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Although the diode pumped alkali laser (DPAL) works in a three-level scheme, higher energy-state excitation and ionization processes exist during operation, which may lead to deleterious effects on laser performance. In this paper, we report the ionization degree measurement in the gain medium of an operational hydrocarbon-free Rb DPAL by using the optogalvanic method. The results show that, at the pulsed mode with a duration of ~1 ms, a maximal ionization degree of ~0.06% is obtained at a pump power of 140 W. While in the CW mode, the plasma reaches an ionization degree as high as ~2% at a pump power of 110 W, which is mainly due to the enough time for sufficient plasma development. A comparison with our previous work [Opt. Lett. 39, 6501 (2014)] as well as modeling results is made and discussed. The influences of different population transfer channels on laser performance are simulated and analyzed. The results show that, for a typical hydrocarbon-free Rb laser (pump intensity of 15 kW/cm2, helium pressure of 10 atm and cell temperature of 438 K), all the high-energy excitation effects give an overall negative influence on laser efficiency of ~3.78%, while the top two influencing channels are the photoionization (~1.8%) and the energy pooling (~1.53%). The work in this paper experimentally reveals the influence of the macroscopic ionization evolution process on an operational DPAL for the first time, which would be helpful for a more comprehensive understanding of the physics in DPALs.
© 2017 Optical Society of America
1. Introduction
Diode pumped alkali vapor lasers (DPALs) have been extensively studied due to their great potential for extremely high power operation [1–3]. Till now, the published power record of DPAL has reached ~1.5 kW with high optical conversion efficiency [4]. The useful energy levels involved in DPALs are the n2S1/2, n2P1/2 and n2P3/2 energy levels (n = 3,4,5 for K, Rb and Cs respectively). But, the n2P1/2, 3/2 states are easily excited to higher levels n2D3/2, 5/2 and (n + 2) 2S1/2 by photoexcitation [5] or energy pooling processes [6]. And these higher lying levels of the alkali atoms will be further ionized by photoionization [7] or penning ionization [8] processes to form plasma. These ionization channels are not obvious at low pump intensities, but may become deleterious in high power DPALs. First, these processes deplete the useful alkali atoms in n2S1/2 and n2P1/2, 3/2 states, which lead to deviation of alkali concentration from the optimal value. Krupke has calculated that, at the extreme medium condition of 1016 cm−3 alkali concentration and 100 kW/cm2 pump intensity, all the alkali atoms will be ionized [9]. Second, these high lying alkali atoms will be collisionally relaxed by alkali atoms, buffer gas atoms/molecules or electrons, which will increase the thermal load and decrease the laser efficiency. Third, both the decrease of useful alkali atoms and the increase of thermal load require higher flow rates to replenish the useful alkali atoms and remove the waste heat, which may dramatically increase the engineering complexity.
The processes and influences of high energy level excitation in DPALs have been theoretically studied in recent years. Wu firstly set up a model considering the high energy level excitation processes, and agreed qualitatively with experimental results [10]. Knize et al. calculated the alkali loss rate due to photoionization effect in different types of DPALs, and suggested a supersonic flow rate in a high pressure Rb laser to sufficiently replenish the neutral medium [11]. Oliker et al. set up a computational fluid dynamics (CFD) and wave optics coupled time-dependent model to simulate the deleterious processes in a static-cell DPAL. The results showed a significant power decrease due to quenching and photoionization effects, while the negative influences of other high energy level excitation processes were relatively small [12]. Barmashenko et al. presented a three-dimensional CFD coupled gas-flow model for DPALs, which predicted a weak effect of ionization on laser performance by convective cooling from flowing gas [13, 14]. And in later works, Waichman et al. showed that, for high pump intensities, the ionization process had significant effect in subsonic Cs DPALs [15]. Recently, Markosyan et al. developed a first principle global model to investigate the plasma characteristics in a pulsed Cs DPAL. The results showed a significant occurrence of plasma at certain conditions, which would decrease the laser intensity by depletion of the alkali atoms and by collisional quenching of the useful populations [16]. As compared with theoretical studies, the experimental researches relating the high energy level excitation were relatively limited. Lun G et al. firstly detected the ionization degree in a Rb hollow cathode lamp [17]. In the experiment, the researchers adopted an optogalvanic method by using two plate electrodes to collect the electrons in the plasma. A subsequent experiment was conducted by Yang et al. in a pumped Rb/He gain medium, with improvements of the electrode’s structure and buffer gas condition. A maximal ionization degree of ∼6.45 × 10−6 has been obtained under a pulsed pump intensity of 0.82 kW∕cm2, temperature of 150 °C and helium pressure of 500 torr [18]. In this experiment, the material of the alkali cell (glass) imposed some limitations for further research. One was the limited helium pressure (less than one atmosphere) which didn’t support lasing. The other was the glass window material which couldn’t resist to an intense CW pumping.
In this work, the experimental conditions were significantly improved. The alkali cell was manufactured with stainless steel rather than glass, which could sustain high pressure helium to realize lasing for Rb DPALs. The newly used sapphire window could resist to intense CW pumping. The plate electrodes were re-designed to cover the entire gain path to collect the electrons as much as possible. Furthermore, the detection process was adjusted from the original method by using lock-in amplifier [17, 18] into direct photocurrent measurement, which allowed measurement in CW operation. Under these conditions, we report, for the first time, the results of ionization degree measurement on an operational hydrocarbon-free Rb DPAL in both pulsed and CW modes.
2. Experimental setup and principle of the optogalvanic method
The schematic of the experimental setup is shown in Fig. 1. The pumping source is a volume Bragg grating (VBG) coupled diode laser stack with a 600 μm fiber output coupler. The central wavelength is tuned exactly to 780.2 nm and the linewidth is narrowed to 0.17 nm (FWHM) by adjusting the VBG’s temperature. After the pump source, there is a confocal telescope that consists of two spherical lenses (Lens1 and Lens2) with the same focal length (f = 15 cm). For the pulsed operation mode, a chopper with duty cycle of 1.4% is placed at the focal position, while for the CW mode the chopper is taken away. Then the pump light is focused into the Rb cell by a spherical lens (Focusing Lens, f = 15 cm). The focus of the pump light is located at the center inside the cell with spot radius of 0.6 mm (86% power included). Considering the loss of optical elements, the pump intensity could reach as high as 18 kW/cm2. The resonator is a Fabry-Perot cavity, which consists of a dichroic mirror, an output coupler and a Rb cell. The dichroic mirror is specially designed with high transmission for the 780.2 nm pump light (T>95%) and high reflection for the 795 nm alkali laser (R>95%). The output coupler is chosen as 70%. The 20 mm-long Rb cell is filled with a small amount of Rb metal and 6 atm He (293 K) as buffer gas. The temperature of the cell could be well adjusted by an electrical heater with accuracy of ± 1 K. The cell windows are made with sapphire material with no coatings on both inner and outer surfaces, which results in a low single-pass transmittance of ~70%. Two 18 mm × 20 mm parallel electrodes are inserted into the Rb cell, with a separated distance of 10 mm. Considering the effect of fraying of the electric field near the edges of the electrodes, the length of the electrodes (~18 mm) are intentionally designed to approximately equal to the gain length, covering the pump region as much as possible. The bias voltage is 10 V. When the medium is pumped, Rb atoms will be partially ionized, and both Rb+ and electrons will drift to the corresponding electrodes, forming photocurrent signal. When the photocurrent signal passes through the resistor (390 KΩ), the signal will be detected be the oscilloscope (with an internal resistor of 10 MΩ), and the photocurrent could be obtained.
Fig. 1 Schematic of the experimental setup. The red, green and black lines represent the diode pump light, the alkali laser and the electrical line, respectively.
The Rb+ density nRb+ as well as the electron density ne is calculated by
where I is the measured photocurrent. Z = 1 is the charge number of electron and Rb+. S = 20 mm2 is the projected area of the pump light that parallel to the electrodes. ve and vRb+ are the drift velocities of electron and Rb+. The relation between drift velocity and mobility rate iswhere is the mobility rate of electron or Rb+, and E is the electrical field that applied to the electrodes. In helium, the mobility rates of electron or Rb+ can be calculated by Eq. (3):where p is the helium pressure in unit of torr, ' is the mobility rate of electron and in one atmosphere helium at 393 K: = 1.132 × 10−1 m2/(V·s), = 2.1 × 10−4 m2/(V·s) [19]. is about 3-4 orders of magnitude larger than , so the contribution to photocurrent by Rb+ could be ignored. With the known buffer gas pressure p and the measured photocurrent I, the Rb+ concentration nRb+ can be calculated. And the ionization degree is calculated bywhere nRb is the total Rb atom concentration in the pump region.3. Experiment results
3.1 Ionization degree measurement in pulsed operation mode
First, we measured the photocurrent in a pulsed operation mode by using the chopper to turn the CW diode pump light into repetitively pulses. The purpose is to decrease the averaged pump power to prevent overheating in a static cell. At low duty cycle (1.4%), the averaged pump power is kept less than 2 W (corresponding to the maximal CW pump power of ~140 W). Although a transient temperature rise exists during a pulse duration [20, 21], the averaged variation of Rb concentration inside the gain medium will not be obvious, and we could approximately use a Rb concentration (nRb), which is decided by saturated vapor pressure, to calculate the ionization degree based on Eq. (4). It should be noted that, in this section, when the pump (or laser) power is discussed, it is the average power during the duration of the pulse (i.e. pulse energy over the pulse duration).
Figure 2 shows typical time evolution signals of pump, laser and photocurrent. The pump power is 110 W with duration of 1 ms (FWHM). The cell is heated to 438 K that produces Rb atoms concentration of 2.1 × 1014 cm−3. The helium pressure is 9 atm at this temperature and the bias voltage is 10 V. The results show that, when the pump signal increases, both the laser and photocurrent signals increase. When pump power decreases, the laser signal decreases rapidly, while the photocurrent takes a longer time to recover, which is to some extent due to the relatively slow recombination processes. It should be noted that, when the cell is pumped at room temperature, no photocurrent occurs. This phenomenon verifies the fact that, the photocurrent is generated from the ionized gain medium rather than the photoelectrons excited by pump light on the electrodes. In fact, the spatial position of pump light is intentionally adjusted with a separation from the adjacent electrode. In this case, the maximal ionization degree is calculated to be ~0.037%.
Fig. 2 Typical time evolution signals of pump, laser and photocurrent. The pump power is 110 W with duration of 1 ms (FWHM). The Rb cell is heated to 438 K with 9 atm helium at this temperature, and the bias voltage is 10 V.
Figure 3(a) shows the laser performance. As the pump power increases, the laser power presents a linear increase trend. The maximal optical conversion efficiency is ~8% at a pump power of 140 W, and the slope efficiency is ~16%. The relative low efficiency is mainly due to the high optical resonator loss (single pass transmittance of ~70%), and the low helium pressure (~9 atm, 438 K) which couldn’t provide sufficient fine-structure mixing rate (52P3/2→52P1/2). Of course, these are not the main concern in this work, and we will improve the efficiency in the future. Figure 3(b) shows the results of the measured photocurrent and the calculated ionization degree. Their relations with pump power show a linear increasing trend. The increase of photocurrent is reasonable, because higher pump intensity together with more populations in 52P1/2 and 52P3/2 energy-levels will enhance both the collisional ionization channels (energy pooling, penning ionization etc.) and laser induced ionization channels (photoexcitation, photoionization etc.). At the maximal pump power of 140 W, the ionization degree is 0.06%, which is two orders of magnitude larger than our previous work [18]. This is mainly due to the significant increase of pump intensity (0.82 kW/cm2→18 kW/cm2) and alkali concentration (1 × 1014 cm−3→2.1 × 1014 cm−3). Another possible reason for higher ionization degree could be much higher pressure resulting in the broadening of the absorption line for photoexcitation (52P3/2→5D) to high electronic levels of Rb, and hence in the increase of the absorption rate [11]. But a calculation shows that, for the excitation from 5P to 5D, the population transfer rates per atom for energy pooling and photoexcitation are 5.3 × 104 s−1 and 1.47 × 103 s−1 respectively, which indicates that energy pooling still dominates the higher level excitation process in this case.
Fig. 3 (a) Laser power versus pump power. (b) Photocurrent and ionization degree versus pump power. The pump duration is 1 ms (FWHM), and the Rb cell is heated to 438 K with 9 atm helium at this temperature.
Figure 4(a) shows the laser power versus temperature, which is essentially the alkali concentration influence on laser power. Experimental data give an optimal temperature of 438 K, which is the best equilibrium point between pump absorption and fluorescence loss [22]. Figure 4(b) gives the results of the measured photocurrent and calculated ionization degree. The increase of photocurrent can be attributed to two reasons: one is the increase of population in 52P1/2 and 52P3/2 energy-levels due to more pump absorption, which enhances the subsequent ionization channels; the second is due to the enhancement of interaction coefficients for collisional processes with the elevated temperature, such as energy pooling, penning ionization etc. An abnormal phenomenon shows that, as the temperature increases, the photocurrent presents rollover after ~460 K. An inferred reason from the observed phenomenon is that, as the temperature increases, the exponentially increased Rb concentration dramatically enhance the pump absorption in a very short distance (several millimeters) just near the entrance window, which could be clearly seen from the strong fluorescence. And a small gas (~1 mm) still exist between the edge of electrode and the inner window surface. Although the extended electric field should cover this area, this may still to some extent decrease the electron collection ability. This phenomenon needs to be further studied. The ionization degree also presents a rollover trend, which is mainly due to the much faster increased Rb concentration that acts as a denominator in Eq. (4).
Fig. 4 (a) Laser power versus cell temperature. (b) Photocurrent and ionization degree versus temperature. The pump power is 110 W with a duration of 1 ms (FWHM), and the Rb cell is heated to 438 K with 9 atm helium at this temperature.
As for the error bars in Figs. 3 and 4, they are the standard deviations of the repetitively sampled experimental data. The errors arise from many reasons, including fluctuation of pump and laser powers, variation of Rb concentrations due to local convection, and the detection errors from the circuit and signal processing systems etc.
3.2 Ionization degree measurement in CW operation mode
In this section, we report the results of ionization measurement under the CW pump case. In our previous work, we used a lock-in amplifier based method which was only suitable for periodic operation. In this paper, we directly measure the photocurrent through a resistor, which is feasible for CW measurement. A significant difference between pulsed and CW cases is the heating effect. In the case of CW pumping, the pump region will experience a significant drop of alkali concentration due to local temperature rise. So the alkali concentration (nRb) doesn’t depend on the saturated vapor pressure again. To solve this problem, a model is set up to calculate the Rb concentration inside the pump region, and is used as nRb in Eq. (4). The model will be briefly introduced in the section of “Discussion”.
Figure 5 shows the typical time evolution signals of the laser power and the photocurrent. The pump power is 110 W with cell temperature of 438 K. Although we presents a time interval of ~9 s due to the limited storage depth of the oscilloscope, the system could sustain lasing for a long time even in the static cell, which is something to our surprise. Further increase of the cell temperature will break the balance between lasing and passive thermal diffusion, and lead to a termination of lasing. The laser signal shows a very similar trend as Oliker et al.’s simulated prediction [12] and Zhdanov et al.’s experimental results [20]. But our result shows a much longer time to achieve a steady state operation (~2 s), while this time in the above two papers were less than 0.05 s. This phenomenon relates to the difference in real experimental conditions, and needs to be further studied. As for the photocurrent, it increases quickly and steeply as the laser starts, tends to be smooth as the laser signal reaches steady-state, and still shows a slowly rising trend over time. The photocurrent (~22 μA) is almost a magnitude larger than in the pulsed case (~2.7 μA in Fig. 3(b) under a pump power of 110 W). This suggests that, in the pulsed case, due to the limited duration (~1 ms), the ionization process doesn’t sufficiently develop, and is just part of the rising edge in the CW case.
Fig. 5 Typical signals of laser and photocurrent under CW pumping. The pump power is 110 W and the Rb cell is heated to 438 K with 9 atm helium at this temperature.
Figure 6(a) shows the calculated temperature and Rb concentration drop at different pump powers (see the “Discussion” for detailed calculation process). It can be seen that, the temperature of the pump region increases as pump power increases, due to the heat release from non-radiative population transfer channels such as fine-structure mixing, quenching and recombination processes. Correspondingly, the Rb concentration experiences a significant drop due to local pressure balance, which is used as denominator (nRb) in Eq. (4). Figure 6(b) shows the relations of photocurrent and ionization degree versus pump power. The photocurrent increases almost linearly which is similar as the pulsed case. According to Eq. (1), the Rb+ concentration nRb+ is not in directly proportion to the photocurrent I, but is also related with the electrical field E, which is not a constant value as the photocurrent changes (see the circuit configuration in Fig. 1). For this reason, the increase of ionization degree doesn’t show a linear trend. The maximal ionization degree reaches as high as ~2%, which is about 28 times larger than the pulsed mode, and even 2800 times larger than our previous work [18]. A large ionization degree in the case of CW pump is mainly due to two reasons: one is the enough time for plasma to get a sufficient development, and the other is the enhancement of the many collisional up-excitation channels by elevated temperature inside the gain medium.
Fig. 6 Photocurrent and ionization degree versus pump power. The Rb cell is heated to 438 K with 9 atm helium at this temperature.
4. Discussion
In this section, we will make a brief introduction of the model, give comparison with experimental results and analyze the influence of different high energy-state excitation channels on laser performance.
Figure 7 shows the energy levels and population transfer channels that being considered in the model. Figure 7(a) presents the radiative channels, including pumping (52S1/2→52P3/2), lasing (52P1/2→52S1/2), radiative decay (5P, 4D, 6S, 6P, 5D, 7S), photoexcitation (52P3/2→5D), photoionization (7S, 6P, 5D→Rb+) and multiphoton ionization (5P→Rb+). The populations on 6P and 7S are due to the ionic recombination processes, with an assumption that the combined neutral Rb atoms are equivalently distributed in 5D, 6P and 7S states [12]. The populations on 4D and 6S are due to the subsequent spontaneous emission from 6P state. Figure 7(b) presents the collisional population transfer channels, including the two-body and three-body fine-structure mixing, quenching, energy pooling, penning ionization, laser induced penning ionization, and recombination processes. The ambipolar diffusion process is also considered in the model [23]. The rate constants and cross sections for different processes are listed in Table 1.
Table 1. Rate constants and cross sections for different processes
Based on the above population transfer channels, a rate-equation based model is set up. As for the treatment of heat, it is solved by using the method that proposed by Barmashenko et al. [14]. The heat source in DPALs mainly comes from the quantum defect, quenching, and recombination processes. And the heat transfer is from the pumped region to the wall and natural convection process in the gas in a static cell. An iterative algorithm is proposed for calculation. By using our model and the energy balance relation [14], we firstly calculates an increased temperature and a decreased Rb concentration, and then we take these values into the model to calculate the temperature and concentration again, until these values converge. Then the steady-state temperature and Rb concentration in the pump region could be obtained [Fig. 6 (a)].
Here, we make a comparison between simulated and experimental results. In fact, we are unable to realize a quantitative agreement between experimental data and modeling results at present. For example, at a pump power of 110 W, the measured ionization degree is ~2%, and the simulation gives a value of ~7%., almost 3 times larger. The reasons of such deviation are discussed below. From the experimental point of view, the ionization degree along the pump path is not uniform, which is strongest where pump light enters and becomes weaker as pump propagates due to absorption. So the collection of electrons gives an averaged effect of the ionization degree. As for the electrons and Rb+, the recombination during the spatial transfer process from the pump region to the electrode decreases the effective collective electrons to some extent. Also the shielding effect will decrease the effective electric field, and lead to a smaller photocurrent as well as the ionization degree. So the experimental data give a relatively smaller ionization degree than the real case. From the theoretical point of view, the plasma formation is a very complex process, and many effects are still not considered in the model, partially due to insufficient interaction coefficients. For example, we only consider the direct three-body recombination and radiative recombination processes [12], but another much faster recombination mechanism also exists which is not considered. This recombination mechanism is a sequence of rapid conversion of Rb+ to Rb2+ followed by dissociative recombination of Rb2+ [14]. Generally, this dissociative recombination has a coefficient of 4-6 orders of magnitudes larger than the two-body radiative and direct three-body recombination mechanisms [11]. Due to lack of data, we artificially assume that, the recombination rates are 101, 102, 103, 104 and 105 times of the present recombination rate, and the resulted ionization degrees are 7%, 3.2%, 1.6%, 0.52%, 0.18% and 0.06%. It could be seen that, for the rate that set as 103 times, the ionization degree is much closer to the experimental result. This result implies that, the dissociative recombination mechanism may plays an important role in the ionization process and the coefficient needs to be further verified. Furthermore, many existing coefficients that used in the model are measured at vacuum, which is far from our conditions. The existence of high pressure helium will certainly decrease the collisional probability between Rb atoms, and lead to a smaller ionization degree. Another important issue is that, we don’t take into account of the detailed three-dimensional temperature field and the fluid effects, which are considered in some advanced models [12, 32, 33]. In general, the experimental data and modeling results are in a same order of magnitude, and a more comprehensive physical research and verification of interaction coefficients need to be done in the future.
Another issue worthy of mention is the importance of the Rydberg states. Although we have only considered relevant energy state with principal quantum number up to 7. Rydberg states with larger principal quantum number exist in the DPAL’s gain medium and play an important role in plasma formation and characteristics. These high lying Rydberg states could be generated by electron impact excitation, that is, the inelastic scattering processes can use the electron kinetic energy to increase the atoms’ internal energy exciting to a broad range of different states including many high-lying Rydberg states. The Rydberg states could also be produced by radiative excitations or collisions between Rb atoms. These high lying Rydberg atoms’ large sizes and susceptibility to perturbation and ionization by electric and magnetic fields, are an important factor determining the properties of plasmas. For example, in a Cs DPAL, the excitation pooling processes between two Cs (62P) states generate the higher Cs (72P) and the Rydberg states, which are then photoionized primarily by the lasing 894 nm photons. This mechanism explains 97% of plasma formation [16, 34].
Finally, we discuss the influence of different high energy level excitation channels on the laser performance. The calculation is made for an efficient hydrocarbon-free Rb DPAL. The main parameters are set as follows. The length of the gain medium is 2 cm. The cell is heated to 438 K with 15 atm helium at this temperature. The pump intensity is 15 kW/cm2 with spectral linewidth of 0.2 nm (FWHM). The single pass transmittance of the alkali cell is 98%, and the output coupler’s reflectivity is 20%. All the population transfer channels are considered as depicted in Fig. 7. In the above conditions, the simulation result gives an optical conversion efficiency of 70.14%, which is set as a baseline. Then, we will study the influence of different channels. For example, if we want to test the influence of energy pooling, we set the corresponding coefficient as zero (that is, close this channel), and compare the result with the baseline. The results are shown in Table 2:
Table 2. Influence of different population transfer channels on laser performance
In Table 2, we choose three typical objects for comparison. The first is the “Effective population proportion”, which is calculated as the sum of 52S1/2, 52P1/2 and 52P3/2 populations that divided by the total Rb concentration. The second is the “Ionization degree”. And the third is the “Efficiency increase degree”, which means the efficiency increased proportion as compared with the baseline (70.14%). The results show a clear influence for different channels. The photoionization gives an efficiency influence of ~1.8%. The energy pooling gives an influence of ~1.53%, and each other effect gives an influence below 1%. As for the effective population fraction and ionization degree, the processes of energy pooling and photoionization play an important role. All the high-energy excitation effects give an overall power influence of ~3.78% (not a simple superposition of each channel’s influence), which is not a negligible amount in a high power DPAL system.
5. Conclusion
In this paper, by significantly improving our previous experimental conditions, we conduct measurement of ionization degree in an operational hydrocarbon-free Rb laser. In the pulsed mode (with duration of 1 ms), a maximal ionization degree of ~0.06% is obtained at a pump power of 140 W. While in the CW mode, the ionization degree reaches as high as ~2% at a pump power of 110 W, which is mainly due to the enough time for sufficient plasma development. Both the influence of pump power and cell temperature are experimentally studied and analyzed. A rate-equation based model is set up, which considers the main high energy level excitation and ionization processes. A comparison between experimental data and simulation results is made and discussed. Finally, the influence of different population transfer channels are studied for a typical hydrocarbon-free Rb laser. The results show that, all the high energy level excitation effects give an overall negative influence on laser efficiency of ~3.78%, while the top two influencing channels are photoionization (~1.8%) and energy pooling (1.53%). The work in this paper, for the first time, reveals the influence of the macroscopic ionization evolution process on an operational DPAL, which provides a useful diagnostic method, and is beneficial for a more comprehensive understanding of the physics in DPALs.
Funding
National Natural Science Foundation of China (NSFC) (No. 11272343, and No. 61308044).
Acknowledgment
We acknowledge support of the National Natural Science Foundation of China.
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