar(2p₁₀)	Ar: k₄₃ = 2.6e-11 He: k₄₃ = 1.6e-11	300K	[18]
Ar(2p₈)→Ar(2p₁₀)	Ar: k₅₃ = 1.1e-11 He: k₅₃ = 4e-12	300K 300K	[18] [13]
Ar(2p₈)→Ar(2p₉)	Ar: k₅₄ = 1.1e-11 He: k₅₄ = 4.5e-11	300K 300K	[18] [13]
Ar(2p₁₀)→Ar(1s₅)	Ar: k₃₁ = 0.6e-11 (to 1s-manifold) He: k₃₁<5e-14 (to 1s-manifold)	300K 300K	[18]
Ar(2p₉)→Ar(1s₅)	Ar: k₄₁ = 2.5e-11 (to 1s-manifold) He: k₄₁ = 2e-12 (to 1s-manifold)	300K 300K	[18] [13]
Ar(2p₈)→Ar(1s₅)	Ar: k₅₁ = 1.5e-11 (to 1s-manifold) He: k₅₁<0.1e-11 (to 1s-manifold)	300K 300K	[18]
Ar(1s₅)→Ar₂*	Ar: k_Ar2 = 36e-32 × T^-0.6 He: k_Ar2 = 0.5 × 36e-32 × T^-0.6		[19] [15]

Modeling of diode pumped metastable rare gas lasers

Abstract

1. Introduction

2. Theoretical model of OPRGLs

3. Comparison with Rawlins et al.’s experimental results

4. Theoretical study of characteristics of OPRGL

5. Conclusions

Acknowledgments

References and links

Cited By

Figures (7)

Tables (1)

Equations (13)

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