## Algorithm for evaluation of temperature distribution of a vapor cell in a diode-pumped alkali laser system: part I |

Optics Express, Vol. 22, Issue 11, pp. 13988-14003 (2014)

http://dx.doi.org/10.1364/OE.22.013988

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### Abstract

A diode-pumped alkali laser (DPAL) is one of the most hopeful candidates to achieve high power performances. As the laser medium is in a gas-state, populations of energy-levels of a DPAL are strongly dependent on the vapor temperature. Thus, the temperature distribution directly determines the output characteristics of a DPAL. In this report, we developed a systematic model by combining the procedures of heat transfer and laser kinetics together to explore the radial temperature distribution in the transverse section of a cesium vapor cell. A cyclic iterative approach is adopted to calculate the population densities. The corresponding temperature distributions have been obtained for different beam waists and pump powers. The conclusion is thought to be useful for realizing a DPAL with high output power.

© 2014 Optical Society of America

## 1. Introduction

4. 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]

6. 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]

7. R. Z. Hua, S. Wada, and H. Tashiro, “Versatile, compact, TEM00-mode resonator for side-pumped single-rod solid-state lasers,” Appl. Opt. **40**(15), 2468–2474 (2001). [CrossRef] [PubMed]

11. W. F. Krupke, “Diode pumped alkali lasers (DPALs)—A review (rev1),” Prog. Quantum Electron. **36**(1), 4–28 (2012). [CrossRef]

_{1}and D

_{2}lines are of the order of 10

^{−13}cm

^{−2}at 110 °C [12

12. 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]

^{6}times larger than a Nd:YAG laser) [13

13. Y. Wang, K. Inoue, H. Kan, T. Ogawa, and S. Wada, “A MOPA with double-end pumped configuration using total internal reflection,” Laser Phys. **20**(2), 447–453 (2010). [CrossRef]

16. C. C. Lai, K. Y. Huang, H. J. Tsai, K. Y. Hsu, S. K. Liu, C. T. Cheng, K. D. Ji, C. P. Ke, S. R. Lin, and S. L. Huang, “Yb^{3+}:YAG silica fiber laser,” Opt. Lett. **34**(15), 2357–2359 (2009). [CrossRef] [PubMed]

17. D. A. Steck, Rubidium 85 D Line Data. Available: http://steck.us/alkalidata.

19. 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]

20. Q. Zhu, B. L. Pan, L. Chen, Y. J. Wang, and X. Y. Zhang, “Analysis of temperature distributions in diode-pumped alkali vapor lasers,” Opt. Commun. **283**(11), 2406–2410 (2010). [CrossRef]

21. Y. F. Liu, B. L. Pan, J. Yang, Y. J. Wang, and M. H. Li, “Thermal Effects in High-Power Double Diode-End-Pumped Cs Vapor Lasers,” IEEE J. Quantum Electron. **48**(4), 485–489 (2012). [CrossRef]

22. 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]

## 2. Theory and method

- (1) The diameter of the DPAL beam is approximately treated to be unchanged along the optical axis;
- (2) The transverse pump distribution holds out a Gaussian intensity profile and keeps unchanged along the optical axis;
- (3) The temperature of every cylindrical annulus is a constant along the optical axis;
- (4) The effects of both end-windows of the enclosed vapor cell are ignored.

26. S. Kiwan and O. Zeitoun, “Natural convection in a horizontal cylindrical annulus using porous fins,” Int. J. Numer. Methods Heat Fluid Flow **18**(5), 618–634 (2008). [CrossRef]

### 2.1. Analyses of laser kinetics

*n*

^{2}P

_{1/2}→

*n*

^{2}S

_{1/2}is called

*D*line and the stimulated absorption transition (pump transition)

_{1}*n*

^{2}S

_{1/2}→

*n*

^{2}P

_{3/2}is called

*D*line, where

_{2}*n*= 4, 5 and 6 for K, Rb and Cs, respectively [12

12. 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]

*D*line can be collisionally broadened to achieve spectrally homogeneous transition by using a buffer gas such as helium. In the presence of helium buffer gas, the D

_{2}_{2}pump transition line-shape changes from Gaussian to Lorentzian. Thus, pump energy absorbed in the spectral wings of the pump transition can dramatically enhance the laser gain by comparing the case of no helium buffer gas. The effectively collision-broadened linewidth is generally at least ten times the Doppler linewidth. The relaxation rate of the fine-structure can be enhanced by adding some alkanes with small hydrocarbon molecules [18

18. C. V. Sulham, G. P. Perram, M. P. Wilkinson, and D. A. Hostutler, “A pulsed, optically pumped rubidium laser at high pump intensity,” Opt. Commun. **283**(21), 4328–4332 (2010). [CrossRef]

19. 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]

28. Z. N. Yang, H. Y. Wang, Q. S. Lu, Y. D. Li, W. H. Hua, X. J. Xu, and J. B. Chen, “Modeling, numerical approach, and power scaling of alkali vapor lasers in side-pumped configuration with flowing medium,” J. Opt. Soc. Am. B **28**(6), 1353–1364 (2011). [CrossRef]

*jth*) among the segments. The outside radius

*r*and the inner radius

_{j}*r*of this cylindrical annulus can be simply expressed bywhere

_{j + 1}*R*is the radius of a vapor cell,

*N*is the total number of segmented cylindrical annuli, respectively.

*jth*cylindrical annulus (see Fig. 3) by using the well-known rate equations as follows [12

12. 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]

*k*is the Boltzmann constant,

_{B}*D*radiative lifetime,

_{1}*D*radiative lifetime, ΔE is the energy gap between the

_{2}^{2}

*P*

_{3/2}and the

^{2}

*P*

_{1/2}states,

*T*is the temperature of the

_{j}*jth*cylindrical annulus,

*γ*(

_{32}*T*) is the fine-structure relaxation rate as given bywhere

_{j}*n*

_{ethane}is the number density of ethane in the cell,

^{−15}cm

^{2},

^{−19}cm

^{2},

*ν*

_{γ}^{Cs-}^{He}(

*T*) and

_{j}*ν*

_{γ}^{Cs-}^{ethane}(

*T*) are respectively the root mean square thermally averaged relative velocities between cesium atoms and He atoms as well as ethane molecules as given by [12

_{j}**21**(12), 2151–2163 (2004). [CrossRef]

*m*,

_{Cs}*m*and

_{He}*m*are qualities of a cesium atom, a helium atom and an ethane molecule, respectively.

_{ethane}*Γ*is the stimulated absorption transition rate caused by pump photons as given by [12

_{P}^{j}**21**(12), 2151–2163 (2004). [CrossRef]

*η*is the fraction of the pump power delivered from the pump excitation source to the input end of the laser gain medium,

_{del}*R*is the reflectance of the pump light at the output coupler of a laser cavity resonator,

_{P}*V*is the volume of the

_{L}^{j}*jth*cylindrical annulus as given by

*P*(

_{j}*λ*) is the spectrally resolved partial pump power of the

*jth*cylindrical annulus as expressed by [29]where is the spectrally resolved FWHM linewidth, is the peak pump power of the

*jth*cylindrical annulus as given bywhere

*jth*cylindrical annulus,

*r*is the radius at the cross-section,

*ω*is the pump waist radius,

_{P}*S*is the cross-section area of the

_{j}*jth*cylindrical annulus:The maximal intensity of the pump power of the

*jth*cylindrical annulus

**21**(12), 2151–2163 (2004). [CrossRef]

*n*is the number density of helium in the vapor cell,

_{He-amagat}*D*line with the value of 2.31 × 10

_{2}^{−9}cm

^{2}, respectively.

*Γ*is the transition rate of laser emission as expressed by [12

_{L}^{j}**21**(12), 2151–2163 (2004). [CrossRef]

*P*is the output alkali laser power,

_{L}^{j}*R*is the reflectance of the output coupler, and

_{oc}*TT*is the one-way cavity transmittance by neglecting the ground-state absorption as well as the output coupler loss.

**21**(12), 2151–2163 (2004). [CrossRef]

*D*line.

_{1}**21**(12), 2151–2163 (2004). [CrossRef]

*jth*cylindrical annulus as expressed by [22

22. 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]

*T*is the temperature of the cell wall,

_{w}30. D. A. Steck, “Cesium D line data,” Available: http://steck.us/alkalidata

*R*is a constant of proportionality with the value of 8.3143

*J/(mol·K), P*is the saturation pressure of the cesium vapor in

_{V}*Torr*and

*N*is Avogadro number, respectively.

_{A}*jth*cylindrical annulus by using the following formula [12

**21**(12), 2151–2163 (2004). [CrossRef]

*E*is the energy gap between 6

*and 6*

^{2}S_{1/2}*levels with the value of 554 cm*

^{2}P_{3/2}^{−1}.

*jth*cylindrical annulus can be obtained by the following calculation:

### 2.2. Theoretical analyses of heat transfer

#### 2.2.1. Calculation of a Transverse Section Except the Central Core

*Ω*stands for the volume density of generated heat and

*K*(

*T*) denotes the coefficient of thermal conductivity, respectively. When the thickness of the segmented cylindrical annulus is small enough, the volume density of the

*jth*cylindrical annulus can be approximately expressed as of the volume density

*Ω*at the exterior side of the cylindrical annulus (

_{j}*j = 1, 2, … (N-1)*). Similarly,

*K*(

*T*) can also be approximately expressed as

*K*(

*T*

_{j}), which is the thermal conductivity at the exterior side of the

*jth*cylindrical annulus as expressed by [24

24. 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]

*jth*cylindrical annulus. According to Fourier’s Law, the quantity of the transferred heat

*Ф*from the

_{j}*jth*cylindrical annulus to the (

*j-1)th*one can be expressed by [31]where

*A*stands for the lateral area of the

*jth*cylindrical annulus as given bywhere

*l*is the cell length. After substituting Eqs. (24) and (26) into Eq. (25), can be calculated by the following formula:Note Ω

_{j}is calculated by use of Eq. (18) of Subsection 2.1. Then, we make a further integral calculation on both sides of Eq. (24) and the temperature distribution inside the

*jth*cylindrical annulus can be given bywhere

*jth*cylindrical annulus which can be solved by substituting

*r*=

*r*

_{j}and

*T*=

*T*into Eq. (28):By substituting

_{j}*jth*cylindrical annulus. The temperature of the inner side of the

*jth*cylindrical annulus,

*(j + 1)th*cylindrical annulus. By employing a circulatory calculation, we can therefore obtain

*T*.

_{2}, T_{3,}…,T_{N}#### 2.2.2. Calculation of Temperature of the Central Core

*r*of the central cylinder (core) can be simply expressed by

_{N}### 2.3. Calculation of radial temperature distribution

*P*. By considering a fact that the heat delivered from the first cylindrical annulus to the cell wall,

_{Thermal}*Φ*, is equal to the total heat release, the following relationship is tenable:The temperature at the outside of the first cylindrical annulus, which is equal to

_{1}*T*in this case, is approximately assigned as the temperature of this cylindrical annulus during the kinetic calculation if the thickness of the segmented thickness is small enough. Therefore, the volume heat density

_{w}*Ω*as well as the generated heat

_{1}*Q*can be deduced by employing the approach introduced in Subsection 2.1. By using

_{1}*Φ*and

_{1}*Ω*, we can evaluate the temperature distribution inside the first cylindrical annulus with Eq. (28).

_{1}*T*, can be then evaluated and is utilized as the initial conditions in calculating the temperature distribution of the second cylindrical annulus. As depictured in Fig. 5, the heat transferred from the second cylindrical annulus to the first one,

_{2}*Φ*, is thus calculated by

_{2}*Q*, we can obtain heat transferred from the

_{1}, Q_{2}, …, Q_{N-1}*jth*cylindrical annulus to the (

*j-1)th*one as expressed bywhere

*j = 1, 2, …, N*.

*P*or not. If the answer is “

_{Thermal}*no*”, the evaluation will be repeated by using the next value of

*P*until the following equation is satisfied (see Fig. 6):The y-axis in Fig. 6 represents the heat generated from all cylindrical annulii or the heat transferred outside from the first cylindrical annulus. By using the correct value

_{Thermal}*P*, the temperature distribution of the vapor cell can be obtained in the transverse section.

_{Thermal}## 3. Results and discussions

### 3.1. Population distributions

#### 3.1.1. Different waists of pump beams

*n*increases with the radial position

_{0}*r*. Such a phenomenon is due to the fact that the temperature at the central area is higher than that near the wall of the vapor cell. Some significant variation of the population densities

*n*and

_{1}*n*can be seen in the figure. The inflection points in the legend give rise to discontinuity of the first derivative or “angles” on the curves for

_{2}*n*and

_{1}*n*. Such inflection points located in the lasing boundary line. In the lasing region,

_{2}*n*is always larger than

_{2}*n*because of population inversion. We also find that, the bigger the spot size of a pump beam is, the lower

_{1}*n*becomes. It means that more electrons will be stimulated into the 6

_{3}^{2}

*P*

_{3/2}level under a higher pump density. However, it also leads to a population accumulation at the top energy-level. One can realize that the higher pump density brings about a relative weak relaxing capability by comparing

*n*and

_{3}*n*in (a), (b), (c), and (d) of Fig. 7.

_{2}#### 3.1.2. Different pump power

*n*decreases with the pump power. The reason is that the central temperature increases with the pump power and the total population density generally exhibits a degressive tendency with the temperature rising by referring Eq. (17). In the calculation, lasing output corresponding to the population distribution in Fig. 8(a) cannot be achieved because the threshold condition is unsatisfied.

_{0}### 3.2. Temperature distributions

_{p}= 500 μm is almost located at the lowest position at the diagram. It means that a big pump density will not always cause a high heat generation. To make the expression clear, we also produced a 3-Dmensional drawing for ω

_{p}= 500 μm as depictured in Fig. 9(b). In Fig. 10, the pump powers is set to 1, 10, 100, and 500 W, respectively, when the waist radius of the pump beam is 500 μm. It is obvious that the temperature gradient increases rapidly with the pump power. Such tendencies can be explained by a fact that the thermal conductivity of a gas-state medium is so small that the generated heat cannot be transferred outside efficiently.

34. N. D. Zameroski, G. D. Hager, W. Rudolph, and D. A. Hostutler, “Experimental and numerical modeling studies of a pulsed rubidium optically pumped alkali metal vapor laser,” J. Opt. Soc. Am. B **28**(5), 1088–1099 (2011). [CrossRef]

*n*becomes higher in this case, and decrease in the population densities

_{3}*n*and

_{1}*n*will lead to a relatively low conversion efficiency.

_{2}## 4. Conclusion

*D*and

_{1}*D*radiative lifetimes, the pump absorption cross section, the collisionally-broadened cross section, and the thermally averaged relative velocities are changed to the new values corresponding to rubidium and potassium.

_{2}## Acknowledgments

## References and links

1. | W. F. Krupke, “Diode Pumped Alkali Laser,” US Patent Application US 2003/0099272 Al, (2003). |

2. | W. F. Krupke, R. J. Beach, V. K. Kanz, and S. A. Payne, “Resonance transition 795-nm rubidium laser,” Opt. Lett. |

3. | W. F. Krupke, R. J. Beach, S. A. Payne, V. K. Kanz, and J. T. Early, “DPAL: A new class of lasers for CW power beaming at ideal photovoltaic cell wavelengths,” 2nd International Symposium on Beamed Energy Propulsion (Japan), (2003). |

4. | R. H. Page, R. J. Beach, V. K. Kanz, and W. F. Krupke, “Multimode-diode-pumped gas (alkali-vapor) laser,” Opt. Lett. |

5. | 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. |

6. | B. V. Zhdanov, A. Stooke, G. Boyadjian, A. Voci, and R. J. Knize, “Rubidium vapor laser pumped by two laser diode arrays,” Opt. Lett. |

7. | R. Z. Hua, S. Wada, and H. Tashiro, “Versatile, compact, TEM00-mode resonator for side-pumped single-rod solid-state lasers,” Appl. Opt. |

8. | Y. Wang and H. Kan, “Improvement on evaluating absorption efficiency of a medium rod for LD side-pumped solid-state lasers,” Opt. Commun. |

9. | Y. Wang, M. Niigaki, H. Fukuoka, Y. Zheng, H. Miyajima, S. Matsuoka, H. Kubomura, T. Hiruma, and H. Kan, “Approaches of output improvement for cesium vapor laser pumped by a volume-Bragg-grating coupled laser-diode-array,” Phys. Lett. A |

10. | B. V. Zhdanov and R. J. Knize, “Diode-pumped 10 W continuous wave cesium laser,” Opt. Lett. |

11. | W. F. Krupke, “Diode pumped alkali lasers (DPALs)—A review (rev1),” Prog. Quantum Electron. |

12. | 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 |

13. | Y. Wang, K. Inoue, H. Kan, T. Ogawa, and S. Wada, “A MOPA with double-end pumped configuration using total internal reflection,” Laser Phys. |

14. | M. Stanghini, M. Basso, R. Genesio, A. Tesi, R. Meucci, and M. Ciofini, “A new three-equation model for the CO |

15. | R. J. Garman, “Modelling of the intracavity optical fields in a copper vapour laser,” Opt. Commun. |

16. | C. C. Lai, K. Y. Huang, H. J. Tsai, K. Y. Hsu, S. K. Liu, C. T. Cheng, K. D. Ji, C. P. Ke, S. R. Lin, and S. L. Huang, “Yb |

17. | D. A. Steck, Rubidium 85 D Line Data. Available: http://steck.us/alkalidata. |

18. | C. V. Sulham, G. P. Perram, M. P. Wilkinson, and D. A. Hostutler, “A pulsed, optically pumped rubidium laser at high pump intensity,” Opt. Commun. |

19. | 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 |

20. | Q. Zhu, B. L. Pan, L. Chen, Y. J. Wang, and X. Y. Zhang, “Analysis of temperature distributions in diode-pumped alkali vapor lasers,” Opt. Commun. |

21. | Y. F. Liu, B. L. Pan, J. Yang, Y. J. Wang, and M. H. Li, “Thermal Effects in High-Power Double Diode-End-Pumped Cs Vapor Lasers,” IEEE J. Quantum Electron. |

22. | 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. |

23. | B. D. Barmashenko and S. Rosenwaks, “Feasibility of supersonic diode pumped alkali lasers: Model calculations,” Appl. Phys. Lett. |

24. | B. D. Barmashenko and S. Rosenwaks, “Detailed analysis of kinetic and fluid dynamic processes in diode-pumped alkali lasers,” J. Opt. Soc. Am. B |

25. | S. Rosenwaks, B. D. Barmashenko and Waichman, “Semi-analytical and 3D CFD DPAL modeling: feasibility of supersonic operation”, Proc. SPIE 8962, High Energy/Average Power Lasers and Intense Beam Applications VII, |

26. | S. Kiwan and O. Zeitoun, “Natural convection in a horizontal cylindrical annulus using porous fins,” Int. J. Numer. Methods Heat Fluid Flow |

27. | P. Teerstra and M. M. Yovanovich, “ Comprehensive review of natural convection in horizontal circular annuli,” in 7th AIAA/ ASME Joint Thermophysics and Heat Transfer Conference, Albuquerque, New Mexico, 15 –18 June 1998 (AIAA, 1998), pp. 141–152. |

28. | Z. N. Yang, H. Y. Wang, Q. S. Lu, Y. D. Li, W. H. Hua, X. J. Xu, and J. B. Chen, “Modeling, numerical approach, and power scaling of alkali vapor lasers in side-pumped configuration with flowing medium,” J. Opt. Soc. Am. B |

29. | S. W. Smith, |

30. | D. A. Steck, “Cesium D line data,” Available: http://steck.us/alkalidata |

31. | M. J. Latif, |

32. | C. L. Yaws, |

33. | H. Cai, Y. Wang, W. Zhang, L. P. Xue, H. Y. Wang, J. H. Han, and Z. Y. Liao, “Characteristic analyses of a diode-pumped rubidium vapor laser using a kinetic algorithm,” Opt. & Laser Technol., to be submitted. |

34. | N. D. Zameroski, G. D. Hager, W. Rudolph, and D. A. Hostutler, “Experimental and numerical modeling studies of a pulsed rubidium optically pumped alkali metal vapor laser,” J. Opt. Soc. Am. B |

**OCIS Codes**

(140.1340) Lasers and laser optics : Atomic gas lasers

(140.3430) Lasers and laser optics : Laser theory

(140.3460) Lasers and laser optics : Lasers

(140.3480) Lasers and laser optics : Lasers, diode-pumped

**ToC Category:**

Atomic and Molecular Physics

**History**

Original Manuscript: April 18, 2014

Revised Manuscript: May 18, 2014

Manuscript Accepted: May 18, 2014

Published: May 30, 2014

**Citation**

Juhong Han, You Wang, He Cai, Wei Zhang, Liangping Xue, and Hongyuan Wang, "Algorithm for evaluation of temperature distribution of a vapor cell in a diode-pumped alkali laser system: part I," Opt. Express **22**, 13988-14003 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-11-13988

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### References

- W. F. Krupke, “Diode Pumped Alkali Laser,” US Patent Application US 2003/0099272 Al, (2003).
- W. F. Krupke, R. J. Beach, V. K. Kanz, S. A. Payne, “Resonance transition 795-nm rubidium laser,” Opt. Lett. 28(23), 2336–2338 (2003). [CrossRef] [PubMed]
- W. F. Krupke, R. J. Beach, S. A. Payne, V. K. Kanz, J. T. Early, “DPAL: A new class of lasers for CW power beaming at ideal photovoltaic cell wavelengths,” 2nd International Symposium on Beamed Energy Propulsion (Japan), (2003).
- R. H. Page, R. J. Beach, V. K. Kanz, 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, 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]
- B. V. Zhdanov, A. Stooke, G. Boyadjian, A. Voci, R. J. Knize, “Rubidium vapor laser pumped by two laser diode arrays,” Opt. Lett. 33(5), 414–415 (2008). [CrossRef] [PubMed]
- R. Z. Hua, S. Wada, H. Tashiro, “Versatile, compact, TEM00-mode resonator for side-pumped single-rod solid-state lasers,” Appl. Opt. 40(15), 2468–2474 (2001). [CrossRef] [PubMed]
- Y. Wang, H. Kan, “Improvement on evaluating absorption efficiency of a medium rod for LD side-pumped solid-state lasers,” Opt. Commun. 226(1-6), 303–316 (2003). [CrossRef]
- Y. Wang, M. Niigaki, H. Fukuoka, Y. Zheng, H. Miyajima, S. Matsuoka, H. Kubomura, T. Hiruma, H. Kan, “Approaches of output improvement for cesium vapor laser pumped by a volume-Bragg-grating coupled laser-diode-array,” Phys. Lett. A 360(4-5), 659–663 (2007). [CrossRef]
- B. V. Zhdanov, R. J. Knize, “Diode-pumped 10 W continuous wave cesium laser,” Opt. Lett. 32(15), 2167–2169 (2007). [CrossRef] [PubMed]
- W. F. Krupke, “Diode pumped alkali lasers (DPALs)—A review (rev1),” Prog. Quantum Electron. 36(1), 4–28 (2012). [CrossRef]
- R. J. Beach, W. F. Krupke, V. K. Kanz, S. A. Payne, M. A. Dubinskii, 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]
- Y. Wang, K. Inoue, H. Kan, T. Ogawa, S. Wada, “A MOPA with double-end pumped configuration using total internal reflection,” Laser Phys. 20(2), 447–453 (2010). [CrossRef]
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