Real-time measurement of temperature rise in a pulsed diode pumped rubidium vapor laser by potassium tracing atom based absorption spectroscopy

Xiaofan Zhao; Zining Yang; Weihong Hua; Hongyan Wang; Xiaojun Xu

doi:10.1364/OE.25.005841

1. Introduction

Firstly being proposed by Krupke in 2003 [1], diode pumped alkali lasers (DPALs) have attracted great attention and achieved significant development till now. These lasers utilize laser diodes to directly excite the $D_{2}$ transition ( $n^{2} S_{1 / 2} \to n^{2} P_{3 / 2}$ ) of alkali atoms (n = 4, 5, 6 for K, Rb and Cs). Collisions between excited alkali atoms and buffer gas, usually helium or small hydrocarbons e.g. methane, transfer populations from $n^{2} P_{3 / 2}$ to $n^{2} P_{1 / 2}$ state. And lasing occurs on the $D_{1}$ transition $(n^{2} P_{1 / 2} \to n^{2} S_{1 / 2}) .$ The most attractive feature of these lasers is the combination of high power diode pumping and convective thermal management, which make DPALs promising for single aperture power scaling [2]. For reasons above, DPALs are regarded as a new generation of high energy laser (HEL) [3], which are attractive for applications such as power beaming over extended distance [4] or military use [5]. Besides HEL applications, low or moderate power DPALs with specific longitudinal or transverse mode characteristics [6, 7] are also very useful for industrial manufacturing, laser cooling [8], spin exchange optical pumping (SEOP) [9], and even promising light sources for the second-generation gravitational wave interferometers [10].

For over a decade of development, a large amount of literatures have been produced for DPALs’ research in various aspects. Some comprehensive review articles could be found in references [11–13]. In 2012, Bogachev et al. firstly realized one kilowatt laser power on a Cs DPAL [14]. In 2016, Pitz et al. realized a high efficient 1.5 kW K DPAL, which held the highest published power record [15]. Besides experimental demonstrations, theoretical studies were continually put forward, from the initial 1-D 3-levels static models to the present 3-D, time-dependent, multi-levels, optical and fluid dynamics fields coupled models [16–19]. Some other similar optically pumped gas laser concepts, e.g. exciplex pumped alkali lasers (XPALs) [20] and optically pumped metastable rare gas lasers (OPRGLs) [21], were also proposed and developed.

Along with the constantly refreshing power records, advanced model simulations and flourishing new ideas, laser medium diagnostics, which are essential for parametric optimization and resonator design, are relatively limited and lagged behind. The pioneering work of Davis et al.’s two-dimensional gain mapping is an exception [22]. With increasing power levels, more diagnostic efforts are urgently needed for more comprehensive diagnostics. In DPALs, a most representative phenomena is the rolling over of laser power as pump power increases in static cells. It was firstly attributed to the drop of alkali concentration due to local temperature rise [23]. In 2012, Fox et al. firstly observed the drop of alkali concentration due to heat effect, by using a tunable diode laser as a probe to detect the absorbance around the pump region [24]. In 2014, Oliker et al. have presented a high fidelity model to clarify this effect [18]. Recently, Shaffer et al. have successfully demonstrated a direct Gladstone-Dale relation based in situ non-perturbative temperature measurement on an end-pumped Cs alkali laser with Mach-Zehnder interferometer. By demodulating the distorted 2-D interference pattern, the spatial variation of temperature in the pump region could be well obtained [25,26]. Their work gave a definite answer to the above questions and firstly showed a practical way for DPALs’ diagnostics. Subsequently, for the reason that most DPALs utilized methane as a fast collisional transfer agent, Wang et al. extended the methane based tunable diode laser spectroscopy (TDLAS) into DPAL’s temperature measurement [27]. A most recent work by Waichman et al. presented a 3-D, time-dependent, optical field and CFD coupled model for a static DPAL [28]. The model has considered all the known temperature induced effects, including changing of light-atom interaction parameters, chemical reaction between alkali atoms and hydrocarbons, drop of alkali concentrations and the influence of laser beam quality etc. The simulation results agreed reasonably with the experimental data [23], which further improved the understanding of thermal effects in DPALs.

In this paper, we firstly propose and demonstrate a new tracing atom based absorption spectroscopy method for temperature measurement inside the gain medium of an operational DPAL. In this method, we artificially add another alkali species (K) into a static DPAL’s medium (Rb) as non-disturbing tracing atoms. When the medium is pumped, both the K and Rb vapors experience the same degree of temperature rise and concentration drop. By directly detecting the absorption signal of the K atoms, the temperature rise could be obtained. The method is mainly favored for its ability to provide a transient and real-time temperature evolution, which could be used in both hydrocarbon-added and hydrocarbon-free systems.

2. Theoretical basis and simulation

As an example, a Rb DPAL with K tracing atoms is considered. Without pumping, the Rb and K concentrations are denoted as $n_{R b}^{u n p u m p e d}$ and $n_{K}^{u n p u m p e d}$ , which depend on the saturated vapor pressure in temperature $T_{1} .$ The probe laser should be tuned precisely to the central frequency of the K $D_{1}$ line’s absorption spectrum. The incident power of the probe laser is $P_{0}$ , and the transmitted power is $P_{1}$ , which is calculated by the Beer-Lambert's law

P_{1} = P_{0} \exp (- n_{K}^{u n p u m p e d} σ_{1} l),

where

l

is the length of gain medium, and

σ_{1}

is the K atom’s central frequency absorption cross-section. For DPALs, the buffer gas pressure is on the order of one to several atmospheres, which leads to a Lorentzian line shape of atomic transitions. When the frequency of probe laser is accurately tuned to the central frequency of alkali

D_{1}

line, the

σ_{1}

could be described without the Lorentzian frequency dependence term

σ_{1} = \frac{A_{21} λ_{D_{1}}^{2}}{4 π^{2}} \cdot Δ v_{1}^{- 1},

where

A_{21}

and

λ_{D_{1}}^{}

are spontaneous emission rate and wavelength of the

D_{1}

transition.

Δ v_{1}

is the spectral linewidth (FWHM) that relates with the buffer gas pressure

p_{1}

and temperature

T_{1}

Δ v_{1} = p_{1} \cdot γ (T_{0}) {(T_{1} / T_{0})}^{- 1 / 2},

where

γ (T_{0})

is the known collisional broadening coefficient at temperature

T_{0}

. Here, we will further explain about the temperature dependence of

γ (T)

. In general, it could be expressed by

γ (T_{0}) = \int_{0}^{\infty} σ (g) g f (g; T) d g,

where

σ (g)

is the broadening cross section, g is the relative speed of collision pairs which is in direct proportion to

T^{1 / 2}

, and

f (g; T)

is the Maxwellian speed distribution. Only if the cross section

σ (g)

is independent of temperature, Eq. (3) holds. The work by Pitz et al. showed that, the broadening cross section of cesium by nitrogen for

D_{1}

transition kept constant in a temperature range of 310-335 K [29]. And this is usually regarded as an assumption to obtain the broadening cross section from measured broadening rate [30].

When the medium is pumped, the temperature of the pumped region increases to $T_{2}$ , the Rb and K concentrations drop to $n_{R b}^{p u m p e d}$ and $n_{K}^{p u m p e d}$ . In this condition, the transmitted probe laser power is

P_{2} = P_{0} \exp (- n_{K}^{p u m p e d} σ_{2} l) .

Here the central frequency absorption cross-section of K is changed to $σ_{2}$ due to the changed temperature $T_{2}$ and buffer gas pressure $p_{2}$

σ_{2} = \frac{A_{21} λ_{D_{1}}^{2}}{4 π^{2}} \cdot Δ v_{2}^{- 1},

Δ v_{2} = p_{2} \cdot γ (T_{0}) {(T_{2} / T_{0})}^{- 1 / 2} .

It should be noticed that, as compared with the line broadening effect, the relatively small frequency shift effect could be ignored [30], which will be simulated in the following content. By applying the ideal gas pressure formula

\frac{p_{2}}{p_{1}} = \frac{n_{2}}{n_{1}} \cdot \frac{T_{2}}{T_{1}},

Together with the Eqs. (1)–(7), we could get the relation for practical use:

\frac{T_{2}}{T_{1}} = {[\frac{\ln (P_{0} / P_{1})}{\ln (P_{0} / P_{2})}]}^{2} .

So, if we know the initial temperature $T_{1}$ , and measure the incident probe power $P_{0}$ , transmitted probe power without pumping $P_{1}$ and with pumping $P_{2}$ , the temperature could be obtained by Eq. (9). By assuming the isobaric condition, which is usually held in DPALs, the alkali concentration variation could be further obtained

\frac{n_{R b}^{u n p u m p e d}}{n_{R b}^{p u m p e d}_{}} = \frac{n_{K}^{u n p u m p e d}}{n_{K}^{p u m p e d}_{}} = \frac{T_{2}}{T_{1}} .

Here, we provide some simulation results for expected absorption under different conditions, and discussion some limitations. Some useful parameters for potassium atom are listed in Table 1:

Table 1. Atomic data for $K^{39}$ $D_{1}$ line transition and interaction parameters with buffer gas.

View Table

Figure 1 provides the influence of different parameters on K absorption. The calculation conditions are chosen as follows (agree with the experimental conditions): cell length $l = 2$ cm, probe laser power $P = 5$ mW, probe intensity $I = 1.8$ W/cm², probe linewidth $Δ ν = 1$ MHz (FWHM), and other parameters are listed in captions.

Fig. 1 Expected potassium absorption under different conditions.

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Figure 1(a) shows the result of temperature influence. Here, the temperature affects many parameters, including K concentration, buffer gas pressure, $D_{1}$ line transition linewidth and central frequency etc. As the temperature increases, the weak probe power tends to be totally absorbed after 420 K. Due to the reason that, we would expect a decrease in absorption under pumping, some small amount of transmitted probe power will satisfy the application, so the operational temperature by using K tracing atom should be limited below 420 K (99% absorption fraction). Figure 1(b) shows the influence of K absorption linewidth. The calculated range from 3.9 GHz to 58.9 GHz in the abscissa corresponds to the methane pressure from 100 torr to 1520 torr. The drop of absorption is due to the decrease of the central-frequency’s absorption cross section $σ$ . The linewidth dependence of absorption has been sufficiently considered in the derivation of Eq. (9). Figure 1(c) give the influence of atomic frequency shift. The atomic frequency shift is decided by both the collisional gas pressure and the temperature [29]. For example, for a Rb cell with 500 torr methane (pressure at 293 K) and 410 K temperature, we assume a temperature rise in the pump region of 230 K, and the buffer gas pressure in the pump region will change into 700 torr. At these conditions, the calculated atomic frequency shift, as compared with the unpumped case, is ~0.52 GHz. Here, we assume a same temperature dependence of frequency shift cross-section as broadening cross-section. Such degree of frequency shift will not affect the absorption significantly, and we will take this factor as an error in the experiment section. Figure 1(d) shows the tolerance of probe wavelength deviation (relative to the atomic central absorption frequency), which gives a same curve as atomic frequency shift. In fact, with high quality current and temperature controllers, the single frequency diode laser could ensure a frequency drift below 100 MHz, so the influence of probe laser’s frequency drift can be ignored.

3. Experimental setup and results

The experimental setup is shown in Fig. 2. The pumping source was a volume Bragg grating (VBG) coupled line-narrowed diode laser stack, with central wavelength tuned exactly to 780.2 nm and linewidth of 0.2 nm (FWHM). The pump light was firstly collimated by a confocal telescope that consisted of two cylindrical lenses ( $f_{1} = 6$ cm and $f_{2} = 10$ cm), and then was focused into the Rb cell by a spherical lens ( $f = 20$ cm). A chopper with duty cycle of 1:40 was used at the focal position. On one hand, it would decrease the averaged pump power to prevent chemical reaction between Rb and methane, and on the other hand, it would provide a convenient way to adjust the pump pulse duration by changing the revolving speed. The “U” shape resonator consisted of a dichroic mirror, an output coupler, an Rb cell and two polarized beam splitters (PBS). The plane dichroic mirror was 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 halfwave plate together with PBS1 was used to adjust the incident pump power. The alkali cell contained Rb for lasing, and K as tracing atoms. The cell was filled with 500 torr methane (293 K) as buffer gas. The shape of the glass cell was a cylinder with diameter of 2.5 cm and inner length of 2 cm, with no coatings on window surfaces. The temperature of the cell could be well controlled by an electrical heater with accuracy of $\pm 1$ K.

Fig. 2 Schematic of the experimental setup. The green, blue and red lines represent pump, probe and alkali lasers, respectively. CL: cylindrical lens, FL: focusing lens, PBS: polarized beam splitter.

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At maximal pump power, the focus of the pump light was located at the center inside the cell with a rectangular beam shape of ~1 mm × 1.5 mm (86% power included). The output coupler was a plane mirror with reflectivity of 50%. The laser power was recorded by a Thorlabs power meter (S310C).

The probe laser was a single frequency DBR diode laser with linewidth of ~1 MHz, which was rather less than the alkali $D_{1}$ line (broadened by the methane buffer gas to ~10 GHz). The probe wavelength was precisely tuned to the central wavelength of the K atom $D_{1}$ absorption line, by detecting the strongest absorption when scanning the wavelength. The halfwave plate together with PBS3 were used to adjust the incident power, and the exact wavelength was monitored by using a wavelength meter (HighFinesse WS7). The collimated and uniform probe beam ( $ϕ ~ 0.6$ mm with 86% power included) was spatially adjusted to be collinear with the pump beam inside the cell. The probe power was several milliwatts which was far below the absorption saturation intensity. Two narrowband filters (central wavelength of 770 nm and bandwidth of 10 nm) were used to block the residual 780 nm pump laser, atomic fluorescence and scattering lights. After passing through a neutral optical attenuator, the probe laser entered the Si-based photo detector (Thorlabs DET36A model). The photo detector has an active area of $13$ mm², which is much larger than the probe laser beam for reliable receiving the total probe power, and has a 14 ns rise time which is much faster than the characteristic time of temperature evolution (on a time scale of ~ms level [18,26]) to realize a real-time measurement.

Figure 3 shows a typical result of the time evolution of pump, laser, K transmitted signals (left y axis) and temperature (right y axis). The alkali cell is heated to 408 K, which corresponds to Rb and K concentrations of $4.7 \times 10^{13}$ cm³ and $7.3 \times 10^{12}$ cm³.

Fig. 3 Typical signal of time evolution of pump, laser, K transmitted signals and temperature. The alkali cell is heated to 408 K, the pump duration is 2 ms (FWHM), and the pump power is 92 W.

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The pump power is 92 W with duration of 2 ms, and the laser power is 10 W. It should be noted that throughout this text, when 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) which is being discussed. We can see that, in the duration of the pump pulse, heat deposition leads to temperature rise and an increase of K transmitted signal, which is due to a drop of the K atom concentration. Meanwhile, a decrease of the Rb laser power is observed which is mainly due to thermal effect. When the pump pulse terminates, the K transmitted signal stops increasing, and decreases gradually due to heat relaxation. And finally it recovers to the original baseline. Based on the K transmitted signal, together with Eq. (9), the temperature evolution can be obtained. There is a maximal temperature rise of ~222 K in this case.

Figure 4(a) shows the results of temperature rise and laser power under different pump powers. The “temperature rise” here represents the maximal temperature rise during a pump pulse. As the pump power increases, the laser power increases linearly with a slope efficiency of ~13%, the relatively low efficiency is mainly due to the large resonator loss (single transmission ~75%) and mismatch between pump linewidth (~0.2 nm) and atomic absorption linewidth (~0.02 nm). The increasing pump power leads to an increasing heat deposition, which is mainly due to the fine-structure relaxation and quenching effects [26]. The temperature rise shows a linear trend as pump power increases, and we obtains a maximal value of ~224 K under the pump power of 92 W. It should be noticed that, the laser power is rather stable with fluctuation less than 2%, so the error bar is not specially depicted. As for the K transmitted signal, the data shows a fluctuation which is given as an error bar in Fig. 4 (discussed below).

Fig. 4 (a) Laser power and temperature rise under different pump powers. The alkali cell is heated to 408 K, the pump duration is 2 ms (FWHM). (b) Laser power and temperature rise under different pump pulse durations. The alkali cell is heated to 408 K, the pump power is 85.3 W.

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Figure 4(b) shows the results of temperature rise and laser power under different pulse durations. It can be seen that, as the pulse duration increases, the temperature rise increases correspondingly. Because longer heat deposition leads to higher temperature rise. Also observed is the decrease of the laser power. For each pulse, the initial instant laser power nearly keeps constant, but when the pump duration increases, more accumulated heat induces a more seriously drop of the instant laser power (just as the trend that shown in Fig. 5). So the laser power, that is, the “average laser power during the pulse duration” (as defined above) decreases. At the same time, the thermal relaxation time (the time of temperature drop from its maximum to $1 / e$ of this value) also increases as pump width increases due to more accumulated heat, e.g. from 3.8ms (1ms pump width) to 8.1ms (5ms pump width).

Fig. 5 Time evolution of laser and pump signals at pump power of 85.3W and alkali cell of 408K. (a) Pump duration is 2 ms (FWHM), (b) Pump duration is 5 ms (FWHM).

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Here, we will give some discussion about the error. As for the error bars in Fig. 4, they are the standard deviations of the repetitively sampled experimental data (5 times). The maximal error value is $\pm 7.6$ K. The error is mainly due to two reasons: one is the power fluctuation of probe laser, the other is the unsteady atom concentration inside the gain medium. For the latter one, because of the existing temperature gradient (causing local convective flow), the existence of buoyancy and unsteady pumping, the K atoms concentration is not a constant value, but shows a variation that causes the absorption fluctuation. Besides, some other factors may also introduce errors: (1) The atomic frequency shift may induces a level of ~0.5 GHz deviation between the probe and central atomic absorption frequency, which can introduce a temperature error of ~1.5 K. (2) The shift of the probe frequency, which is less than 100 MHz, will introduce a much less temperature error of ~0.7 K. Totally, the uncertainty of measured temperature is $\pm 9.8$ K.

4. Discussion

A quantitatively comparison between measured result and theoretical simulation needs a 3-D, time-dependent multi-physics coupled model. A simple calculation [23] for the case in Fig. 3 gives a steady-state temperature rise of ~600 K, which is much higher than our measured result. However, it is reasonable, because our experiment is transient. Here, we will give a comparison with other groups’ results. Based on the interference measuring method [25], Zhdanov et al. has also performed temperature measurement in a pulsed Cs DPAL [26]. In their experiment, the Cs cell was 2.5 cm long, filled with 600 torr methane and heated to 398 K. Under a pumping pulse with duration of 100 ms and power of 50 W, the temperature increased up to ~620 K. In Waichman’s simulation results for a static Cs DPAL, with 2 cm cell filled with 600 torr methane and heated to 367 K, the temperature was ~600 K under 100 W pump power [28]. As a comparison, we have measured the temperatures of ~590 K and 635 K under pump power of 58 W and 92 W respectively. We can see that, although the system conditions have many differences, the temperatures were on a same level. Comparing with the successful interference measuring method, our method benefits from the faster measurement feature, due to the reason that the response time of photodiode is usually much faster than CMOS or CCD.

In this method, a restriction is that, the tracing atoms should not be opaque for the low power probe laser. For example, in our case, the cell temperature was 408 K which resulted in a K concentration of $7.3 \times 10^{12}$ cm⁻³, but for 433 K (the usually case for a hydrocarbon free Rb laser), the K concentration increases to $3 \times 10^{13}$ cm⁻³, which may become opaque for the 770 nm probe laser. In this case, the Na atoms become a better choice, due to much lower saturated vapor pressure at the same temperature. In this case, the 589 nm single frequency laser could be adopted as a probe laser, which was well developed in the sodium vapor guide laser (SLGS) technologies [32,33]. Another concern of this method is the disturbance of the K probe laser due to existing Rb energy levels. The most adjacent transition is the 776 nm $5^{2} P_{3 / 2} \to 5 D$ , which is far away from resonance, even with consideration of collisionally induced linewidth broadening effect. The existing absorption channels are the photoionization transitions from the 7S, 6P and 5D states, with cross sections of $0.1 \times 10^{- 18}$ cm², $16 \times 10^{- 18}$ cm², $16 \times 10^{- 18}$ cm² [34], and ionization limit energy <1.36 μm, 1.01 μm, 1.25 μm respectively. We have made a theoretical calculation for a typical Rb laser, with parameters of 10 kW/cm² pump intensity, 200 torr methane and 1520 torr helium buffer gases, 2 cm gain length and 433 K cell temperature, the result gave a total population fraction, including 7S, 6P and 5D, of 0.35%, and an absorbance of the 770 nm probe laser of 4.2 × 10⁻⁴%, which could be well ignored. Other dimer, e.g. Rb-K, Rb-He, absorptions can also be neglected due to their low concentrations. In general, the tracing K atoms will bring no deleterious effects on the Rb laser performance, what’s more, they may enhance the efficiency although not remarkably, due to the slightly increased K-Rb fine structure mixing rate [35]. Additionally, from the operational point of view, our scheme could also be adjusted by using a scanning scheme, which will further enhance the ability to overcome the negative effects induced by atomic frequency shift and probe wavelength deviation. In the scanning scheme, each data point will be chosen when the probe wavelength is tuned to the line center of the K absorption spectrum, so we will obtain an envelope curve which consists of a series of points that being separated by the scan period. But it should be noticed that, by using this scheme, the scanning period should be much less than both the characteristic time of temperature rise and the measured time interval, or the “real-time” feature will be destroyed. Finally, a good diagnostic method should contain spatial information [25,26]. In the present work, we have demonstrated a single point temperature measurement. However, by using a larger cross section probe beam which covers the whole pump region and a plane-array detector (CMOS or CCD), the method could be further improved to realize a spatially resolved measurement.

5. Conclusion

In conclusion, we have firstly proposed a novel tracing atom based absorption spectroscopy for non-contact and real-time measurement of the temperature rise in a pulsed alkali laser. By adding K atom as tracing species, the time evolution of temperature inside the pump region of an operational Rb DPAL was successfully obtained. The method provides a useful and convenient way for diagnostics, which will be helpful for further development of high power DPALs.

Funding

National Natural Science Foundation of China (No. 11272343, and No. 61308044).

Acknowledgment

We acknowledge support of the National Natural Science Foundation of China.

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Property	Value	Reference
Wavelength, $λ$	$770.108385049 (123)$ nm	[31]
Lifetime, $τ$	$26.37 (5)$ ns	[31]
Natural linewidth, $1 / 2 π τ$	$6.03 (1)$ MHz	[31]
Collisional broadening rate by methane, $γ$	$29.35 \pm 0.12$ MHz/torr (328 K)	[30]
Collisional shift rate by methane, $δ$	$- 7.41 \pm 0.02$ MHz/torr (328 K)	[30]
Central cross section for $D_{1}$ line absorption buffered by 500torr methane at 408K, $σ$	$2.9449 \times 10^{- 13}$ cm²	Calculated

Real-time measurement of temperature rise in a pulsed diode pumped rubidium vapor laser by potassium tracing atom based absorption spectroscopy

Abstract

1. Introduction

2. Theoretical basis and simulation

3. Experimental setup and results

4. Discussion

5. Conclusion

Funding

Acknowledgment

References and links

Cited By

Figures (5)

Tables (1)

Equations (10)

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