Abstract

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

1. Introduction

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 [10]. 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) [11].

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 [12]. 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 [11]. 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 [16]. 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

rj=R(j1)·R/N,rj+1=Rj·R/N,
where R is the radius of the vapor cell, N is the total number of segmented cylindrical annuli, respectively. For an end-pumped structure, the optical axis of these coaxial cylindrical annuli coincides with that of the pump laser beam. Actually, every cylindrical annulus is thought as a heat source and a laser emitting source at the same time in the calculation. In this study, the effective length L and radius R of the vapor cell in a DPAL system are 25 mm and 7.5 mm, respectively. The partial pressure is 500 Torr for helium and 100 Torr for ethane, respectively. The buffer gas and the alkali vapor are forced to flow inside the cell with the velocity of U. Convection and heat radiation are so small that they have been ignored in the system. In addition, the temperature distribution along the axial direction and the effects of both end-windows are also neglected.

 

Fig. 1 Schematic illustration for segmentation procedure of a flowing-gas cell.

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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 [17]:

dn1jdt=0=Γpj+ΓLj+n2jτD1+n3jτD2,dn2jdt=0=ΓLj+γ32(Tj)[n3j2n2jexp(ΔEkBTj)]n2jτD1,dn3jdt=0=Γpjγ32(Tj)[n3j2n2jexp(ΔEkBTj)]n3jτD2,
where ΓPj is the stimulated absorption transition rate caused by pump photons, ΓLj is the transition rate of laser emission, Tj is the temperature of the jth cylindrical, τD1is the D1 radiative lifetime, τD2is the D2 radiative lifetime, γ32(Tj)is the relaxation rate of the fine-structure mixing (n2P3/2n2P1/2), ΔE is the energy gap between the n2P3/2 and the n2P1/2 levels, kB is the Boltzmann constant, respectively.

For a steady-state laser emission, the number density of every energy-level must satisfy the following two equations [18]:

exp[2(n2j(Tj)-n1j(Tj))σD1He-broadened(Tj)l]×TT2Roc=1,
n0j(Tj)=n1j(Tj)+n2j(Tj)+n3j(Tj),
wheren0j(Tj)is the cesium number density of the jth cylindrical annulus as expressed by [10]
n0j(Tj)=n01(Tw)(TwTj),
where Tw is the temperature of the cell wall, n01(Tw) is the saturated alkali number density inside the first cylindrical annulus which is adjacent to the internal surface of the cell wall. By solving Eqs. (2)-(5), n1j, n2j, n3j, and ΓLjcan be obtained if Tj is assumed as a known value.

Thus, the generated heat of the jth cylindrical annulus can be then calculated by the following formula [17]:

Qj=VLiγ32(Tj)[n3j2n2jexp(ΔEkBTj)]ΔE,
where VLi is the volume of the jth cylindrical annulus. The value of Qjwill be used in the next calculation process.

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]:

Re2ρURμ,
where ρ, μ, and U are the density, viscosity, and velocity of mixed flowing gases in the vapor cell, respectively. In our model, the maximal value of U is limited to 10 m/s. It is easy to deduce the maximum Re as about 1800. For circular tubes, the transition from laminar to turbulent flow occurs over a range of Reynolds numbers from approximately 2300 to 4000, regardless of the nature of the fluid or the dimensions of the pipe or the average velocity [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]:
xD0.05Re(2R)=1350mm.
Since such a value is much longer than the gain medium length L (25 mm), the velocity distribution at the transverse section of the cell can be ignored in the calculation. Thus, flowed heat Fj in the jth cylindrical annulus can be expressed by [20]
Fj=SjUn(Tj)NATwTjCp(T)dT,
where Sj is the cross-sectional area of the jth cylindrical annulus, n(Tj) denotes the number density of the total mixed gases in the jth cylindrical annulus, NA presents the Avogadro constant, Cp(T) is the molar heat capacity of the total buffer gases resulting from the temperature T as given by [21, 22]
CP(T)=PHePHe+PC2H6CPHe(T)+PC2H6PHe+PC2H6CPC2H6(T),
wherePHeandPC2H6 are the partial pressures of helium and ethane,CPHe(T)andCPC2H6(T)are the molar heat capacity of helium and ethane, respectively. The transferred heat Φj in the jth cylindrical annulus can be expressed by [20]
Φj=[K(Tj)AjdTdr]|T=Tj.
When the thickness of the segmented cylindrical annulus is small enough, Φj can be approximately expressed as
Φj=K(Tj)AjTj+1Tjrj+1rj,
where K(Tj) denotes the thermal conductivity of the total buffer gases in the jth cylindrical annulus as given by [12, 23–25]
K(Tj)=PHePHe+PC2H6KHe(Tj)+PC2H6PHe+PC2H6KC2H6(Tj),
where KHe(Tj) andKC2H6(Tj) are respectively the molar heat capacity of helium and ethane [8], Aj stands for the contact area between the jth and the (j + 1)th cylindrical annuli as given by
A=2πrjL.
Appointing the total heat transferred out from a vapor cell as PThermal , the relationship between PThermal and the total generated heat i=1NQi as well as the flowed heat i=1NFican be described as
Pthermal=i=1NQii=1NFi.
Equation (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.

 

Fig. 2 Diagram for representing the relationship of generated heat, transferred heat and flowed heat in the cross-section of a vapor cell.

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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.

 

Fig. 3 Temperature distributions in the cross-section of a cell with different velocities of the mixed gases when the pump power is 1000 W.

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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.

 

Fig. 4 Population distributions with different velocities of the mixed gases when the pump power is 1000 W.

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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.

 

Fig. 5 Output power (a) and heat features (b) of a Cs-DPAL system versus the flowing velocity of mixed gases with the pump power of 1000 W.

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4. Conclusions

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.

Acknowledgments

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

1. W. F. Krupke, R. J. Beach, V. K. Kanz, and S. A. Payne, “Resonance transition 795-nm rubidium laser,” Opt. Lett. 28(23), 2336–2338 (2003). [CrossRef]   [PubMed]  

2. R. H. Page, R. J. Beach, V. K. Kanz, and W. F. Krupke, “Multimode-diode-pumped gas (alkali-vapor) laser,” Opt. Lett. 31(3), 353–355 (2006). [CrossRef]   [PubMed]  

3. Y. Wang, T. Kasamatsu, Y. Zheng, H. Miyajima, H. Fukuoka, S. Matsuoka, M. Niigaki, H. Kubomura, T. Hiruma, and H. Kan, “Cesium vapor laser pumped by a volume-Bragg-grating coupled quasi-continuous-wave laser-diode array,” Appl. Phys. Lett. 88(14), 141112 (2006). [CrossRef]  

4. B. V. Zhdanov, A. Stooke, G. Boyadjian, A. Voci, and R. J. Knize, “Rubidium vapor laser pumped by two laser diode arrays,” Opt. Lett. 33(5), 414–415 (2008). [CrossRef]   [PubMed]  

5. V. Venkatraman, S. Kang, C. Affolderbach, H. Shea, and G. Mileti, “Optical pumping in a microfabricated Rb vapor cell using a microfabricated Rb discharge light source,” Appl. Phys. Lett. 104(5), 054104 (2014). [CrossRef]  

6. M. K. Shaffer, T. C. Lilly, B. V. Zhdanov, and R. J. Knize, “In situ non-perturbative temperature measurement in a Cs alkali laser,” Opt. Lett. 40(1), 119–122 (2015). [CrossRef]   [PubMed]  

7. G. P. Gupta, S. Mathur, and S. C. Saxena, “Certain Methods for Calculating Thermal Conductivity of ulticomponent Mixtures Involving Polyatomic Gases,” Def. Sci. J. 18(4), 195–204 (2014).

8. C. L. Yaws and W. Braker, eds., Matheson Gas Data Book, VII (McGraw-Hill & Matheson Tri-Gas, 2001), Appendix 23.

9. W. Zhang, Y. Wang, H. Cai, L. P. Xue, J. H. Han, H. Y. Wang, and Z. Y. Liao, “Theoretical study on temperature features of a sealed cesium vapor cell pumped by laser diodes,” Appl. Opt. 53(19), 4180–4186 (2014). [CrossRef]   [PubMed]  

10. B. D. Barmashenko and S. Rosenwaks, “Modeling of flowing gas diode pumped alkali lasers: dependence of the operation on the gas velocity and on the nature of the buffer gas,” Opt. Lett. 37(17), 3615–3617 (2012). [CrossRef]   [PubMed]  

11. J. H. Han, Y. Wang, H. Cai, W. Zhang, L. Xue, and H. Wang, “Algorithm for evaluation of temperature distribution of a vapor cell in a diode-pumped alkali laser system: part I,” Opt. Express 22(11), 13988–14003 (2014). [CrossRef]   [PubMed]  

12. B. D. Barmashenko and S. Rosenwaks, “Detailed analysis of kinetic and fluid dynamic processes in diode-pumped alkali lasers,” J. Opt. Soc. Am. B 30(5), 1118–1126 (2013). [CrossRef]  

13. B. D. Barmashenko and S. Rosenwaks, “Feasibility of supersonic diode pumped alkali lasers: Model calculations,” Appl. Phys. Lett. 102(14), 141108 (2013). [CrossRef]  

14. S. Rosenwaks, B. D. Barmashenko, and F. Waichman, “Semi-analytical and 3D CFD DPAL modeling: feasibility of supersonic operation,” Proc. SPIE High Energy/Average Power Lasers and Intense Beam Applications VII 8962(896209), 1–9 (2014).

15. K. Waichman, B. D. Barmashenko, and S. Rosenwaks, “Computational fluid dynamics modeling of subsonic flowing gas diode pumped alkali lasers: comparison with semi-analytical model calculations and with experimental results,” J. Opt. Soc. Am. B 31(11), 2628–2637 (2014). [CrossRef]  

16. Z. N. Yang, H. Y. Wang, Q. S. Lu, W. H. Hua, and X. J. Xu, “Modeling of an optically side-pumped alkali vapor amplifier with consideration of amplified spontaneous emission,” Opt. Express 19(23), 23118–23131 (2011). [CrossRef]   [PubMed]  

17. H. Cai, Y. Wang, L. P. Xue, W. Zhang, J. H. Han, H. Wang, and G. An, “Theoretical study of relaxation oscillations in a free-running diode-pumped rubidium vapor laser,” Appl. Phys. B 117(4), 1201–1210 (2014). [CrossRef]  

18. R. J. Beach, W. F. Krupke, V. K. Kanz, S. A. Payne, M. A. Dubinskii, and L. D. Merkle, “End-pumped continuous-wave alkali vapor lasers: experiment, model, and power scaling,” J. Opt. Soc. Am. B 21(12), 2151–2163 (2004). [CrossRef]  

19. J. C. Tannehill, D. A. Anderson, and R. H. Pletcher, eds., Computational Fluid Dynamics and Heat Transfer, II (Taylor & Francis, 1997), Chap. 5.

20. M. J. Latif, ed., Heat Conduction, III (Verlag GmbH & Co. K, 2009), Chap. 1.

21. B. P. Dailey and W. A. Felsing, “The Heat Capacities at Higher Temperatures of Ethane and Propane,” JACS 65(1), 42–44 (1943). [CrossRef]  

22. S. M. Gatica, E. S. Hernández, and L. Szybisz, “Heat capacity of helium in cylindrical environments,” Phys. Rev. 68(14), 144501 (2003).

23. G. P. Gupta and S. C. Saxena, “Calculation of Thermal Conductivity of Polyatomic Gas Mixtures at high Temperatures,” Def. Sci. J. 16(3), 165–176 (1966).

24. S. Mathur and S. C. Saxena, “Calculation of Thermal Conductivity of ternary mixture of polyatomic gases,” Indian J. Pure Appl. Phys. 5(4), 114 (1967).

25. X. D. Shan and M. R. Wang, “Understanding of Thermal Conductance of Thin Gas Layers,” Adv. Mech. Eng. 2013, 1–7 (2013). [CrossRef]  

References

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  1. W. F. Krupke, R. J. Beach, V. K. Kanz, and S. A. Payne, “Resonance transition 795-nm rubidium laser,” Opt. Lett. 28(23), 2336–2338 (2003).
    [Crossref] [PubMed]
  2. R. H. Page, R. J. Beach, V. K. Kanz, and W. F. Krupke, “Multimode-diode-pumped gas (alkali-vapor) laser,” Opt. Lett. 31(3), 353–355 (2006).
    [Crossref] [PubMed]
  3. Y. Wang, T. Kasamatsu, Y. Zheng, H. Miyajima, H. Fukuoka, S. Matsuoka, M. Niigaki, H. Kubomura, T. Hiruma, and H. Kan, “Cesium vapor laser pumped by a volume-Bragg-grating coupled quasi-continuous-wave laser-diode array,” Appl. Phys. Lett. 88(14), 141112 (2006).
    [Crossref]
  4. B. V. Zhdanov, A. Stooke, G. Boyadjian, A. Voci, and R. J. Knize, “Rubidium vapor laser pumped by two laser diode arrays,” Opt. Lett. 33(5), 414–415 (2008).
    [Crossref] [PubMed]
  5. V. Venkatraman, S. Kang, C. Affolderbach, H. Shea, and G. Mileti, “Optical pumping in a microfabricated Rb vapor cell using a microfabricated Rb discharge light source,” Appl. Phys. Lett. 104(5), 054104 (2014).
    [Crossref]
  6. M. K. Shaffer, T. C. Lilly, B. V. Zhdanov, and R. J. Knize, “In situ non-perturbative temperature measurement in a Cs alkali laser,” Opt. Lett. 40(1), 119–122 (2015).
    [Crossref] [PubMed]
  7. G. P. Gupta, S. Mathur, and S. C. Saxena, “Certain Methods for Calculating Thermal Conductivity of ulticomponent Mixtures Involving Polyatomic Gases,” Def. Sci. J. 18(4), 195–204 (2014).
  8. C. L. Yaws and W. Braker, eds., Matheson Gas Data Book, VII (McGraw-Hill & Matheson Tri-Gas, 2001), Appendix 23.
  9. W. Zhang, Y. Wang, H. Cai, L. P. Xue, J. H. Han, H. Y. Wang, and Z. Y. Liao, “Theoretical study on temperature features of a sealed cesium vapor cell pumped by laser diodes,” Appl. Opt. 53(19), 4180–4186 (2014).
    [Crossref] [PubMed]
  10. B. D. Barmashenko and S. Rosenwaks, “Modeling of flowing gas diode pumped alkali lasers: dependence of the operation on the gas velocity and on the nature of the buffer gas,” Opt. Lett. 37(17), 3615–3617 (2012).
    [Crossref] [PubMed]
  11. J. H. Han, Y. Wang, H. Cai, W. Zhang, L. Xue, and H. Wang, “Algorithm for evaluation of temperature distribution of a vapor cell in a diode-pumped alkali laser system: part I,” Opt. Express 22(11), 13988–14003 (2014).
    [Crossref] [PubMed]
  12. B. D. Barmashenko and S. Rosenwaks, “Detailed analysis of kinetic and fluid dynamic processes in diode-pumped alkali lasers,” J. Opt. Soc. Am. B 30(5), 1118–1126 (2013).
    [Crossref]
  13. B. D. Barmashenko and S. Rosenwaks, “Feasibility of supersonic diode pumped alkali lasers: Model calculations,” Appl. Phys. Lett. 102(14), 141108 (2013).
    [Crossref]
  14. S. Rosenwaks, B. D. Barmashenko, and F. Waichman, “Semi-analytical and 3D CFD DPAL modeling: feasibility of supersonic operation,” Proc. SPIE High Energy/Average Power Lasers and Intense Beam Applications VII 8962(896209), 1–9 (2014).
  15. K. Waichman, B. D. Barmashenko, and S. Rosenwaks, “Computational fluid dynamics modeling of subsonic flowing gas diode pumped alkali lasers: comparison with semi-analytical model calculations and with experimental results,” J. Opt. Soc. Am. B 31(11), 2628–2637 (2014).
    [Crossref]
  16. Z. N. Yang, H. Y. Wang, Q. S. Lu, W. H. Hua, and X. J. Xu, “Modeling of an optically side-pumped alkali vapor amplifier with consideration of amplified spontaneous emission,” Opt. Express 19(23), 23118–23131 (2011).
    [Crossref] [PubMed]
  17. H. Cai, Y. Wang, L. P. Xue, W. Zhang, J. H. Han, H. Wang, and G. An, “Theoretical study of relaxation oscillations in a free-running diode-pumped rubidium vapor laser,” Appl. Phys. B 117(4), 1201–1210 (2014).
    [Crossref]
  18. R. J. Beach, W. F. Krupke, V. K. Kanz, S. A. Payne, M. A. Dubinskii, and L. D. Merkle, “End-pumped continuous-wave alkali vapor lasers: experiment, model, and power scaling,” J. Opt. Soc. Am. B 21(12), 2151–2163 (2004).
    [Crossref]
  19. J. C. Tannehill, D. A. Anderson, and R. H. Pletcher, eds., Computational Fluid Dynamics and Heat Transfer, II (Taylor & Francis, 1997), Chap. 5.
  20. M. J. Latif, ed., Heat Conduction, III (Verlag GmbH & Co. K, 2009), Chap. 1.
  21. B. P. Dailey and W. A. Felsing, “The Heat Capacities at Higher Temperatures of Ethane and Propane,” JACS 65(1), 42–44 (1943).
    [Crossref]
  22. S. M. Gatica, E. S. Hernández, and L. Szybisz, “Heat capacity of helium in cylindrical environments,” Phys. Rev. 68(14), 144501 (2003).
  23. G. P. Gupta and S. C. Saxena, “Calculation of Thermal Conductivity of Polyatomic Gas Mixtures at high Temperatures,” Def. Sci. J. 16(3), 165–176 (1966).
  24. S. Mathur and S. C. Saxena, “Calculation of Thermal Conductivity of ternary mixture of polyatomic gases,” Indian J. Pure Appl. Phys. 5(4), 114 (1967).
  25. X. D. Shan and M. R. Wang, “Understanding of Thermal Conductance of Thin Gas Layers,” Adv. Mech. Eng. 2013, 1–7 (2013).
    [Crossref]

2015 (1)

2014 (7)

G. P. Gupta, S. Mathur, and S. C. Saxena, “Certain Methods for Calculating Thermal Conductivity of ulticomponent Mixtures Involving Polyatomic Gases,” Def. Sci. J. 18(4), 195–204 (2014).

W. Zhang, Y. Wang, H. Cai, L. P. Xue, J. H. Han, H. Y. Wang, and Z. Y. Liao, “Theoretical study on temperature features of a sealed cesium vapor cell pumped by laser diodes,” Appl. Opt. 53(19), 4180–4186 (2014).
[Crossref] [PubMed]

J. H. Han, Y. Wang, H. Cai, W. Zhang, L. Xue, and H. Wang, “Algorithm for evaluation of temperature distribution of a vapor cell in a diode-pumped alkali laser system: part I,” Opt. Express 22(11), 13988–14003 (2014).
[Crossref] [PubMed]

S. Rosenwaks, B. D. Barmashenko, and F. Waichman, “Semi-analytical and 3D CFD DPAL modeling: feasibility of supersonic operation,” Proc. SPIE High Energy/Average Power Lasers and Intense Beam Applications VII 8962(896209), 1–9 (2014).

K. Waichman, B. D. Barmashenko, and S. Rosenwaks, “Computational fluid dynamics modeling of subsonic flowing gas diode pumped alkali lasers: comparison with semi-analytical model calculations and with experimental results,” J. Opt. Soc. Am. B 31(11), 2628–2637 (2014).
[Crossref]

H. Cai, Y. Wang, L. P. Xue, W. Zhang, J. H. Han, H. Wang, and G. An, “Theoretical study of relaxation oscillations in a free-running diode-pumped rubidium vapor laser,” Appl. Phys. B 117(4), 1201–1210 (2014).
[Crossref]

V. Venkatraman, S. Kang, C. Affolderbach, H. Shea, and G. Mileti, “Optical pumping in a microfabricated Rb vapor cell using a microfabricated Rb discharge light source,” Appl. Phys. Lett. 104(5), 054104 (2014).
[Crossref]

2013 (3)

X. D. Shan and M. R. Wang, “Understanding of Thermal Conductance of Thin Gas Layers,” Adv. Mech. Eng. 2013, 1–7 (2013).
[Crossref]

B. D. Barmashenko and S. Rosenwaks, “Detailed analysis of kinetic and fluid dynamic processes in diode-pumped alkali lasers,” J. Opt. Soc. Am. B 30(5), 1118–1126 (2013).
[Crossref]

B. D. Barmashenko and S. Rosenwaks, “Feasibility of supersonic diode pumped alkali lasers: Model calculations,” Appl. Phys. Lett. 102(14), 141108 (2013).
[Crossref]

2012 (1)

2011 (1)

2008 (1)

2006 (2)

R. H. Page, R. J. Beach, V. K. Kanz, and W. F. Krupke, “Multimode-diode-pumped gas (alkali-vapor) laser,” Opt. Lett. 31(3), 353–355 (2006).
[Crossref] [PubMed]

Y. Wang, T. Kasamatsu, Y. Zheng, H. Miyajima, H. Fukuoka, S. Matsuoka, M. Niigaki, H. Kubomura, T. Hiruma, and H. Kan, “Cesium vapor laser pumped by a volume-Bragg-grating coupled quasi-continuous-wave laser-diode array,” Appl. Phys. Lett. 88(14), 141112 (2006).
[Crossref]

2004 (1)

2003 (2)

S. M. Gatica, E. S. Hernández, and L. Szybisz, “Heat capacity of helium in cylindrical environments,” Phys. Rev. 68(14), 144501 (2003).

W. F. Krupke, R. J. Beach, V. K. Kanz, and S. A. Payne, “Resonance transition 795-nm rubidium laser,” Opt. Lett. 28(23), 2336–2338 (2003).
[Crossref] [PubMed]

1967 (1)

S. Mathur and S. C. Saxena, “Calculation of Thermal Conductivity of ternary mixture of polyatomic gases,” Indian J. Pure Appl. Phys. 5(4), 114 (1967).

1966 (1)

G. P. Gupta and S. C. Saxena, “Calculation of Thermal Conductivity of Polyatomic Gas Mixtures at high Temperatures,” Def. Sci. J. 16(3), 165–176 (1966).

1943 (1)

B. P. Dailey and W. A. Felsing, “The Heat Capacities at Higher Temperatures of Ethane and Propane,” JACS 65(1), 42–44 (1943).
[Crossref]

Affolderbach, C.

V. Venkatraman, S. Kang, C. Affolderbach, H. Shea, and G. Mileti, “Optical pumping in a microfabricated Rb vapor cell using a microfabricated Rb discharge light source,” Appl. Phys. Lett. 104(5), 054104 (2014).
[Crossref]

An, G.

H. Cai, Y. Wang, L. P. Xue, W. Zhang, J. H. Han, H. Wang, and G. An, “Theoretical study of relaxation oscillations in a free-running diode-pumped rubidium vapor laser,” Appl. Phys. B 117(4), 1201–1210 (2014).
[Crossref]

Barmashenko, B. D.

Beach, R. J.

Boyadjian, G.

Cai, H.

Dailey, B. P.

B. P. Dailey and W. A. Felsing, “The Heat Capacities at Higher Temperatures of Ethane and Propane,” JACS 65(1), 42–44 (1943).
[Crossref]

Dubinskii, M. A.

Felsing, W. A.

B. P. Dailey and W. A. Felsing, “The Heat Capacities at Higher Temperatures of Ethane and Propane,” JACS 65(1), 42–44 (1943).
[Crossref]

Fukuoka, H.

Y. Wang, T. Kasamatsu, Y. Zheng, H. Miyajima, H. Fukuoka, S. Matsuoka, M. Niigaki, H. Kubomura, T. Hiruma, and H. Kan, “Cesium vapor laser pumped by a volume-Bragg-grating coupled quasi-continuous-wave laser-diode array,” Appl. Phys. Lett. 88(14), 141112 (2006).
[Crossref]

Gatica, S. M.

S. M. Gatica, E. S. Hernández, and L. Szybisz, “Heat capacity of helium in cylindrical environments,” Phys. Rev. 68(14), 144501 (2003).

Gupta, G. P.

G. P. Gupta, S. Mathur, and S. C. Saxena, “Certain Methods for Calculating Thermal Conductivity of ulticomponent Mixtures Involving Polyatomic Gases,” Def. Sci. J. 18(4), 195–204 (2014).

G. P. Gupta and S. C. Saxena, “Calculation of Thermal Conductivity of Polyatomic Gas Mixtures at high Temperatures,” Def. Sci. J. 16(3), 165–176 (1966).

Han, J. H.

Hernández, E. S.

S. M. Gatica, E. S. Hernández, and L. Szybisz, “Heat capacity of helium in cylindrical environments,” Phys. Rev. 68(14), 144501 (2003).

Hiruma, T.

Y. Wang, T. Kasamatsu, Y. Zheng, H. Miyajima, H. Fukuoka, S. Matsuoka, M. Niigaki, H. Kubomura, T. Hiruma, and H. Kan, “Cesium vapor laser pumped by a volume-Bragg-grating coupled quasi-continuous-wave laser-diode array,” Appl. Phys. Lett. 88(14), 141112 (2006).
[Crossref]

Hua, W. H.

Kan, H.

Y. Wang, T. Kasamatsu, Y. Zheng, H. Miyajima, H. Fukuoka, S. Matsuoka, M. Niigaki, H. Kubomura, T. Hiruma, and H. Kan, “Cesium vapor laser pumped by a volume-Bragg-grating coupled quasi-continuous-wave laser-diode array,” Appl. Phys. Lett. 88(14), 141112 (2006).
[Crossref]

Kang, S.

V. Venkatraman, S. Kang, C. Affolderbach, H. Shea, and G. Mileti, “Optical pumping in a microfabricated Rb vapor cell using a microfabricated Rb discharge light source,” Appl. Phys. Lett. 104(5), 054104 (2014).
[Crossref]

Kanz, V. K.

Kasamatsu, T.

Y. Wang, T. Kasamatsu, Y. Zheng, H. Miyajima, H. Fukuoka, S. Matsuoka, M. Niigaki, H. Kubomura, T. Hiruma, and H. Kan, “Cesium vapor laser pumped by a volume-Bragg-grating coupled quasi-continuous-wave laser-diode array,” Appl. Phys. Lett. 88(14), 141112 (2006).
[Crossref]

Knize, R. J.

Krupke, W. F.

Kubomura, H.

Y. Wang, T. Kasamatsu, Y. Zheng, H. Miyajima, H. Fukuoka, S. Matsuoka, M. Niigaki, H. Kubomura, T. Hiruma, and H. Kan, “Cesium vapor laser pumped by a volume-Bragg-grating coupled quasi-continuous-wave laser-diode array,” Appl. Phys. Lett. 88(14), 141112 (2006).
[Crossref]

Liao, Z. Y.

Lilly, T. C.

Lu, Q. S.

Mathur, S.

G. P. Gupta, S. Mathur, and S. C. Saxena, “Certain Methods for Calculating Thermal Conductivity of ulticomponent Mixtures Involving Polyatomic Gases,” Def. Sci. J. 18(4), 195–204 (2014).

S. Mathur and S. C. Saxena, “Calculation of Thermal Conductivity of ternary mixture of polyatomic gases,” Indian J. Pure Appl. Phys. 5(4), 114 (1967).

Matsuoka, S.

Y. Wang, T. Kasamatsu, Y. Zheng, H. Miyajima, H. Fukuoka, S. Matsuoka, M. Niigaki, H. Kubomura, T. Hiruma, and H. Kan, “Cesium vapor laser pumped by a volume-Bragg-grating coupled quasi-continuous-wave laser-diode array,” Appl. Phys. Lett. 88(14), 141112 (2006).
[Crossref]

Merkle, L. D.

Mileti, G.

V. Venkatraman, S. Kang, C. Affolderbach, H. Shea, and G. Mileti, “Optical pumping in a microfabricated Rb vapor cell using a microfabricated Rb discharge light source,” Appl. Phys. Lett. 104(5), 054104 (2014).
[Crossref]

Miyajima, H.

Y. Wang, T. Kasamatsu, Y. Zheng, H. Miyajima, H. Fukuoka, S. Matsuoka, M. Niigaki, H. Kubomura, T. Hiruma, and H. Kan, “Cesium vapor laser pumped by a volume-Bragg-grating coupled quasi-continuous-wave laser-diode array,” Appl. Phys. Lett. 88(14), 141112 (2006).
[Crossref]

Niigaki, M.

Y. Wang, T. Kasamatsu, Y. Zheng, H. Miyajima, H. Fukuoka, S. Matsuoka, M. Niigaki, H. Kubomura, T. Hiruma, and H. Kan, “Cesium vapor laser pumped by a volume-Bragg-grating coupled quasi-continuous-wave laser-diode array,” Appl. Phys. Lett. 88(14), 141112 (2006).
[Crossref]

Page, R. H.

Payne, S. A.

Rosenwaks, S.

Saxena, S. C.

G. P. Gupta, S. Mathur, and S. C. Saxena, “Certain Methods for Calculating Thermal Conductivity of ulticomponent Mixtures Involving Polyatomic Gases,” Def. Sci. J. 18(4), 195–204 (2014).

S. Mathur and S. C. Saxena, “Calculation of Thermal Conductivity of ternary mixture of polyatomic gases,” Indian J. Pure Appl. Phys. 5(4), 114 (1967).

G. P. Gupta and S. C. Saxena, “Calculation of Thermal Conductivity of Polyatomic Gas Mixtures at high Temperatures,” Def. Sci. J. 16(3), 165–176 (1966).

Shaffer, M. K.

Shan, X. D.

X. D. Shan and M. R. Wang, “Understanding of Thermal Conductance of Thin Gas Layers,” Adv. Mech. Eng. 2013, 1–7 (2013).
[Crossref]

Shea, H.

V. Venkatraman, S. Kang, C. Affolderbach, H. Shea, and G. Mileti, “Optical pumping in a microfabricated Rb vapor cell using a microfabricated Rb discharge light source,” Appl. Phys. Lett. 104(5), 054104 (2014).
[Crossref]

Stooke, A.

Szybisz, L.

S. M. Gatica, E. S. Hernández, and L. Szybisz, “Heat capacity of helium in cylindrical environments,” Phys. Rev. 68(14), 144501 (2003).

Venkatraman, V.

V. Venkatraman, S. Kang, C. Affolderbach, H. Shea, and G. Mileti, “Optical pumping in a microfabricated Rb vapor cell using a microfabricated Rb discharge light source,” Appl. Phys. Lett. 104(5), 054104 (2014).
[Crossref]

Voci, A.

Waichman, F.

S. Rosenwaks, B. D. Barmashenko, and F. Waichman, “Semi-analytical and 3D CFD DPAL modeling: feasibility of supersonic operation,” Proc. SPIE High Energy/Average Power Lasers and Intense Beam Applications VII 8962(896209), 1–9 (2014).

Waichman, K.

Wang, H.

J. H. Han, Y. Wang, H. Cai, W. Zhang, L. Xue, and H. Wang, “Algorithm for evaluation of temperature distribution of a vapor cell in a diode-pumped alkali laser system: part I,” Opt. Express 22(11), 13988–14003 (2014).
[Crossref] [PubMed]

H. Cai, Y. Wang, L. P. Xue, W. Zhang, J. H. Han, H. Wang, and G. An, “Theoretical study of relaxation oscillations in a free-running diode-pumped rubidium vapor laser,” Appl. Phys. B 117(4), 1201–1210 (2014).
[Crossref]

Wang, H. Y.

Wang, M. R.

X. D. Shan and M. R. Wang, “Understanding of Thermal Conductance of Thin Gas Layers,” Adv. Mech. Eng. 2013, 1–7 (2013).
[Crossref]

Wang, Y.

H. Cai, Y. Wang, L. P. Xue, W. Zhang, J. H. Han, H. Wang, and G. An, “Theoretical study of relaxation oscillations in a free-running diode-pumped rubidium vapor laser,” Appl. Phys. B 117(4), 1201–1210 (2014).
[Crossref]

W. Zhang, Y. Wang, H. Cai, L. P. Xue, J. H. Han, H. Y. Wang, and Z. Y. Liao, “Theoretical study on temperature features of a sealed cesium vapor cell pumped by laser diodes,” Appl. Opt. 53(19), 4180–4186 (2014).
[Crossref] [PubMed]

J. H. Han, Y. Wang, H. Cai, W. Zhang, L. Xue, and H. Wang, “Algorithm for evaluation of temperature distribution of a vapor cell in a diode-pumped alkali laser system: part I,” Opt. Express 22(11), 13988–14003 (2014).
[Crossref] [PubMed]

Y. Wang, T. Kasamatsu, Y. Zheng, H. Miyajima, H. Fukuoka, S. Matsuoka, M. Niigaki, H. Kubomura, T. Hiruma, and H. Kan, “Cesium vapor laser pumped by a volume-Bragg-grating coupled quasi-continuous-wave laser-diode array,” Appl. Phys. Lett. 88(14), 141112 (2006).
[Crossref]

Xu, X. J.

Xue, L.

Xue, L. P.

W. Zhang, Y. Wang, H. Cai, L. P. Xue, J. H. Han, H. Y. Wang, and Z. Y. Liao, “Theoretical study on temperature features of a sealed cesium vapor cell pumped by laser diodes,” Appl. Opt. 53(19), 4180–4186 (2014).
[Crossref] [PubMed]

H. Cai, Y. Wang, L. P. Xue, W. Zhang, J. H. Han, H. Wang, and G. An, “Theoretical study of relaxation oscillations in a free-running diode-pumped rubidium vapor laser,” Appl. Phys. B 117(4), 1201–1210 (2014).
[Crossref]

Yang, Z. N.

Zhang, W.

Zhdanov, B. V.

Zheng, Y.

Y. Wang, T. Kasamatsu, Y. Zheng, H. Miyajima, H. Fukuoka, S. Matsuoka, M. Niigaki, H. Kubomura, T. Hiruma, and H. Kan, “Cesium vapor laser pumped by a volume-Bragg-grating coupled quasi-continuous-wave laser-diode array,” Appl. Phys. Lett. 88(14), 141112 (2006).
[Crossref]

Adv. Mech. Eng. (1)

X. D. Shan and M. R. Wang, “Understanding of Thermal Conductance of Thin Gas Layers,” Adv. Mech. Eng. 2013, 1–7 (2013).
[Crossref]

Appl. Opt. (1)

Appl. Phys. B (1)

H. Cai, Y. Wang, L. P. Xue, W. Zhang, J. H. Han, H. Wang, and G. An, “Theoretical study of relaxation oscillations in a free-running diode-pumped rubidium vapor laser,” Appl. Phys. B 117(4), 1201–1210 (2014).
[Crossref]

Appl. Phys. Lett. (3)

B. D. Barmashenko and S. Rosenwaks, “Feasibility of supersonic diode pumped alkali lasers: Model calculations,” Appl. Phys. Lett. 102(14), 141108 (2013).
[Crossref]

Y. Wang, T. Kasamatsu, Y. Zheng, H. Miyajima, H. Fukuoka, S. Matsuoka, M. Niigaki, H. Kubomura, T. Hiruma, and H. Kan, “Cesium vapor laser pumped by a volume-Bragg-grating coupled quasi-continuous-wave laser-diode array,” Appl. Phys. Lett. 88(14), 141112 (2006).
[Crossref]

V. Venkatraman, S. Kang, C. Affolderbach, H. Shea, and G. Mileti, “Optical pumping in a microfabricated Rb vapor cell using a microfabricated Rb discharge light source,” Appl. Phys. Lett. 104(5), 054104 (2014).
[Crossref]

Def. Sci. J. (2)

G. P. Gupta, S. Mathur, and S. C. Saxena, “Certain Methods for Calculating Thermal Conductivity of ulticomponent Mixtures Involving Polyatomic Gases,” Def. Sci. J. 18(4), 195–204 (2014).

G. P. Gupta and S. C. Saxena, “Calculation of Thermal Conductivity of Polyatomic Gas Mixtures at high Temperatures,” Def. Sci. J. 16(3), 165–176 (1966).

Indian J. Pure Appl. Phys. (1)

S. Mathur and S. C. Saxena, “Calculation of Thermal Conductivity of ternary mixture of polyatomic gases,” Indian J. Pure Appl. Phys. 5(4), 114 (1967).

J. Opt. Soc. Am. B (3)

JACS (1)

B. P. Dailey and W. A. Felsing, “The Heat Capacities at Higher Temperatures of Ethane and Propane,” JACS 65(1), 42–44 (1943).
[Crossref]

Opt. Express (2)

Opt. Lett. (5)

Phys. Rev. (1)

S. M. Gatica, E. S. Hernández, and L. Szybisz, “Heat capacity of helium in cylindrical environments,” Phys. Rev. 68(14), 144501 (2003).

Proc. SPIE High Energy/Average Power Lasers and Intense Beam Applications VII (1)

S. Rosenwaks, B. D. Barmashenko, and F. Waichman, “Semi-analytical and 3D CFD DPAL modeling: feasibility of supersonic operation,” Proc. SPIE High Energy/Average Power Lasers and Intense Beam Applications VII 8962(896209), 1–9 (2014).

Other (3)

C. L. Yaws and W. Braker, eds., Matheson Gas Data Book, VII (McGraw-Hill & Matheson Tri-Gas, 2001), Appendix 23.

J. C. Tannehill, D. A. Anderson, and R. H. Pletcher, eds., Computational Fluid Dynamics and Heat Transfer, II (Taylor & Francis, 1997), Chap. 5.

M. J. Latif, ed., Heat Conduction, III (Verlag GmbH & Co. K, 2009), Chap. 1.

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Figures (5)

Fig. 1
Fig. 1 Schematic illustration for segmentation procedure of a flowing-gas cell.
Fig. 2
Fig. 2 Diagram for representing the relationship of generated heat, transferred heat and flowed heat in the cross-section of a vapor cell.
Fig. 3
Fig. 3 Temperature distributions in the cross-section of a cell with different velocities of the mixed gases when the pump power is 1000 W.
Fig. 4
Fig. 4 Population distributions with different velocities of the mixed gases when the pump power is 1000 W.
Fig. 5
Fig. 5 Output power (a) and heat features (b) of a Cs-DPAL system versus the flowing velocity of mixed gases with the pump power of 1000 W.

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

r j =R( j1 )·R/N, r j+1 =Rj·R/N,
d n 1 j dt =0= Γ p j + Γ L j + n 2 j τ D 1 + n 3 j τ D 2 , d n 2 j dt =0= Γ L j + γ 32 ( T j )[ n 3 j 2 n 2 j exp( ΔE k B T j ) ] n 2 j τ D 1 , d n 3 j dt =0= Γ p j γ 32 ( T j )[ n 3 j 2 n 2 j exp( ΔE k B T j ) ] n 3 j τ D 2 ,
exp[ 2( n 2 j ( T j )- n 1 j ( T j ) ) σ D 1 He-broadened ( T j )l ]×T T 2 R oc =1,
n 0 j ( T j )= n 1 j ( T j )+ n 2 j ( T j )+ n 3 j ( T j ),
n 0 j ( T j )= n 0 1 ( T w )( T w T j ),
Q j = V L i γ 32 ( T j )[ n 3 j 2 n 2 j exp( ΔE k B T j )]ΔE,
Re 2ρUR μ ,
x D 0.05Re( 2R )=1350 mm.
F j = S j Un( T j ) N A T w T j C p (T)dT ,
C P (T)= P He P He + P C 2 H 6 C PHe (T)+ P C 2 H 6 P He + P C 2 H 6 C P C 2 H 6 (T),
Φ j =[ K( T j ) A j dT dr ] | T= T j .
Φ j =K( T j ) A j T j+1 T j r j+1 r j ,
K( T j )= P He P He + P C 2 H 6 K He ( T j )+ P C 2 H 6 P He + P C 2 H 6 K C 2 H 6 ( T j ),
A=2π r j L.
P thermal = i=1 N Q i i=1 N F i .

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