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Abstract
Optically pumped rare gas lasers (OPRGLs) have shown great potential to generate high energy laser radiation with high beam quality. As an alternative to the diode-pumped alkali vapor lasers (DPALs), they have similar working principles and characteristics, but OPRGLs have the advantage that the gain medium is chemically inert and is appropriate for closed-cycle operation. One of the challenges OPRGLs are faced with is the bottleneck caused by the slow 1s4-1s5 collisional relaxations at room temperature. A 1s4-2p10 dual-wavelength pump method had been proposed to transfer the populations pooled on the 1s4 level to the lasing cycle using a steady-state laser model. We explored this method further through 1s4-2p8 and 1s4-2p7 dual-wavelength pump schemes. The enhancement efficiencies at room temperature for a repetitively pulsed discharge, CW dual-wavelength pump system were examined using a dynamic model, and an experiment with a pulsed secondary pump was conducted for qualitative evaluations.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Diode-pumped alkali vapor lasers have shown considerable promise for the construction of efficient high energy lasers with good beam quality and long-range propagation characteristics [1–4]. However, there are some technical challenges in DPALs’ development resulting from the chemically aggressive nature of the alkali metal vapors. Optically pumped rare gas lasers have been investigated as an alternative to DPALs since the first demonstration in 2012 [5–31]. They can circumvent the chemical problems of DPALs by using inert gas medium, and have similar primary optical and kinetic performance. The metastables excited from rare gas atoms (Rg = Ne, Ar, Kr, Xe), used as the gain medium, have spectroscopic properties that are similar to those of the alkali atoms [32]. The metastables are usually produced through electric discharges. In Ar/He OPRGLs, population from 1s5 is transferred at wavelength of 811.5 nm to 2p9, and then to 2p10 through fast collisional relaxation (with He), establishing a population inversion between 2p10 and 1s5. This results in lasing at 912.3 nm. To date, there are two main methods that have realized continuous-wave (CW) Ar/He OPRGLs. One employed a micro-discharge array [20], which has generated an output laser power of 22 mW with an optical-optical efficiency (ratio of the output laser power to the absorbed pump power) of 55%. The other is a repetitively pulsed discharge system with parallel plate electrodes, and a CW output laser of 4.1 W with an optical-optical efficiency of 31% was reported [26]. Many computational models have been developed for OPRGLs [6–19], including steady laser models [8,12,13] based on stationary-state solutions of the rate equations, time-dependent discharge models [10,11] which identified key discharge reaction pathways, and combined models [15,17,18] that contain both the electrical and optical excitations.
One restriction for the room-temperature operation of OPRGLs is that a considerable proportion of populations radiated from the upper levels (2p) will accumulate in the 1s4 state, rather than contribute to the lasing cycle, as suggested by Han et al [5]. Rawlins et al [20] speculated that 1s4-1s5 relaxation would be faster at higher gas temperature, but heating the gain medium may not be an optimal approach since the gas temperature management would also be a challenge. A dual-wavelength pump scheme [12] was proposed to solve this problem, in which a secondary pump source is applied to transfer population from 1s4 to 2p10. Simulation results of a steady-state five-level laser model demonstrated that, for a 20 cm Ar/He gain medium at 300 K and 760 Torr, the output laser intensity can be increased by 1.5 times with a 1% secondary pump (relative to the primary pump intensity) pump intensity. A 2-8% secondary pump can achieve an enhancement of output laser with a relatively high optical-optical efficiency.
In this paper we investigate Ar/He dual-wavelength pump schemes, in which a secondary pump laser tuned to the 1s4-2p10 (965.8 nm), 1s4-2p8 (842.5 nm) or 1s4-2p7 (810.4 nm) transitions is applied in combination with the primary pump. Collisional transfers from 2p8 and 2p7 to 2p9 and 2p10 are known to be rapid [7,33]. Consequently, there should be less population accumulation in the 2p8 and 2p7 states than accumulation in 2p10, as the 2p8 and 2p7 levels are not parts of the three-level cycle, and the Einstein coefficients of the absorption cross sections for 1s4-2p8 and 1s4-2p7 transitions are one order of magnitude larger than 1s4-2p10 transition [34]. A dynamic zero-dimensional model is carried out to analyze the secondary pumping effects for a pulsed discharge CW dual-wavelength pump Ar/He device, which would be applicable for the experimental method [26] that successfully generated a quasi-CW laser. The model performs simultaneous time-dependent calculations for both the discharge and laser excitations. Not only spontaneous radiative relaxation, but collisional relaxation from the upper levels to 1s4 are considered. The latter was neglected in previous models [12] but may contribute significantly to the calculated number density of Ar(1s4). Preliminary experimental verifications were made using a pulsed discharge, CW primary pump, pulsed secondary pump device.
2. Model description
The energy levels and transitions that were included in the model are shown in Fig. 1. Note that the three secondary pump paths were applied separately for each scheme. The model was modified from the one we developed before [17] for a single-wavelength pump Ar/He device. For the discharge excitation calculations, the species considered were e−, Ar, Ar+, Ar2+, Ar2*, Ar(1s5), Ar(1s4), Ar(2p10), Ar(2p9), Ar(2p8), Ar(2p7), Ar(hl), He, He+, He*, He2+, He2* and HeAr+, in which hl represents all energy levels of Ar above 2p7 (populated using the cross-section for excitation of Ar(3d6)). The time evolution of the number densities of these species was simulated through the ZDPlasKin software [35]. This program computed the time integration of rate equations through the built-in DVODE solver, and updated the electron-related reaction rate coefficients with updated reduced electric field from the Boltzmann equation solver (BOLSIG+) for each time step [36]. Cross sections used for the electron-related reactions were mainly downloaded from LXCat (https://fr.lxcat.net). Cross sections for ionization reactions for Ar(2p10), Ar(2p9), Ar(2p8), Ar(2p7) and Ar(hl) were calculated using the Deutsch-Märk formalism [37]. The discharge processes included electron impact, recombination, two-heavy-body, three-heavy-body and radiative reactions. Uncertain coefficients of Ar(2p7)-related reactions were assumed approximately equal to those of Ar(2p8)-related reactions, as the known coefficients listed in [35] for Ar(2p7) and Ar(2p8) of the same type reactions are almost of the same order of magnitude. The branching ratio from the upper levels to the specific 1s4 and 1s5 levels of the collisional rate coefficients for Ar(2p) + He $\to $ Ar(1s) + He is uncertain, and has been proved very significant for OPRGLs output power simulations [18]. Obviously, this can directly affect the calculated number density of Ar(1s4) along with the dual-wavelength pump efficiency. Here we assumed that the reaction rate coefficients for collisional relaxations from 2p back to 1s4 and 1s5 are proportional to the degeneracy ratio of 1s4 and 1s5.
The simulated discharge circuit consisted a voltage power supply, a ballast resistor, and a pair of parallel plate electrodes (Fig. 2). The key parameter determining the discharge characteristics, the reduced electric field $E/N$, was calculated through $E/N = {V_{\textrm{pc}}}/({N \cdot {d_\textrm{g}}} )$, where E is the electric field in the transverse direction, N is the total number density of neutral species, and ${d_\textrm{g}}$ is the electrode gap. ${V_{\textrm{pc}}}$ is the voltage across the positive column, solved by
Three transitions were added to the discharge package for the optical excitation calculations: the primary pump transition 1s5-2p9, the secondary pump transition 1s4-2p10 (or 1s4-2p8, 1s4-2p7 for corresponding scheme) and the lasing transition 2p10-1s5. The rates for the primary pump transition ${W_\textrm{p}}$, the secondary pump transition ${W_\textrm{s}}$, the laser transition ${W_\textrm{l}}$, the average intracavity laser intensity ${I_{\textrm{ave}}}$, the absorbed primary pump power density ${I_{\textrm{pabs}}}$, the absorbed secondary pump power density ${I_{\textrm{pabs}}}$ and the output laser power density ${I_{\textrm{out}}}$ were time-dependently solved by
3. Simulation and experimental results
The parameters we set in the simulations are applicable for a pulsed discharge CW laser device. Repetitive voltage pulses of 80 ns duration, 100 kHz repetition frequency and 1500 V amplitude were applied to a pair of parallel electrodes of 3 cm length, 0.63 cm width and 0.26 cm gap distance. The voltage was approximately a triangle profile. The ballast resistor was 75 Ω, and the cathode fall voltage was assumed to be 160 V. The gas medium was a 5.3% Ar/He mixture [26] at 760 Torr gas pressure. The line shape of the two pump sources was a Gaussian profile with the full width at half maximum of 30 GHz. The length of the optical cavity was 30 cm, with a 60% reflective OC for the output laser. OC reflectivity for the primary pump and the secondary pump was set as zero, assuming that the divergence of pump beams is strong. The spatial overlap ratio $\eta $ was 95%, single-pass cell window transmissions for the pump and laser were 99%, and other round-trip intracavity losses were assumed to be 5% in total (${t_\textrm{o}} = 95\%$). Collisional broadening coefficients (He at 300 K) for the pump transitions was 3.2 × 10−10 cm3s−1 [23], and for the laser transition was 2.65 × 10−10 cm3s−1 (half width at half maximum) [27]. Simulations at 300 K were the primary focus, assuming that water-cooling was applied for steady-state performance at room temperature.
Simulations of CW dual-wavelength pump schemes of 1s4-2p10, 1s4-2p8 and 1s4-2p7 were carried out, with the primary pump power density of 1-10 kW/cm2, and 1-10% secondary pump power density. A beam area of 3 mm2 was used. With the assistance of a secondary pump, the output power, the absorbed power and the optical-optical efficiency can be greatly enhanced. In addition, the dual-wavelength pump system can realize an output power beyond the maximum saturation value which the single-wavelength pump method can reach. Figure 3 shows the effects of 1s4-2p10 1-10% secondary pump for the primary pump power density from 1 kW/cm2 to 10 kW/cm2. The enhancement ratio refers to the ratio of the output power density of the dual-wavelength pump scheme to the output of the single-wavelength pump scheme. It suggests that the enhancement ratio is positively correlated with the primary pump power density and the secondary pump proportion.
Fig. 3. Effects of 1s4-2p10 secondary pump in the range of 1% – 10% for primary pump of power density from 1 kW/cm2 to 10 kW/cm2.
Figure 4 shows the effects of 1s4-2p10, 1s4-2p8 and 1s4-2p7 secondary pump schemes of 1% and 10% proportion. It demonstrates that with a primary pump of 10 kW/cm2 and a 1% 1s4-2p10 secondary pump, the averaged output power density can be scaled from 265.8 W/cm2 (saturated) to 395.6 W/cm2, nearly enhanced by 1.5 times, which is roughly consistent with the enhancement efficiency reported in [12]. With a 10% 1s4-2p10 secondary pump, the output power density can be increased by nearly 3.1 times, and the optical-optical efficiency can be enhanced from 40.8% to 49.9%. For 10% 1s4-2p8 and 1s4-2p7 schemes, the averaged output power density can be scaled to about 1080 W/cm2, which is a 4.1 times enhancement. 10% 1s4-2p10 secondary pump at 400 K (not displayed) could only provide a 1.99 times enhancement, using the rate coefficient of 1s4-1s5 collisional relaxation at 397 K measured experimentally in [7], which is 2.3 times as the coefficient at 300 K. The effects of the secondary pump are expected to be lower at the higher temperature, but high temperature may cause problems on discharge performance and structure stability.
Fig. 4. Output power density and optical-optical efficiency of single-wavelength pump and dual-wavelength pump schemes. (a) Output power density, single and 1% dual-wavelength pump; (b) Output power density, single and 10% dual-wavelength pump; (c) Optical-Optical efficiency, single and 1% dual-wavelength pump; (d)Optical-Optical efficiency, single and 10% dual-wavelength pump.
The averaged number density of Ar(1s5) before optical pumping was 4.0 × 1012 cm−3. Figure 5 shows the evolution of the number densities of Ar(1s5), Ar(1s4), Ar(2p10), Ar(2p9), Ar(2p8) and Ar(2p7) in two discharge pulse periods with a primary pump of 10 kW/cm2 and a 10% 1s4-2p7 secondary pump. These densities are decaying shortly after the discharge pulse during each period. It is obvious that most excited Ar-species accumulated in the 1s4 state for the single-wavelength pump situation. With the assistance of a secondary pump, there was a great decrease in the number density of Ar(1s4) and increases for other five species. The averaged number density of Ar(1s4) was decreased from 6.79 × 1012 cm−3 (single-wavelength pump method) to 4.23 × 1012 cm−3, 1.72 × 1012 cm−3 and 1.66 × 1012 cm−3 for 1s4-2p10, 1s4-2p8 and 1s4-2p7 schemes, respectively. The recycling effectiveness of the 1s4-2p8 and 1s4-2p7 schemes were similar, and both were much higher than in 1s4-2p10 scheme, which is also reflected by their differences in output power densities shown in Fig. 4(a) and (b). In this situation, the absorption efficiency of the secondary pump power was 10.8%, 19.5% and 20.5% in 1s4-2p10, 1s4-2p8 and 1s4-2p7 schemes, respectively, which could be explained by their differences in the cross sections of the secondary pump transitions and the number density differences between the upper level and 1s4. The relative increase in output power density for the secondary pump to 2p8/2p7 compared to 2p10 is due to the increase in absorption efficiencies, coupled with the fast rates of collisional relaxations with helium to 2p9 and 2p10. The output power would be enhanced by 3.1 times if all collisional relaxations from the upper levels were assumed to contribute to 1s5, and by 3.6 times if all were assumed to contribute to 1s4.
Fig. 5. Number densities of Ar(1s5), Ar(1s4), Ar(2p10), Ar(2p9), Ar(2p8) and Ar(2p7), in (a) 10 kW/cm2 single-wavelength pump scheme, and (b) with an additional 10% 1s4-2p7 secondary pump.
We carried out a pulsed discharge, CW primary pump, pulsed secondary pump experiment to demonstrate the effects of 1s4-2p8 and 1s4-2p7 dual-wavelength pump schemes. The setup was based on the device which had generated a 4.1 W quasi-CW laser using a CW single-wavelength pump method with pump power of 21 W [26]. This discharge system generates Ar(1s5) number densities in excess of $2 \times {10^{13}}$ cm−3. For the experimental setup used in the present measurements, the discharge was driven by 1500 V maximum amplitude pulses of 80 ns duration. The pulse repetition frequency was 100 kHz, and the discharge volume was close to 0.6 cm3. A tunable diode laser (OptiGrate, Shark Laser) was used as the primary pump source, which can generate an output power of 41 W at 50 A current. A pulsed tunable dye laser (Lambda Physik Compex Pro 201/FL3002) was used as the pulsed secondary pump source. Figure 6(a) shows the evolution of output power density (in arbitrary unit), in which the first spike and the second spike correspond to the moments when the discharge pulse and when the secondary pump was applied, respectively. It demonstrates that during a discharge period (10 µs), the later the secondary pump is applied, the weaker the related laser spike would be, which generally follows the decaying trend of Ar(1s4) in the simulations. The gain medium was nearly transparent for such a strong secondary pump, so the dual-wavelength pump effect was expected to be proportional to the populations accumulated in 1s4. In addition, the efficiencies of 1s4-2p8 and 1s4-2p7 schemes were almost the same, as shown in Fig. 6(b), which is also qualitatively consistent with the CW dual-wavelength pump simulation results. We found in the 1s4-2p7 experiment that the effect of the secondary pump would be weaker when the primary pump power is higher. The current model needs to be improved for better analyses for the pulsed secondary pump situation. Moreover, pulsed discharge, CW dual-wavelength pump experiments need further investigations.
Fig. 6. Pulsed discharge, CW primary pump, pulsed secondary pump experimental results. The discharge voltage was 1500 V amplitude, 80 ns duration and 100 kHz repetition frequency. The discharge pulse and the secondary pump was applied at the first spike and the second spike, respectively. (a) Output power with different delay of pulsed secondary pumping to 2p7 (primary pump current is 30 A); (b) Output power with pulsed secondary pumping to 2p8 or 2p7 (primary pump current is 25 A).
4. Conclusions
Dual-wavelength pump schemes with the secondary pump transitions 1s4-2p10, 1s4-2p8 and 1s4-2p7 were studied using a time-dependent computational model that we developed for a pulsed discharge, CW dual-wavelength pump Ar/He system. The simulations indicated that, with a 10% secondary pump via the 1s4-2p8 or 1s4-2p7 transition, the output laser power can be enhanced by 4.7 times, and both of these secondary pump transitions were nearly 50% more efficient than the 1s4-2p10 transition. The main reason for this difference is that the absorption efficiencies of the secondary pump for the 1s4-2p8 and 1s4-2p7 schemes are higher than that of the 1s4-2p10 scheme. Some coefficients, including the branching ratio from 2p levels to 1s levels and uncertain rate coefficients of Ar(2p7)-related reactions, need further experimental measurements for more accurate simulations. The 1s4-2p8 and 1s4-2p7 schemes were experimentally tested through a pulsed discharge, CW primary pump, pulsed secondary pump device. The effect of the secondary pump generally followed the evolution of Ar(1s4) concentrations. The enhancement efficiencies of these two schemes were almost the same, which was qualitatively consistent with the simulation results. The wavelength of the secondary pump transition in 1s4-2p7 scheme (810.4 nm) is very close to the primary pump transition 1s5-2p9 (811.5 nm), and can be made from the same high-power diode laser of the primary one, so CW 1s4-2p7 dual-wavelength pump lasers would be worth more attention as this approach may be easy to implement.
Funding
Army Research Laboratory (W911NF-17-1-042721); China Scholarship Council (201906160193).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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