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Abstract
Accurate modeling of the operation of diode-pumped alkali lasers is a critical step toward the design of high-powered devices. We present precision measurements for the Cs-CH4 62P3/2 → 62P1/2 mixing cross section and the 62P3/2,1/2 → 62S1/2 quenching cross section, which are important parameters in understanding the operation and, in particular, the heat generated in a cesium vapor laser. Measurements are carried out using ultrafast laser pulse excitation and observation of fluorescence due to collisional excitation transfer in time is done using the technique of time-correlated single-photon counting. Mixing rate measurements are acquired over methane pressures of 10 – 40 Torr, resulting in a Cs-CH4 62P3/2 → 62P1/2 mixing cross section of (1.40 ± 0.08) × 10−15 cm2, while quenching rate measurements are carried out over methane pressures of 500 – 4000 Torr, resulting in a 62P3/2,1/2 → 62S1/2 quenching cross section of (1.57 ± 0.03) × 10−18 cm2. These results suggest only a slight contribution to the heating of a cesium vapor laser is due to Cs 62P quenching, contrary to previous studies. We also discuss additional possible sources of energy transfer from upper excited states of Cs.
1. Introduction
Measurements of alkali-metal atom mixing and quenching cross sections have gained renewed interest due to their importance in diode-pumped alkali lasers (DPALs) [1–3]. A DPAL relies on a buffer gas to quickly transfer (mix) atomic populations between fine-structure states relative to their spontaneous excited state lifetimes. In the case of a typical Cs DPAL [4,5], a diode laser at 852 nm pumps Cs atoms to the 62P3/2 state, collisions with a buffer gas provide energy transfer between the 62P3/2 → 62P1/2 states, with lasing occurring at 894 nm. Methane gas is often used to carry out Cs 62P fine-structure mixing since it possesses a much larger mixing cross section compared to inert gases, but it does not quench as readily as some other hydrocarbon gases [6]. Collisional quenching is important in DPALs since these collisions reduce the number of atoms available for the lasing cycle, while also releasing much more energy (per transition) into the gain medium compared to fine-structure mixing. In particular, the heat generated due to mixing and quenching collisions contributes to a temperature rise along the gain medium which can result in deleterious effects to DPAL performance [7,8]. Recent high power DPAL systems incorporate flowing gas designs in order to avoid the high temperatures involved in static cell configurations [5,9,10]. In order to accurately model DPAL laser performance and thermal effects, accurate measurements of collisional mixing and quenching cross sections are necessary.
Two previous measurements of the Cs-CH4 62P3/2 → 62P1/2 mixing cross section have been carried out with results of (2.1 ± 0.3) × 10−15 cm2 [11] and (1.68 ± 0.17) × 10−15 cm2 [12]. Both results use the experimental technique of sensitized fluorescence, whereby continuous excitation is used to populate one of the fine-structure states while the fluorescence from both fine-structure states is monitored as a function of the methane gas pressure. We note the work of Walentynowicz et al. [12] includes Cs-CH4 mixing cross sections over a range of temperatures from 290 – 650 K. The Cs-CH4 62P3/2,1/2 → 62S1/2 collisional quenching cross section has not been precisely measured; however, indirect measurements have been performed. Pitz et al. [11] estimated an upper bound of (1.4 ± 0.6) × 10−16 cm2 for the Cs-CH4 quenching cross section. Recent results obtained by analyzing the operation of cesium DPALs resulted in quenching cross sections of approximately 5 × 10−18 cm2 [13,14] and (5 ± 3) × 10−18 cm2 [15].
In this work, we present for the first time a precise measurement of the Cs-CH4 62P3/2,1/2 → 62S1/2 quenching cross section, along with a measurement of the Cs-CH4 62P3/2 → 62P1/2 mixing cross section. These measurements are carried out using ultrafast laser pulse excitation to populate one of the Cs 62P fine-structure states and subsequently observing the time evolution of the fluorescence due to collisional excitation transfer. This technique has been used to measure mixing rates at high buffer gas pressures where three-body collisions occur [16,17], along with a recent measurement of the mixing and quenching cross sections for Rb 52P states in methane [18]. As our results suggest a minimal contribution to the heating of a cesium vapor laser is due to 62P3/2,1/2 → 62S1/2 quenching, we also excite a Cs vapor cell using a typical DPAL pump laser and observe the fluorescence produced over a broad range of wavelengths as a function of methane gas pressure. Fluorescence from multiple upper excited states of Cs is observed and is efficiently relaxed with methane buffer gas, suggesting additional sources of heat within a Cs DPAL.
2. Experimental method and setup
2.1. Theoretical background
A diagram of the Cs energy levels and transitions considered in this study is shown in Fig. 1(a). Our experimental technique relies on exciting one state of the Cs 62P fine-structure doublet with an ultrafast laser pulse and observing the fluorescence due to collisional excitation transfer from the other fine-structure state. A detailed theoretical background is presented in Ref. [18], while here only a summary is given. The rate equations describing the time evolution of the populations of the two fine-structure states after termination of the laser pulse are:
where n1 and n2 represent the populations of the 62P1/2 and 62P3/2 states, respectively, γ10 and γ20 are the spontaneous (radiative) decay rates of the two states, R12 is the collisional excitation transfer (mixing) rate from 62P1/2 → 62P3/2, R21 is the mixing rate from 62P3/2 → 62P1/2, and Q10 and Q20 are the collisional quenching (non-radiative) rates from 62P1/2 → 62S1/2 and 62P3/2 → 62S1/2, respectively.
Fig. 1 (a) Cesium energy level diagram, illustrating the states involved in these experiments. (b) Schematic of the experimental setup used to carry out cesium 62P mixing rate and quenching rate measurements in methane gas.
The principle of detailed balance relates the two mixing rates R12 and R21:
where g2 and g1 are the degeneracies of the 62P3/2 and 62P1/2 states, respectively, ΔE is the 62P fine-structure splitting, kB is the Boltzmann constant, and T is the temperature in kelvin.If, for example, the 62P3/2 state is excited using a 852 nm laser pulse, Eqs. (1) and (2) can be combined to obtain an equation describing the temporal evolution of the 62P1/2 state population:
where the rate coefficients s+ and s− are given by with α1 = γ10 + R12 + Q10 and α2 = γ20 + R21 + Q20. Coefficients A and B are determined from the initial conditions. The evolution in time of the 62P1/2 state population is therefore described by a double exponential, with the rate coefficients providing the mixing and quenching rates. If excitation is instead performed to the Cs 62P1/2 state at 894 nm, the same Eqs. (1) and (2) can be used to obtain an expression describing the evolution in time of the 62P3/2 state population.2.2. Experimental apparatus
Our experimental apparatus is designed to provide fast excitation, with subsequent observation of the fluorescence photons in time using the technique of time-correlated single-photon counting [19]. While the fluorescence from either state could be detected, we choose to only detect the fluorescence due to collisional excitation transfer from the Cs 62P state which is not excited by the initial laser pulse. As this state is not initially populated, the fluorescence exhibits a sharp rise in time followed by an exponential decay according to Eq. (4). This detection method also allows the use of interference filters in the detection system to largely block the scattered light produced at the wavelength of the excitation laser.
A schematic of our experimental setup is shown in Fig. 1(b). A commercial mode-locked Ti:sapphire laser (Coherent Mira) produces laser pulses of ∼ 150 fs in duration with a pulse energy of approximately 7 nJ at wavelengths of either 852 nm or 894 nm. An electronic clock divider (Conoptics 305) synchronized to the optical pulses divides the initial 76 MHz laser pulse repetition rate signal to approximately 500 kHz. This signal is then sent to a pulse and delay generator (Stanford Research Systems DG535) which provides the appropiately timed electrical signals to two electro-optic modulators (Conoptics 350-160). The two electro-optic modulators (EOMs) combined in series achieve an extinction ratio between selected to background laser pulses of ≥ 104 : 1.
The laser-atom interaction region consists of a cylindrical glass cell 25 mm long with an inner diameter of 2 mm which is connected to a vacuum system. The vacuum system allows the glass cell to be evacuated to pressures of ≤ 10−7 Torr. A Cs reservoir is attached to the vacuum system along with a source of methane gas. Two capacitance manometers are used, the first to monitor methane gas pressures between 0 – 100 Torr (MKS Baratron 626A12TBE), and a second to monitor methane gas pressures between 100 – 4000 Torr (MKS Baratron 625D14THAEB). A sample of the laser pulse is used to trigger a time-to-digital converter (Agilent Acqiris TC890). The time-to-digital converter (TDC) is stopped when a photon is detected. Collecting photons over a period of typically 10 – 15 minutes results in a histogram of the fluorescence photons as a function of time. The detection system uses a 1:1 imaging system (f/3) to collect the fluorescence from the glass cell and focus it onto a photomultiplier tube (Hamamatsu R636-10). Multiple interference filters are used at either 852 nm or 894 nm to attenuate scattered laser light at the excitation wavelength.
3. Experimental results and discussion
A preliminary examination of the observed fluorescence as a function of time determined very different methane gas pressure ranges would be required to measure Cs 62P mixing rates and quenching rates, similar to our previous work with Rb-CH4 [18]. Measurements of the Cs 62P3/2 ↔ 62P1/2 collisional excitation transfer (mixing) rates were performed in the low-pressure regime (10 – 40 Torr), while measurements of the 62P3/2,1/2 → 62S1/2 quenching rates were performed in the high-pressure regime (50 – 4000 Torr).
Typical fluorescence histograms recorded in the low-pressure regime are presented in Fig. 2, in this case with fluorescence observed at 894 nm. Also shown in Fig. 2 is the 852 nm excitation laser pulse which we purposefully observe at the beginning of a data run in order to calibrate the origin of the time axis. Individual data sets are fit to Eq. (4), using a Levenberg-Marquardt nonlinear least-squares fitting routine in MATLAB. The quenching rates Q10 and Q20 are neglected in this fit, which yields the collisional mixing rate R21 for a particular methane pressure. The inset in Fig. 2 shows the 62P3/2 → 62P1/2 mixing rates plotted as a function of the methane pressure along with a linear fit through the data. The mixing rate R21 is related to the (velocity averaged) cross-section σ21 by
where n is the methane gas density and vrel is the mean relative velocity of the colliding partners.Fig. 2 The time evolution of 894 nm fluorescence induced by collisional excitation transfer with methane gas at the pressures listed. Also shown is the excitation laser pulse at 852 nm. The solid lines are fits to the data according to Eq. (4) and are used to extract the mixing rates. The inset shows the mixing rates as a function of methane gas pressure and a linear fit to the data is used to extract the mixing cross-section.
Fluorescence curves are also recorded with laser excitation at 894 nm and fluorescence detection at 852 nm, with the ratio between R21 and R12 fixed by detailed balance (Eq. (3)). Multiple data sets are acquired for both excitation and detection wavelength combinations and the resulting mixing cross sections are combined using a weighted average. A final result of σ21 = (1.40 ± 0.08) × 10−15 cm2 is determined for the Cs-CH4 62P3/2 → 62P1/2 mixing cross section. The uncertainty of this result is determined by analyzing several systematic errors such as pressure measurement uncertainties, calibrating the origin of the time axis to the initial laser pulse, and radiation trapping, to highlight a few of the largest systematic errors. The statistical error in this result is only ±0.02%, thus systematic errors dominate the uncertainty of this measurement. The largest systematic error comes from determining the arrival time of the laser pulse, which could be improved through the use of a detection system and, in particular, a photomultiplier tube with a faster time response. Further details on how these systematic uncertainties are determined can be found in Refs. [17,18]. Our result can be compared to two previous measurements of the Cs-CH4 62P3/2 → 62P1/2 mixing cross section: (2.1±0.3)×10−15 cm2 [11] and (1.68 ± 0.17) × 10−15 cm2 [12]. We note that our measurement and both of the previous measurements were taken at a temperature of 298 K. While not significantly different from previous results, our measurements do improve upon the experimental uncertainty by more than a factor of two, along with using a much different experimental technique.
At high methane gas pressures, the mixing rates are much larger than the decay rates and thus the time required to mix the fine-structure states is much shorter than their natural lifetimes. Under these conditions, the three-level system behaves as a quasi-two-level system with the population ratio fixed by the vapor cell temperature. As shown in Ref. [18,20], both states decay as a single exponential with the s− rate given by
where γav = fγ10 + (1 − f)γ20 and Qav = fQ10 + (1 − f)Q20, with f and 1 − f the fraction of the population in the 62P1/2 and 62P3/2 states, respectively. As a result, a measurement of s− cannot determine the individual quenching rates Q10 and Q20, but only the statistically weighted average quenching rate Qav.Figure 3 shows typical fluorescence curves recorded in the high-pressure regime with the fluorescence observed at 894 nm and using laser excitation at 852 nm. Since the rise in the collisionally induced fluorescence is nearly instantaneous compared to the time response of our detection system, only the decay portion of the fluorescence curve is shown and fitted. The fitting is done in OriginPro using a Levenberg-Marquardt iteration algorithm to an exponential decay function,
where s−, C, and D are fitting parameters. The inset in Fig. 3 shows the quenching rate measured as a function of the methane gas pressure, with a linear fit to the data used to extract the statistically weighted average quenching cross-section. Multiple data sets are collected in the high pressure regime for both excitation and detection wavelengths and are combined using a weighted average. A final result of σQ = (1.57 ± 0.03) × 10−18 cm2 is achieved. The calculation of the uncertainty of this result is carried out in a similar manner to the mixing rate analysis above and is discussed further in Ref. [18]. The uncertainty in the quenching cross section is significantly smaller than in our measurement of the mixing cross section since fitting the arrival time of the laser pulse is no longer necessary for quenching rate measurements.Fig. 3 The decay in time of 894 nm fluorescence induced by collisional excitation transfer in the high pressure regime. The solid lines are fits to the data according to Eq. (8) and are used to extract the quenching rates. The inset shows the quenching rates as a function of the methane gas pressure and a linear fit to the data is used to extract the quenching cross-section.
Our measured quenching cross section of σQ = (1.57 ± 0.03) × 10−18 cm2 is significantly smaller than the upper bound of σQ ≤ (1.4 ± 0.6) × 10−16 cm2 determined in Ref. [11], but in reasonable agreement with recent results of σQ ∼ 5 × 10−18 cm2 [13] and σQ = (5 ± 3) × 10−18 cm2 [15] obtained from modeling the operation of a Cs DPAL. Our experimental technique has the advantage of working well even at very high buffer gas pressures, where the quenching effect is largest, in contrast to sensitized fluorescence experiments which typically do not go above 100 Torr buffer gas pressure. The small quenching cross section reported here may change some of the conclusions in a recent study examining the heating observed in a DPAL gain medium [8]. In that work, the heating reported for a Cs DPAL had 30% attributed to spin-orbit relaxation and 70% attributed to collisional quenching which was based on the previously estimated quenching cross section of σQ ∼ 1.4 × 10−16 cm2 [11]. In light of this new measurement, there must be an additional and significant source of heating within a Cs DPAL to account for this discrepancy.
To further investigate the sources of heating in a Cs DPAL laser we performed additional measurements using a narrowband (12 GHz linewidth) 852 nm laser pulse (100 μs duration) to excite the Cs 62P3/2 state while observing the emitted fluorescence using a spectrometer (Ocean Optics Red Tide USB 650). A laser pulse of 100 μs duration was chosen as it will be sufficiently long to achieve steady-state lasing conditions, but also sufficiently short to eliminate any thermal effects. We use a static vapor cell attached to a vacuum system and a gas manifold which allows us to examine the fluorescence of the Cs vapor under various buffer gas conditions. We begin with 600 Torr of pure helium mixed with Cs vapor at a temperature of 388 K, and examine the spectrum from the excited Cs vapor. The results can be seen in Fig. 4, where the peaks at 602, 620, 673 and 698 nm correspond to 8D → 62P1/2, 8D → 62P3/2, 7D → 62P1/2 and 7D → 62P3/2 transitions, respectively, according to the energy level diagram in Fig. 1(a). Even though the probe laser is only exciting the 62P3/2 state, it is clear that either through energy pooling or two-photon absorption, the 7D and 8D upper states of Cs are being excited and, possibly, even ionized.
Fig. 4 Fluorescence emitted by upper atomic states of Cs after laser pulse excitation at 852 nm for various methane pressures. The peaks at 602, 620, 673 and 698 nm correspond to Cs 8D → 62P1/2, 8D → 62P3/2, 7D → 62P1/2 and 7D → 62P3/2 transitions, respectively.
We then proceed to add small quantities of methane and observe the changes in the fluorescence. As can be seen in Fig. 4, even with small quantities of methane, the fluorescence from the 7D and 8D states of Cs is reduced and ultimately completely attenuated at less than 50 Torr methane pressure. This indicates that the methane is collisionally relaxing the excited upper atomic states of Cs which will produce additional heating in a DPAL gain medium. Since our measurements of the Cs 62P quenching cross section suggest only a small contribution to the heating of the gain medium can be attributed to this effect, it is likely that a significant amount of heating occurs from the relaxation of upper excited atomic states.
4. Conclusion
In this paper we present the first precise measurement of the Cs-CH4 62P3/2,1/2 → 62S1/2 quenching cross-section along with improved measurements of the 62P3/2 → 62P1/2 mixing cross-section. The study was performed using the techniques of ultrafast laser-pulse excitation and time-correlated single-photon counting to observe the time evolution of the fluorescence induced by collisional excitation transfer. These precision measurements are relevant for the operation of an alkali laser, as well as for understanding collisional processes in alkali-buffer gas mixtures. Our results suggest that quenching from the Cs 62P states is not a significant source of heating in a cesium vapor laser, but relaxation from upper excited atomic states should also be considered. The techniques reported here can be used to precisely measure the mixing and quenching cross-sections for a variety of alkali-buffer gas combinations, including temperature-dependent cross-sections.
Funding
National Science Foundation (NSF) (1531107, 1708165); Directed Energy Joint Transition Office (JTO-14-UPR-0525); Air Force Office of Scientific Research (AFOSR); Society of Physics Students (SPS).
Acknowledgments
Support for this work by the National Science Foundation, the Directed Energy Joint Transition Office, the Air Force Office of Scientific Research and the Society of Physics Students is gratefully acknowledged.
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