With high efficiency and small thermally-induced effects in the near-infrared wavelength region, a diode-pumped alkali laser (DPAL) is regarded as combining the major advantages of solid-state lasers and gas-state lasers and obviating their main disadvantages at the same time. Studying the temperature distribution in the cross-section of an alkali-vapor cell is critical to realize high-powered DPAL systems for both static and flowing states. In this report, a theoretical algorithm has been built to investigate the features of a flowing-gas DPAL system by uniting procedures in kinetics, heat transfer, and fluid dynamic together. The thermal features and output characteristics have been simultaneously obtained for different gas velocities. The results have demonstrated the great potential of DPALs in the extremely high-powered laser operation.
© 2015 Optical Society of America
With high Stokes efficiency, good thermal performance, narrow linewidth, compact size, non-toxic system, etc., a diode-pumped alkali laser (DPAL) becomes one of the most hopeful high-powered laser sources of the next generation and has been rapidly developed in the last ten years [1–5]. However, the thermal effects will bring about some serious problems in nonuniformity of the temperature distribution for a high-powered DPAL system because the thermal conductivity of a gas-state medium is so small that the generated heat cannot be transferred outside efficiently [6–9]. Unlike a conventional electrically-excited gas-state laser, the number densities of alkali vapors and buffer gases (generally being helium and small hydrocarbons such as methane and ethane) in a DPAL often exhibit inhomogeneous distributions resulting from the temperature gradient inside a vapor cell . Actually, the inhomogeneous of the alkali vapor directly influences the output performances of a DPAL. Furthermore, the nonuniformity of buffer gases affects the line-center cross sections of both the D1 line (n 2P1/2 → n2S1/2) and the D2 line (n2S1/2 → n2P3/2) of an alkali atom as well as the rapid rate of fine-structure mixing (n2P3/2 → n2P1/2) .
Therefore, diminishing the temperature inhomogeneous is one of the key points to realize a high-powered DPAL with good beam quality. Generally, flowing the gaseous medium in an enclosed system is thought as an effective way to reduce the thermally-induced effects of a DPAL configuration . In our previous study, a systematic model is constructed to explore the radial temperature distribution in the transverse section of a cesium vapor cell with static state . In this report, we improve our theoretical model by uniting the laser kinetics, fluid dynamic, and heat transfer procedures together to analyze the features of a flowing-gas Cs-DPAL system. Until now, only two research groups have referred the physical characteristics of a DPAL with a flowing approach. One is the team led by B. D. Barmashenko and S. Rosenwaks who have undertaken a series of fruitful studies on flowing-gas DPALs [9, 12–15]. The other is the team of National University of Defense Technology of China. Although they developed an effective approach to describe the features of alkali vapor lasers in side-pumped configuration with flowing medium, the effects of heat transfer on the laser performance have not been considered in their study . In this report, we reveal that the temperature gradient can be dramatically alleviated by using the flowing procedure. Improvement on both the laser output and the beam quality in a flowing-gas DPAL should be meaningful for realization of a high-powered alkali vapor laser system.
2. Theoretical analyses
As shown in Fig. 1, a vapor cell which connects to an enclosed circulatory system is divided into many coaxial cylindrical annuli. For the jth cylindrical annulus (an arbitrarily one) among the segments, the outside radius rj and inner radius rj + 1 can be simply expressed by
2.1. Analyses of laser kinetics
The population densities of 62S1/2, 62P1/2, and 62P3/2levels in a three energy-level cesium system of the jth cylindrical annulus can be deduced by solving the following rate equations :
For a steady-state laser emission, the number density of every energy-level must satisfy the following two equations :10]Eqs. (2)-(5), , , , and can be obtained if is assumed as a known value.
Thus, the generated heat of the jth cylindrical annulus can be then calculated by the following formula :
2.2. Analyses of fluid dynamic and heat transfer
Next, we investigate how heat transfer works in the flowing gaseous medium. To explore the heat characteristics in a flowing-gas cell, we first determine the flowing state inside the cell. Generally, the Reynolds Number Re, as expressed in the following formula, can be used to determine whether the flow is laminar or turbulent :19]. So we believe that only laminar flow exist in our flowing-gas system. Furthermore, the corresponding laminar entrance length xD can be calculated by :20]21, 22]20]12, 23–25]8], Aj stands for the contact area between the jth and the (j + 1)th cylindrical annuli as given byEquation (15) indicates that the total generated heat is equal to the sum of the heat removed by the flowing mixed gases and the heat conducted to the cell wall from the gas-state medium. Such a process is schematically illustrated in Fig. 2.The temperature distribution and the output characteristics can be simultaneously evaluated by using Eqs. (2)-(15) and relations shown in Fig. 2.
3. Results and discussions
By using the theoretical model introduced in Section 2, we calculate the thermal features of a cesium cell and the physical characteristics of a Cs-DPAL. In the computation, the temperature of the cell wall Tw is 400 K, the waist radius of the pump Gaussian beam is 1000 μm, and the other parameters are the same as those in Ref. 11.
Figure 3 shows the radial temperature distribution with the velocity of mixed gases of 0, 1, 5, and 10 m/s, respectively, while the pump power is set to 1000 W. The horizontal axis indicates the distance to the center of a vapor cell and the vertical axis of the graph denotes the temperature. The temperature distribution has an obvious gradient in the cross section of a vapor cell for the pump power of 1000 W and the temperature peaks appear at the cell center for every curve. It can be found that the absorbed pump power has led to a more obvious temperature rise if the mixed gases are not flown. The maximum temperature rise even reaches about 550 K for the static medium. However, such a temperature gradient can be effectively decreased with a flowing approach. The faster the flowing velocity is, the lower the temperature rise becomes. The results demonstrate the essentiality and effectiveness of the flowing-gas procedure for an even-higher DPAL system.
The population distributions with different velocity of the mixed gases are shown in Fig. 4 with the pump power of 1000 W. The velocity of the flowing-gas is 0, 1, 5, and 10 m/s, respectively. It is seen that the cesium number density n0 increases with the radial position, which means that the temperature gradient in the cell cross-section must influence the distribution of the gain medium. The inflection points in n1 and n2 curves are located in the lasing boundary line. With increase of the flowing velocity of the mixed gases, the cesium number density n0 obviously increases in both the lasing region and the no-lasing region. One can suppose that the absorbed capability inside the cell can be greatly improved by the flowing process.
Figure 5(a) shows the variation trend of the output characteristics of a Cs-DPAL with different flowing velocities of mixed gases when the pump power is 1000 W. The output power first rapidly raises and then flattens out with increase of the flowing-gas velocity. If the flowing velocity is up to 10 m/s, the output power can be increased as about two times of a static DPAL system. The reason can be explained to the enhancement of the absorbed power inside a vapor cell when using the flowing procedure. In Fig. 5(b), we can observe that the generated heat is totally transferred to the outside in a static cell, but, in a flowing-gas cell, the generated heat is mainly taken away from the cell by the flowing gas if the speed is larger than 4 m/s. For a DPAL system with the output of tens of thousands watts, the flowing velocity should be raised as high as several tens meter per second or even more.
In this paper, we introduce a theoretical scheme to analyze the temperature distribution of the flowing-gas cell in a Cs-DPAL system by simultaneously considering the laser kinetics, heat transfer and fluid dynamic. The population distributions at the cross-section of a vapor cell and the output characteristics have been systematically evaluated with the different flowing velocities. From the calculation results, we can understand that the flowing-gas procedure is effective to dramatically eliminate the temperature gradient and increase the output power. The theoretical analyses would be helpful to construct a feasible high-powered DPAL with good beam quality in the future.
We are very grateful to Dr. Boris D. Barmashenko in Ben-Gurion University of the Negev for his meaningful helps in calculating the saturated alkali number densities inside a static alkali vapor cell.
References and links
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