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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 15 — Jul. 28, 2014
  • pp: 18421–18432
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3kW liquid–cooled elastically-supported Nd:YAG multi-slab CW laser resonator

Xing Fu, Peilin Li, Qiang Liu, and Mali Gong  »View Author Affiliations


Optics Express, Vol. 22, Issue 15, pp. 18421-18432 (2014)
http://dx.doi.org/10.1364/OE.22.018421


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Abstract

A 3kW liquid-convection-cooled Nd:YAG CW laser resonator with a novel design is developed and demonstrated, in which the straight-through geometry is adopted that the oscillating laser propagates through multiple thin slabs and multiple cooling flow layers in Brewster angle. Using the elastically-supported Nd:YAG single-crystal thin slabs at different doping levels, a multimode laser output with the output power of 3006 W is obtained from the stable cavity at the pump power of 19960 W, corresponding to an optical-optical efficiency of 15.1%, and a slope efficiency of 21.2%.

© 2014 Optical Society of America

1. Introduction

However, there are only a few reports revealing the development of high power solid-state lasers with liquid-convection-cooled configuration. One successful case is ThinZag approach that uses Nd:YAG ceramic slabs, which are immersed in a flowing cooling fluid. Using zigzag beam path for energy extraction, 100 kW average output power was produced with six modules placed within the cavity [8

8. A. Mandl and D. E. Klimek, “Textron’s J-HPSSL 100 kW ThinZag® Laser Program” in Conference on Lasers and Electro-Optics, JThH2 (2010). [CrossRef]

]. Another state-of-the-art case is the “liquid laser” scheme proposed by General Atomics Corp., based on which a 150 kW output power is expected to be achieved with the weight of no more than 750 kg [9], the detail of which has not been disclosed yet.

Recently, our group reported several experimental and theoretical results on liquid-convection-cooled solid-state lasers. A large-aperture liquid-cooled Nd:YAG thin-slab pulsed laser was presented [10

10. P. Li, Q. Liu, X. Fu, and M. Gong, “Large-aperture end-pumped Nd:YAG thin-disk laser directly cooled by liquid,” Chin. Opt. Lett. 11(4), 041408 (2013). [CrossRef]

], in which only one surface of the gain medium is cooled by the flowing water. With the 276-μs pump pulse, a peak output power of 1346 W was obtained at a peak pump power of 4627 W, corresponding to a slope efficiency of 54.9%. Furthermore, a Nd:YAG thin disk continuous-wave (CW) laser was studied at the 10-W level [11

11. X. Fu, Q. Liu, P. Li, and M. Gong, “Direct-liquid-cooled Nd:YAG thin disk laser oscillator,” Appl. Phys. B 111(3), 517–521 (2013). [CrossRef]

, 12

12. X. Fu, Q. Liu, P. Li, and M. Gong, “Wavefront aberration induced by beam passage through a water-convection-cooled Nd:YAG thin disk,” J. Opt. 15(5), 055704 (2013). [CrossRef]

], in which all the surface of the gain medium were cooled by the flowing liquid and the laser beam passed through the flowing liquid. The Nd:YAG multimode oscillator produced the output power of 17 W at the optical-optical efficiency of 31.2% [11

11. X. Fu, Q. Liu, P. Li, and M. Gong, “Direct-liquid-cooled Nd:YAG thin disk laser oscillator,” Appl. Phys. B 111(3), 517–521 (2013). [CrossRef]

]. Microscale eddies were observed at the upper and lower edge of the disk, and the turbulent flow brought degradation to the power and beam quality comparing to the case with laminar flow. Also, we verified that the wavefront distortion due to the modulation of refractive index by micro-scale eddies, can be well described by the Zernike polynomial of a few certain orders [12

12. X. Fu, Q. Liu, P. Li, and M. Gong, “Wavefront aberration induced by beam passage through a water-convection-cooled Nd:YAG thin disk,” J. Opt. 15(5), 055704 (2013). [CrossRef]

]. In addition, using the large-eddy-simulation model, wavefront aberration induced by turbulent flow field in liquid-convection-cooled solid-state laser was investigated [13

13. P. Li, X. Fu, Q. Liu, and M. Gong, “Analysis of wavefront aberration induced by turbulent flow field in liquid-convection-cooled disk laser,” J. Opt. Soc. Am. B 30(8), 2161–2167 (2013). [CrossRef]

], which well demonstrated the structure of time-random turbulent eddies and the effects of turbulent eddies on wavefront aberration.

2. Design and experimental setup

The scheme design of the liquid-convection-cooled large-aperture laser oscillator is shown in Fig. 1
Fig. 1 Configuration of large-aperture multi-slab laser oscillator.
. Nd:YAG single-crystal is chosen as the gain medium. Eleven pieces of parallel-arranged Nd:YAG thin slab are sandwiched between a pair of fused silica windows. The resonator consists of a total-reflection mirror (HR) and an output mirror (OC), both with a clear aperture of ϕ60 mm. All the thin slabs and windows are uncoated, while the oscillating laser beam within the cavity passes the windows and the Nd:YAG thin slabs near the incidence of Brewster angle with low reflection losses.

2.1 Pump system

One laser diode (LD) stack as the pump source is located at each side of the gain medium module. In the stack there are 15 LD arrays, arranged in a fan shape in order to achieve a most uniform possible pump distribution, while the relative position and emission direction of each array is elaborately optimized both in design and mounting process. Each LD array contains 20 LD bars with an emitting area of 35 × 10 (mm). With the fast axis collimated by microlenses, each array emits a maximum output power of 2000 W at a wavelength around 808 nm at the coolant temperature of 25 °C. The simulation results of the pump system using Tracepro software are presented in Fig. 2
Fig. 2 Simulated pump intensity distribution at the pump surface.
. As Fig. 2 indicates, the central region of the slab surface from x = −30 mm to x = 10 mm has a high uniformity of pump intensity distribution, with the root meam square (RMS) value calculated as 5.1%. The realized pump density at the pump surface of the nearest Nd:YAG slab is around 1200 W/cm2, while the total pump absorption efficiency by all the thin slabs is about 88% in the simulation.

2.2 Cooling fluid

Heavy water with the deuteration degree of 99.8% is used as the cooling liquid. The absorption coefficients at the pump wavelength (808 nm) and the output laser wavelength (1064 nm) of heavy water with different deuteration degree are measured using a spectrometer, while the results are depicted in Fig. 3
Fig. 3 Absorption coefficient of heavy water with different deuteration degree, compared with the deionized water.
, together with the absorption coefficients of deionized water (marked as the black spot in Fig. 3). It is shown that the absorption coefficient at 808 nm of the heavy water and the deionized water is roughly equal. However, the absorption coefficient of heavy water at 1064 nm greatly reduces as the deuteration degree increases up to 100%. To balance the loss parameter and cost, we used the heavy water with the deuteration degree of 99.8% that has the absorption coefficient of 0.023 cm−1 at 1064 nm, corresponding to an absorption loss of 2.3% for an absorption length of 1 cm, which is 83% lower than the case of deionized water (absorption loss of 13.3%).

In addition, to achieve a relatively uniform distribution of flow intensity along the slab length, a flow homogenizer consisting of multiple guide plates is used. As shown in Fig. 4
Fig. 4 Flow optimization: (a) flow rate homogenizer; (b) flow rate distribution at the thin slab.
, after optimization the distribution of flow rate at the thin slab location is fairly uniform along the slab length.

2.3 Thin slab

Figure 5
Fig. 5 Beam path through the gain medium module (fused silica window, heavy water layers and Nd:YAG thin slabs).
describes the relative positions of the Nd:YAG slabs, heavy water layers, and fused silica windows, illustrating the incident angle and refraction angle at each interface. As the refractive indexes of fused silica, heavy water and Nd:YAG at the laser wavelength of 1064 nm are respectively nf = 1.450, nh = 1.323, and ny = 1.823, the Brewster angles at interface 1, 2, 3 can be calculated as β1 = 55.4?, β2 = 42.4? and β3 = 54.0? respectively for the oscillating laser beam. As shown in Fig. 5, the wedge angle of the fused silica window is determined as 13.0?, making both the incident angle at the interface 1 and interface 3 equal to the Brewster angle. However, the designed incident angle of 47.6? at interface 2 is larger than the Brewster angle (42.4?), leading to a reflective loss of 0.05% per passage, which is acceptable for our laser system.

The Nd:YAG slab has the dimension of 86?40?1 mm (length ? width ? thickness), with the clear aperture of 80?40 mm. Various doping concentrations from 0.6 at.% to 1.1 at.% are employed individually for the eleven slabs to balance the thermal load [14

14. C. Orth, R. Beach, C. Bibeau, E. Honea, K. Jancaitis, J. Lawson, C. Marshall, R. Sacks, K. Schaffers, J. Skidmore, and S. Sutton, “Design modeling of the 100-J diode-pumped solid-state laser for Project Mercury,” Proc. SPIE 3265, Solid State Lasers VII, 114 (1998).

] that the slab closer to the pump source has smaller doping concentration, as indicated in Fig. 6
Fig. 6 The doping concentration and pump absorption efficiency of the eleven slabs.
. It can be shown in Fig. 6 that the ratio of the absorbed pump power in each slab to the total pump power is within the range between 8% and 9%, demonstrating a highly uniform profile of the heat load distribution along the pump direction.

Specifically, it should be noted that the Nd:YAG thin slabs in our experimental setup are elastically held by a flexible supporter. It is known that rigid fixation of a gain medium would induce the thermal stress, because it restricts the slab displacement when the slab expands or contracts in response to temperature changes. Adoption of a flexible supporter serves to greatly reduce the external constraint on the slab, permitting the deformation caused by the thermal gradient to occur freely to its fullest extent, thus in an elastically-held slab the temperature stress under high thermal load is dramatically alleviated. The flexible supporter we used in the experiment is made of an elastical material and has several tiny grooves to hold the thin slabs.

To compare the performance of slabs in both mounting methods, we conducted the thermal simulation by the commercial finite element software Ansys, while we assume that the maximum thermal stress a Nd:YAG slab can bear is no more than 110 MPa (lower than the typical stress fracture limit of 130 MPa~260 MPa [15

15. S. Tidwell, J. Seamans, M. Bowers, and A. Cousins, “Scaling CW diode-end-pumped Nd:YAG lasers to high average powers,” IEEE J. Quantum Electron. 28(4), 997–1009 (1992). [CrossRef]

]). The simulation results show that for a 1 at.% doped Nd:YAG slab with the dimension of 50?50?1 mm, the maximum heat power that a rigidly fixed slab can sustain is merely 0.45 kW, while the maximum heat power that an elastically held slab can sustain is 6 kW, about 13 times higher, as listed in Table 1

Table 1. Comparison between the Rigidly Fixed Slab and Elastically Held Slab in Terms of Thermal Effect and Depolarization Loss

table-icon
View This Table
. In other words, the elastic supporter indeed enhances the upper limit of affordable pump power. Moreover, the flexible supporter helps to reduce the depolarization loss induced by the thermal stress. To estimate the depolarization loss, the amplitude distribution of electrical field of the beam are numerically calculated based on the method presented by [16

16. Y. Chen, B. Chen, M. Patel, A. Kar, and M. Bass, “Calculation of thermal-gradient-induced stress birefringence in slab lasers-II,” IEEE J. Quantum Electron. 40(7), 917–928 (2004). [CrossRef]

]. Fig. 7
Fig. 7 Depolarization loss after 1 piece of slab: (a) rigidly fixed slab; (b) elastically held slab.
compares the simulated beam amplitude distribution due to depolarization loss after going through the slab with the size of 50?50?1 mm for the case of rigidly fixed slab and elastically held slab. As listed in Table 1, under the same thermal stress of 110 MPa, the beam going through 100 pieces of rigidly fixed slab is calculated to have the accumulative depolarization loss of 29.54% while for the case of elastically held slab the depolarization loss is 0.74%, significantly reduced by 97.5%. Therefore, the flexible supporter design is extremely important for the high power laser oscillator, where the beam light passes through the slab for a great number of times.

3. Experimental results

The experiment of liquid–cooled elastically-supported Nd:YAG multi-slab laser resonator was carried out, with the setup described in Section 2. The measured pump distribution from one of the two 15-array-stacks was shown in Fig. 8
Fig. 8 Measured pump light distribution of one stack.
. The heavy water flow layer between adjacent slabs has the thickness of 0.5 mm, and the flow velocity is around 2 m/s at the cooling channels with the turbulent flow pattern. At the total pump power of 19960 W, the maximum CW output power of 3006 W was successfully obtained from the oscillator at a 30-seconds run, corresponding to an optical-optical efficiency of 15.1%, and a slope efficiency of 21.2%. Fig. 9
Fig. 9 CW output power as a function of the pump power.
shows the oscillator output power varying as a function of the pump power.

Different output coupling of the cavity were used as R = 85%, 90%, and 95%, while the curvature radius of the high reflector is 500 mm. As shown in Fig. 10
Fig. 10 CW output power with different output coupling (Rcurv = 500 mm).
, the case with R = 90% has the largest slope efficiency and thus the highest output power. In addition, three different curvature radius of the high reflector were performed as Rcurv = 300 mm, 500 mm and 1000 mm while the reflectivity of the output coupler is 90%, and in each case stable laser output was obtained. As illustrated in Fig. 11
Fig. 11 CW output power with different curvature radius of the high reflector (R = 90%).
, for the case of Rcurv = 500 mm, the measured output power was slightly higher than the other two cases, due to a better mode matching between the pump mode and the oscillating laser mode.

To investigate the influence of pump uniformity and pump width on the output characteristic, an experiment with only central eight arrays of both stacks turning on was carried out. For the case of pumping with 16 arrays, 1420 W was obtained with the pump power of 12835 W, corresponding to an optical-optical efficiency of 11.1%, and a slope efficiency of 18.9%, which is lower than the case of pumping with 30 arrays, as described by Fig. 12
Fig. 12 CW output power with different LD arrays.
, in which the output coupler with the reflectivity of 90% and the curvature radius of 500 mm is used. The efficiency drop for the case of pumping with 16 arrays can be well explained by the simulated pump profiles in Fig. 13
Fig. 13 The simulated pump light profile at the pump surface: (a) 30 arrays pumping; (b) 16 arrays pumping.
. Despite the fact that both cases have the peak pump intensity of around 1200 W/cm2 at the pump surface, the peak pump intensity region has a width of about 40 mm along the horizontal direction, with a fairly uniform profile for the case of pumping with 30 arrays, while for the case of pumping with 16 arrays the pump distribution along the horizontal direction has a guassian-like shape, the width of peak pump intensity region less than 10 mm. Therefore the latter case suffers from a lower efficiency, since the gain outside the peak pump intensity region does a minor contribution to the laser output power.

Cooling capacity is another important element for enhancing the output efficiency. The output curves with the flow layer thickness of 0.5 mm and 1.0 mm are compared in Fig. 14
Fig. 14 CW output power with different thickness of cooling flow layer.
. For the case of pumping with 30 arrays, when the flow layer thickness increases from 0.5 mm to 1.0 mm, the output power drops by 30.3% from 3006 W to 2096 W at the pump power of 20 kW, with the optical-optical efficiency reduced to 10.5%. In addition, in the latter case, the slope of the output curve obviously reduces, exhibiting a sign of saturation, while the curve with excellent linearity for the case of 0.5 mm of thickness indicates a strong power scaling capability at higher level. Power stability was measured when adopting the 0.5-mm-thick layer. At the output power of 1.2 kW, the laser can operates for more than 20 minutes with the power instability of 3.5%. At the output power of 3 kW, the laser can run for 30 seconds, with the power instability lower than 5%. To avoid the potential risk, operation at 3 kW with more than 1 minute has not been tested.

The near-field distribution of the 3 kW laser output is shown in Fig. 15
Fig. 15 Near-field profile of the laser output.
. The beam quality M2 of the laser output was estimated as 50 and 10, in the vertical and horizontal direction respectively. The multimode beam profile is due to the nature of large-aperture stable cavity with large Fresnel number. A better beam quality would be produced at multi-kW level from an unstable cavity that has a strong ability of mode selection.

4. Conclusion

In this letter, a novel design of liquid-convection-cooled solid-state high power laser oscillator is presented, in which the straight-through geometry rather than a zigzag geometry is adopted that the oscillating laser propagates through multiple thin slab and multiple cooling flow layers in Brewster angle. With the elastically-supported Nd:YAG single-crystal thin slabs doped at different levels, and the 0.5-mm-thick layers of heavy water, a CW output power of 3006 W is obtained from the stable cavity at the pump power of 19960 W, corresponding to an optical-optical efficiency of 15.1%, and a slope efficiency of 21.2%. The beam quality M2 of the laser output is estimated as 50 and 10, in the vertical and horizontal direction respectively.

The experiment results demonstrate the feasibility and validity of the new configuration of liquid-convection-cooled laser, in terms of gain optimization, heat management, and multi-kW stable operation. High power scaling with this configuration is expected in the future with further injection of pump power, while the beam quality improvement can be realized with unstable cavity, which will be studied in the later work.

Acknowledgments

The research was supported in part by Tsinghua University Initiative Scientific Research Program, in part by the National Natural Science Foundation of China (grant 51021064), and in part by China Postdoctoral Science Foundation funded project (2013T60108).

References and links

1.

A. Giesen and J. Speiser, “Fifteen years of work on thin-disk lasers: results and scaling laws,” IEEE J. Sel. Top. Quantum Electron. 13(3), 598–609 (2007). [CrossRef]

2.

H. Bruesselbach and D. S. Sumida, “A 2.65-kW Yb:YAG single-rod laser,” IEEE J. Sel. Top. Quantum Electron. 11(3), 600–603 (2005). [CrossRef]

3.

V. Sazegari, M. R. J. Milani, and A. K. Jafari, “Structural and optical behavior due to thermal effects in end-pumped Yb:YAG disk lasers,” Appl. Opt. 49(36), 6910–6916 (2010). [CrossRef] [PubMed]

4.

J. Vetrovec, A. Koumvakalis, R. Shah, and T. Endo, “Development of solid-state disk laser for high-average power,” Proc. SPIE 4968, 54–64 (2003). [CrossRef]

5.

G. D. Goodno, S. Palese, J. Harkenrider, and H. Injeyan, “Yb:YAG power oscillator with high brightness and linear polarization,” Opt. Lett. 26(21), 1672–1674 (2001). [CrossRef] [PubMed]

6.

A. Minassian, B. A. Thompson, G. Smith, and M. J. Damzen, “High-power scaling (>100 W) of a diode-pumped TEM00 Nd:GdVO4 laser system,” IEEE J. Sel. Top. Quantum Electron. 11(3), 621–625 (2005). [CrossRef]

7.

R. Brockmann and D. Havrilla, “Disk laser: a new generation of industrial lasers,” Proc. SPIE 7193, 71931R (2009). [CrossRef]

8.

A. Mandl and D. E. Klimek, “Textron’s J-HPSSL 100 kW ThinZag® Laser Program” in Conference on Lasers and Electro-Optics, JThH2 (2010). [CrossRef]

9.

http://en.wikipedia.org/wiki/High_Energy_Liquid_Laser_Area_Defense_System

10.

P. Li, Q. Liu, X. Fu, and M. Gong, “Large-aperture end-pumped Nd:YAG thin-disk laser directly cooled by liquid,” Chin. Opt. Lett. 11(4), 041408 (2013). [CrossRef]

11.

X. Fu, Q. Liu, P. Li, and M. Gong, “Direct-liquid-cooled Nd:YAG thin disk laser oscillator,” Appl. Phys. B 111(3), 517–521 (2013). [CrossRef]

12.

X. Fu, Q. Liu, P. Li, and M. Gong, “Wavefront aberration induced by beam passage through a water-convection-cooled Nd:YAG thin disk,” J. Opt. 15(5), 055704 (2013). [CrossRef]

13.

P. Li, X. Fu, Q. Liu, and M. Gong, “Analysis of wavefront aberration induced by turbulent flow field in liquid-convection-cooled disk laser,” J. Opt. Soc. Am. B 30(8), 2161–2167 (2013). [CrossRef]

14.

C. Orth, R. Beach, C. Bibeau, E. Honea, K. Jancaitis, J. Lawson, C. Marshall, R. Sacks, K. Schaffers, J. Skidmore, and S. Sutton, “Design modeling of the 100-J diode-pumped solid-state laser for Project Mercury,” Proc. SPIE 3265, Solid State Lasers VII, 114 (1998).

15.

S. Tidwell, J. Seamans, M. Bowers, and A. Cousins, “Scaling CW diode-end-pumped Nd:YAG lasers to high average powers,” IEEE J. Quantum Electron. 28(4), 997–1009 (1992). [CrossRef]

16.

Y. Chen, B. Chen, M. Patel, A. Kar, and M. Bass, “Calculation of thermal-gradient-induced stress birefringence in slab lasers-II,” IEEE J. Quantum Electron. 40(7), 917–928 (2004). [CrossRef]

OCIS Codes
(140.3410) Lasers and laser optics : Laser resonators
(140.3530) Lasers and laser optics : Lasers, neodymium
(140.3580) Lasers and laser optics : Lasers, solid-state

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: June 11, 2014
Revised Manuscript: July 12, 2014
Manuscript Accepted: July 14, 2014
Published: July 22, 2014

Citation
Xing Fu, Peilin Li, Qiang Liu, and Mali Gong, "3kW liquid–cooled elastically-supported Nd:YAG multi-slab CW laser resonator," Opt. Express 22, 18421-18432 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-15-18421


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References

  1. A. Giesen and J. Speiser, “Fifteen years of work on thin-disk lasers: results and scaling laws,” IEEE J. Sel. Top. Quantum Electron.13(3), 598–609 (2007). [CrossRef]
  2. H. Bruesselbach and D. S. Sumida, “A 2.65-kW Yb:YAG single-rod laser,” IEEE J. Sel. Top. Quantum Electron.11(3), 600–603 (2005). [CrossRef]
  3. V. Sazegari, M. R. J. Milani, and A. K. Jafari, “Structural and optical behavior due to thermal effects in end-pumped Yb:YAG disk lasers,” Appl. Opt.49(36), 6910–6916 (2010). [CrossRef] [PubMed]
  4. J. Vetrovec, A. Koumvakalis, R. Shah, and T. Endo, “Development of solid-state disk laser for high-average power,” Proc. SPIE4968, 54–64 (2003). [CrossRef]
  5. G. D. Goodno, S. Palese, J. Harkenrider, and H. Injeyan, “Yb:YAG power oscillator with high brightness and linear polarization,” Opt. Lett.26(21), 1672–1674 (2001). [CrossRef] [PubMed]
  6. A. Minassian, B. A. Thompson, G. Smith, and M. J. Damzen, “High-power scaling (>100 W) of a diode-pumped TEM00 Nd:GdVO4 laser system,” IEEE J. Sel. Top. Quantum Electron.11(3), 621–625 (2005). [CrossRef]
  7. R. Brockmann and D. Havrilla, “Disk laser: a new generation of industrial lasers,” Proc. SPIE7193, 71931R (2009). [CrossRef]
  8. A. Mandl and D. E. Klimek, “Textron’s J-HPSSL 100 kW ThinZag® Laser Program” in Conference on Lasers and Electro-Optics, JThH2 (2010). [CrossRef]
  9. http://en.wikipedia.org/wiki/High_Energy_Liquid_Laser_Area_Defense_System
  10. P. Li, Q. Liu, X. Fu, and M. Gong, “Large-aperture end-pumped Nd:YAG thin-disk laser directly cooled by liquid,” Chin. Opt. Lett.11(4), 041408 (2013). [CrossRef]
  11. X. Fu, Q. Liu, P. Li, and M. Gong, “Direct-liquid-cooled Nd:YAG thin disk laser oscillator,” Appl. Phys. B111(3), 517–521 (2013). [CrossRef]
  12. X. Fu, Q. Liu, P. Li, and M. Gong, “Wavefront aberration induced by beam passage through a water-convection-cooled Nd:YAG thin disk,” J. Opt.15(5), 055704 (2013). [CrossRef]
  13. P. Li, X. Fu, Q. Liu, and M. Gong, “Analysis of wavefront aberration induced by turbulent flow field in liquid-convection-cooled disk laser,” J. Opt. Soc. Am. B30(8), 2161–2167 (2013). [CrossRef]
  14. C. Orth, R. Beach, C. Bibeau, E. Honea, K. Jancaitis, J. Lawson, C. Marshall, R. Sacks, K. Schaffers, J. Skidmore, and S. Sutton, “Design modeling of the 100-J diode-pumped solid-state laser for Project Mercury,” Proc. SPIE 3265, Solid State Lasers VII, 114 (1998).
  15. S. Tidwell, J. Seamans, M. Bowers, and A. Cousins, “Scaling CW diode-end-pumped Nd:YAG lasers to high average powers,” IEEE J. Quantum Electron.28(4), 997–1009 (1992). [CrossRef]
  16. Y. Chen, B. Chen, M. Patel, A. Kar, and M. Bass, “Calculation of thermal-gradient-induced stress birefringence in slab lasers-II,” IEEE J. Quantum Electron.40(7), 917–928 (2004). [CrossRef]

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