## Influences of spherical aberration on resonator’s stable zones and fundamental mode output power scaling of solid state laser oscillators |

Optics Express, Vol. 20, Issue 10, pp. 10605-10616 (2012)

http://dx.doi.org/10.1364/OE.20.010605

Acrobat PDF (2493 KB)

### Abstract

A parameter *x* is introduced to characterize the strength of thermal lens spherical aberration, whose influences on resonator’s stable zones are analyzed theoretically. Some new and helpful results are obtained. For symmetrical plane-plane cavity, spherical aberration has just influence on the back edge of stable zone. For asymmetrical plane-plane cavity, spherical aberration has influence on the back edges of the two stable zones and the front edge of the second stable zone. Effects of transverse mode collapsing to TEM_{00} mode and stable zones separation of different order’s transverse modes are pointed out, which is the foundation of TEM_{00} mode output power scaling for solid state laser oscillator. Influences of parameters such as resonator’s long arm length, short arm length, and pump beam radius on the extent to which of stable zones separation of different order transverse modes are discussed. An experimental setup of a high power diodes dual-end pumped Nd:YVO_{4} TEM_{00} mode laser oscillator is built up and investigated experimentally. 51.2 W TEM_{00} mode output power in CW operation is achieved with an optical-to-optical efficiency of about 50% and beam quality factor M^{2} being 1.2.

© 2012 OSA

## 1. Introduction

_{00}mode laser output from end pumped solid state laser is an active domain in laser technology [1

1. N. Hodgson, K. Griswold, W. Jordan, S. L. Knapp, A. A. Peirce, C. C. Pohaiski, E. Cheng, J. Cole, D. R. Dudley, A. B. Petersen, and W. L. Nighanjr, “High power TEM_{00} mode operation of diode-pumped solid state lasers,” Proc. SPIE **3611**, 119–131 (1999). [CrossRef]

4. A. Starodoumov and N. Hodgson, “Harmonic generation with fiber MOPAs and solid state lasers–technical challenges, state-of-the-art comparison and future developments,” Proc. SPIE **7912**, 79120H, 79120H-14 (2011). [CrossRef]

_{00}mode laser output with high output power and high efficiency [5

5. Z. Zhao, Y. Dong, C. Liu, M. Hu, Z. Xiang, J. Ge, and J. Chen, “Diodes-double-end-pumped high efficiency continuous wave 36 W TEM_{00} mode Nd:GdVO_{4} laser,” Laser Phys. **19**(11), 2073–2076 (2009). [CrossRef]

6. N. Hodgson and H. Weber, “Influence of spherical aberration of the active medium on the performance of Nd:YAG lasers,” IEEE J. Quantum Electron. **29**(9), 2497–2507 (1993). [CrossRef]

_{00}mode power scaling.

*K*and thermo-optical coefficient

*dn/dT*on temperature distribution [6

6. N. Hodgson and H. Weber, “Influence of spherical aberration of the active medium on the performance of Nd:YAG lasers,” IEEE J. Quantum Electron. **29**(9), 2497–2507 (1993). [CrossRef]

_{00}mode laser [7

7. Y. F. Chen, T. M. Huang, C. F. Kao, C. L. Wang, and S. C. Wang, “Optimization in scaling fiber-coupled laser-diode end-pumped lasers to higher power: influence of thermal effect,” IEEE J. Quantum Electron. **33**(8), 1424–1429 (1997). [CrossRef]

_{00}mode laser beam and degrade the beam quality by coupling TEM

_{00}mode laser to higher modes. N. Hodgson et al. applied the Fox-Li algorithm to analyze the influence of spherical aberration on stable resonators. The numerical results showed that the diffraction losses increase for stable resonators operated near the limit of stability [6

6. N. Hodgson and H. Weber, “Influence of spherical aberration of the active medium on the performance of Nd:YAG lasers,” IEEE J. Quantum Electron. **29**(9), 2497–2507 (1993). [CrossRef]

8. I. Buske and U. Wittrock, “Diffraction analysis of aberrated laser resonators,” Appl. Phys. B **83**(2), 229–233 (2006). [CrossRef]

10. Y. Lumer, I. Moshe, S. Jackel, and A. Meir, “Use of phase corrector plates to increase the power of radially polarized oscillators,” J. Opt. Soc. Am. B **27**(7), 1337–1342 (2010). [CrossRef]

_{4}master oscillator and two Nd:YAG power amplifiers by using a micro-machined deformable mirror to correct spherical aberrations and thus increase output power and beam quality by U. Wittrock [11

11. U. Wittrock, I. Buske, and H. Heuck, “Adaptive aberration control in laser amplifiers and laser resonators,” Proc. SPIE **4969**, 122–136 (2003). [CrossRef]

12. C. Liu, T. Riesbeck, X. Wang, J. Ge, Z. Xiang, J. Chen, and H. J. Eichler, “Influence of spherical aberrations on the performance of dynamically stable resonators,” Opt. Commun. **281**(20), 5222–5228 (2008). [CrossRef]

13. C. Liu, T. Riesbeck, X. Wang, Z. Xiang, J. Chen, and H. J. Eichler, “Asymmetric TEM_{00} mode cavity for birefringence compensated two-rod solid state lasers,” IEEE J. Quantum Electron. **44**(11), 1107–1115 (2008). [CrossRef]

_{00}mode laser output from a flash lamp pumped birefringence compensated two-rod Nd:YAG laser in CW operation, which is the state of the art for a lamp pumped laser [14

14. C. Liu, “A birefringence compensated two-rod Nd:YAG laser operating in TEM_{00} mode with a CW 61 W output power,” Laser Phys. **19**(12), 2155–2158 (2009). [CrossRef]

*x*that characterizes the strength of spherical aberration, we give some new insights on spherical aberration’s influence on resonator’s stable zones and make a comparison with the results obtained previously. The influences of several key parameters involved in resonator on the cavity design are analyzed theoretically. Some guidelines for optimizing the spherical aberration based TEM

_{00}mode resonator are given and the way to higher TEM

_{00}mode laser output is pointed out. Finally, a high power diodes double ends pumped Nd:YVO

_{4}laser oscillator setup is built up and investigated experimentally. The experimental results verify and support the prediction of our theoretical analysis.

## 2. Theory and discussions

### 2.1 Basic theory of thermal lens with spherical aberration in a strongly pumped laser rod

17. R. B. Chesler and D. Maydan, “Convex-concave resonators for TEM_{00} operation of solid-state ion lasers,” J. Appl. Phys. **43**(5), 2254–2257 (1972). [CrossRef]

18. J. Steffen, J. P. Lortscher, and G. Herziger, “Fundamental mode radiation with solid-state lasers,” IEEE J. Quantum Electron. **8**(2), 239–245 (1972). [CrossRef]

*f*. However, thermal loading in actual gain medium always introduces spherical aberration of the thermal lens, especially in strongly pumped laser rods [6

_{0}**29**(9), 2497–2507 (1993). [CrossRef]

*f*(

*r*) instead of a constant

*f*.

_{0}*f*(

_{T}*ω*) with different mode radii [19

_{L}19. S. Fan, X. Zhang, Q. Wang, S. Li, S. Ding, and F. Su, “More precise determination of thermal lens focal length for end-pumped solid-state lasers,” Opt. Commun. **266**(2), 620–626 (2006). [CrossRef]

20. C. Mafusire and A. Forbes, “Mean focal length of an aberrated lens,” J. Opt. Soc. Am. A **28**(7), 1403–1409 (2011). [CrossRef] [PubMed]

19. S. Fan, X. Zhang, Q. Wang, S. Li, S. Ding, and F. Su, “More precise determination of thermal lens focal length for end-pumped solid-state lasers,” Opt. Commun. **266**(2), 620–626 (2006). [CrossRef]

*f*(4

_{0}= ω_{p}^{2}/*A*) is thermal lens’s focal length for paraxial zone,

_{0}*ω*is the oscillating laser mode radius,

_{L}*ω*is the average pump beam radius, and

_{P}*x*is the parameter we introduced to characterize the strength of spherical aberration.

*A*is defined as

_{0}*A*(

_{0}= η_{h}P_{abs}*dn/dT*)

*/*4

*πK*, where

*η*is thermal load coefficient,

_{h}*P*is absorbed pump power,

_{abs}*dn/dT*is thermal-optical coefficient, and

*K*is thermal conductivity. Because we use a dual-end composite Nd:YVO

_{4}crystal in experiments, end-faces bulging out and the stress-induced birefringence effect are neglected in

*A*.

_{0}*x*in Eq. (1) represents the strength of spherical aberration. If

*x*= 0 is applied in Eq. (1), the focal length

*f*goes to a constant

_{T}*f*, which means an ideal thermal lens without spherical aberration. For an actual thermal lens with spherical aberration, one could always have

_{0}*x*> 0 in Eq. (1). That is, the thermal lens shows longer focal length for a laser beam with larger diameter.

### 2.2 Influence of spherical aberration on symmetrical resonator

*g*,

_{1}* = 1-Dd_{2}, g_{2}* = 1-Dd_{1}, L* = d_{1}+ d_{2}-Dd_{1}d_{2}*λ*is laser wavelength,

*D*is the dioptric power and

*d*(i = 1,2) is the resonator’s arm length.

_{i}*ω*in crystal by Eq. (3) and beam radius

_{L}*ω*in crystal in turn can influences the focal length of thermal lens seen by itself by Eq. (1), which is a iterative and coupling process. In the limit condition that spherical aberration coefficient

_{L}*x*in Eq. (1) goes to zero, the interrelation between focal length of thermal lens and beam radius

*ω*in crystal disappears. When spherical aberration coefficient

_{L}*x*is nonzero, we can solve the simultaneous Eq. (1) and Eq. (3) with different

*x*.

_{00}, TEM

_{01}and TEM

_{10}modes when Eq. (1) and Eq. (3) are simultaneously solved with spherical aberration coefficient

*x*= 0.1,

*x*= 0.2,

*x*= 0.3 and

*x*= 0.5. As a reference, the TEM

_{00}mode stable zone obtained without spherical aberration considered is also shown in Fig. 2. Compared with that shown in Fig. 1, some new results appear in Fig. 2. Spherical aberration affects not only the extent of high order mode’s stable zone, but also that of fundamental mode’s. The strength of spherical aberration directly determines the extent to which the stable zone’s back edge extends. Regardless of higher order modes and fundamental mode, the beam radius in crystal reaches their maximum value at almost the same pump power, which is higher for condition with larger spherical aberration

*x*. In sum, for plane-plane symmetrical resonator, the introduction of spherical aberration has main influence on back edge of stable zone, the extent to which is determined by the strength of spherical aberration.

### 2.3 Influence of spherical aberration on asymmetrical resonator

_{2}= 310 mm, short arm length of d

_{1}= 55 mm, pump beam radius of ω

_{p}= 0.8 mm. Stable zones for transverse modes of different orders have the same ranges. Figure 3(b) shows the stable zones diagrams for plane-plane asymmetrical cavity with spherical aberration considered when a simple suppose that

*f*,

_{01}= 1.1 × f_{00}*f*is employed. Some new phenomenon appears. Firstly, for the first stable zone (corresponding to low pump power), the presence of spherical aberration broadens its back edge. Secondly, for the second stable zone (corresponding to high pump power), transverse modes with different order experience different focal length, which makes each transverse mode has its own critical pump power from which the second stable zone enters. Therefore, separation of stable zones is formed because of the aspherical profile of the thermal lens, which means a large discrimination between fundamental mode and higher-order modes. Efficient TEM

_{10}= 1.2 × f_{00}_{00}mode operation can be achieved if one chooses the beginning of the second stable zone of the TEM

_{00}mode as the working point for the TEM

_{00}mode without an internal aperture needed. When combined with proper adjustment of two arm’s lengths, large TEM

_{00}mode volume and appropriate working point can be realized.

_{2}= 310 mm and pump beam radius of ω

_{p}= 0.8 mm, when short arm length is increased to 550 mm, the separation effect of stable zones strengthens. When long arm length is decreased to 110 mm, the separation effect of stable zones weakens. (2). The length of long arm should be long enough. In this way, △D narrows according to the relationship of ω

_{30}

^{2}△D = 2λ/π and efficient separation of stable zones can be achieved. However, it is at the cost of increasing the beam radius ω

_{30}in crystal. This should be carefully considered based on the reality. Figure 4(c) and 4(d) shows this trend. Keeping a short arm length of d

_{1}= 55 mm and pump beam radius of ω

_{p}= 0.8 mm, when long arm length is increased to 550 mm, the separation effect of stable zones strengthens. When short arm length is decreased to 110 mm, the separation effect of stable zones weakens. (3). The pump beam radius should be selected carefully. If the pump beam radius increases and pump power keeps same, the focal length of paraxial zone certainly will increases. Under the condition that keeping the resonator’s configuration unchanged, higher pump power is needed to shift the second stable zone. Figure 4(e) and 4(f) shows this trend. Appropriate pump beam radius should be selected by considering the available pump power, available configuration room and laser crystal’s thermal characteristics, comprehensively.

_{00}, TEM

_{01}and TEM

_{10}mode when Eq. (1) and Eq. (3) are simultaneously solved with spherical aberration coefficient

*x*= 0.1,

*x*= 0.2,

*x*= 0.3 and

*x*= 0.5. The TEM

_{00}mode stable zone obtained without spherical aberration considered is also shown in Fig. 5 as a reference. Compared with that shown in Fig. 3, some new results appear in Fig. 5. For the first stable zone, spherical aberration mainly affects back edge of stable zone and the strength of spherical aberration directly determines the extent to which the stable zone’s back edge extends. Regardless of higher order modes and fundamental mode, the beam radius in crystal reaches their maximum value at almost the same pump power, which is higher for condition with larger spherical aberration

*x*. For second stable zone, spherical aberration makes the critical pump power at which the second stable zone enters different for transverse modes of different orders, which forms the separation effect of sable zones of transverse modes. Larger spherical aberration coefficient

*x*leads to larger separation effect. But the back edges of transverse modes with different orders converge at almost same pump power, which is similar to that of the first stable zone.

_{00}mode can be predicted. The shapes of stable zone change from U-shape to √-shape and the short side of “√” shortens with the spherical aberration coefficient

*x*increased, which means that the beam radius supported by the resonator will have a sudden break from a large beam radius in so-called unstable zone to a small beam radius when the second stable zone is reached. Third, it predicts larger TEM

_{00}mode working zone with spherical aberration coefficient

*x*increased, shown by the shadow region in Fig. 5.

## 3. Experiments

^{3}Nd:YVO

_{4}composite crystal with a Nd

^{3+}-doped level as low as 0.3 atm.% was used as the laser gain medium. Two high-brightness and high-power fiber-coupler laser diode (made by DILAS Inc.) with each maximum output power of 50 W and wavelength of 808 nm are used as the double ends pumping source. The output fibers have a fiber-core diameter of 400 μm and a numerical aperture of 0.22. For each one, the fiber end is imaged to the closer end face of Nd:YVO

_{4}laser crystal with a diameter of 800 μm through a pair of positive aspherical lenses. For better thermal contact and reducing the deleterious thermal effects, the Nd:YVO

_{4}crystal is wrapped with a piece of 0.1 mm thick indium foil and mounted in a four sides edge water-cooled copper. The temperature of cooler for crystal is set at 18 degrees Celsius and 22 degrees Celsius for the laser diode’s cooler. The both end faces of the Nd:YVO

_{4}crystal are high transmittance (HT) coated at 808 nm and 1064 nm. Two dichotic mirrors, high-reflectivity (HR) coated at 1064 nm for 45° incidence angle and HT coated at 808 nm, are used to form a “U”-type resonator with a mirror HR coated at 1064 nm and an output coupler with 50% transmittance for 1064 nm. For efficient TEM

_{00}mode operation, the lengths of resonator’s two arms are optimized to be 55 mm and 310 mm.

_{4}laser with the optimized asymmetrical cavity configuration and a 50% OC transmission. The blue triangle figures the output power with optimized asymmetric cavity and a maximum TEM

_{00}mode power of 51.2 W is achieved at pump power of 104 W. The red shadow zone represents the TEM

_{00}mode operation zone. Figure 8 shows the two- and three-dimensional beam profiles captured at TEM

_{00}mode output power of 51.2 W, which are taken at 2 m far away from the laser exit. Its beam quality factor M

^{2}is measured to be 1.2, shown in Fig. 9 .

_{00}mode without any halo light’s concomitance. This TEM

_{00}mode operation can keep up to pump power of 108 W, after which the laser will oscillate in multimode again and output power decreases. This process is shown in Fig. 10 . In experiments, we also pump the Nd:YVO

_{4}crystal with just one laser diode. Though it can deliver about 25 W TEM

_{00}mode laser output power, its TEM

_{00}mode operation zone is very narrow compared with the dual-end pumped configuration.

_{00}mode output power is finally restricted to 54 W in our experiments, obtained with a very short short-arm-length and laser diode’s full load operation. So it is pump power limited. Higher TEM

_{00}output power can be expected with stronger pump source. However, that is not all. We think there are some principles that should be considered. Firstly, if we want to further scale the TEM

_{00}mode output power with higher pump power, the length of short arm should be further shortened, which will lead to the beam radius on HR mirror too small and increase the damage possibility. In this condition, one can consider making the short arm’s length longer and beam radius on HR mirror larger by using an appropriate concave HR mirror. Secondly, we need choose an appropriate pump beam radius according to the available pump power and the crystal’s thermal characteristics. For keeping the crystal’s thermal lens dioptric power same, higher pump power available will inevitably lead to larger pump beam radius. Third, we should choose a proper laser crystal with enough large cross section to support the pump beam radius. In addition, larger laser beam radius in crystal necessitates a longer length of long arm. Longer length of long arm will make the laser configuration not so compact and the pulse width longer when the laser is Q-switched. However, they can be easily settled by inserting an appropriate positive lens to shorten the length of long arm or incorporating a cavity damping technique. Anyway, higher TEM

_{00}mode output power can be expected with our method, combining some other artifice when needed.

## 4. Conclusions

*x*, we give a thoroughly comprehensive analysis on the spherical aberration’s influence on the stable zones of plane-plane resonators. Theoretically, it is very convenient for us to include the parameter x in the calculation process of the stable zones for modes with different orders. Some new results different to that what have been reported before is obtained, including spherical aberration’s influence on the front and back edges of stable zones, the shapes of stable zone change from U-shape to √-shape, prediction of the narrow of unstable zone between the two stable zones, prediction of that the output power drops in unstable zone but cannot drops to zero, prediction of that transverse mode collapsed to near TEM

_{00}mode, and prediction of that larger TEM

_{00}mode working zone can be achieved with larger spherical aberration coefficient

*x*. All these new results are observed in our experiment, which is performed with a homemade high power dual-end pumped Nd:YVO

_{4}laser oscillator. Guidelines for scaling TEM

_{00}mode output power directly from an oscillator are analyzed and discussed.

## Acknowledgments

## References and links

1. | N. Hodgson, K. Griswold, W. Jordan, S. L. Knapp, A. A. Peirce, C. C. Pohaiski, E. Cheng, J. Cole, D. R. Dudley, A. B. Petersen, and W. L. Nighanjr, “High power TEM |

2. | N. Hodgson, M. Li, A. Held, and A. Krueger, “Diode-pumped TEM |

3. | C. X. Wang, G. Y. Wang, A. V. Hicks, D. R. Dudley, H. Y. Pang, and N. Hodgson, “High-power Q-switched TEM |

4. | A. Starodoumov and N. Hodgson, “Harmonic generation with fiber MOPAs and solid state lasers–technical challenges, state-of-the-art comparison and future developments,” Proc. SPIE |

5. | Z. Zhao, Y. Dong, C. Liu, M. Hu, Z. Xiang, J. Ge, and J. Chen, “Diodes-double-end-pumped high efficiency continuous wave 36 W TEM |

6. | N. Hodgson and H. Weber, “Influence of spherical aberration of the active medium on the performance of Nd:YAG lasers,” IEEE J. Quantum Electron. |

7. | Y. F. Chen, T. M. Huang, C. F. Kao, C. L. Wang, and S. C. Wang, “Optimization in scaling fiber-coupled laser-diode end-pumped lasers to higher power: influence of thermal effect,” IEEE J. Quantum Electron. |

8. | I. Buske and U. Wittrock, “Diffraction analysis of aberrated laser resonators,” Appl. Phys. B |

9. | E. Leibush, S. Jackel, S. Goldring, I. Moshe, Y. Tzuk, and A. Meir, “Elimination of spherical aberration in multi-kW, Nd:YAG, rod pump-chambers by pump distribution control,” in |

10. | Y. Lumer, I. Moshe, S. Jackel, and A. Meir, “Use of phase corrector plates to increase the power of radially polarized oscillators,” J. Opt. Soc. Am. B |

11. | U. Wittrock, I. Buske, and H. Heuck, “Adaptive aberration control in laser amplifiers and laser resonators,” Proc. SPIE |

12. | C. Liu, T. Riesbeck, X. Wang, J. Ge, Z. Xiang, J. Chen, and H. J. Eichler, “Influence of spherical aberrations on the performance of dynamically stable resonators,” Opt. Commun. |

13. | C. Liu, T. Riesbeck, X. Wang, Z. Xiang, J. Chen, and H. J. Eichler, “Asymmetric TEM |

14. | C. Liu, “A birefringence compensated two-rod Nd:YAG laser operating in TEM |

15. | C. Kennedy, “Improved brightness laser oscillator with spherical aberration,” in |

16. | A. M. Bonnefois, M. Gilbert, and P. Y. Thro, “Near-diffraction-limited high power cw Nd:YAG laser using the spherical aberration of laser rods,” in |

17. | R. B. Chesler and D. Maydan, “Convex-concave resonators for TEM |

18. | J. Steffen, J. P. Lortscher, and G. Herziger, “Fundamental mode radiation with solid-state lasers,” IEEE J. Quantum Electron. |

19. | S. Fan, X. Zhang, Q. Wang, S. Li, S. Ding, and F. Su, “More precise determination of thermal lens focal length for end-pumped solid-state lasers,” Opt. Commun. |

20. | C. Mafusire and A. Forbes, “Mean focal length of an aberrated lens,” J. Opt. Soc. Am. A |

21. | N. Hodgson and H. Weber, |

22. | N. Hodgson and H. Weber, |

**OCIS Codes**

(140.3410) Lasers and laser optics : Laser resonators

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

(140.3580) Lasers and laser optics : Lasers, solid-state

(140.6810) Lasers and laser optics : Thermal effects

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: February 7, 2012

Revised Manuscript: April 9, 2012

Manuscript Accepted: April 18, 2012

Published: April 24, 2012

**Citation**

Zhigang Zhao, Sunqiang Pan, Zhen Xiang, Yantao Dong, Jianhong Ge, Chong Liu, and Jun Chen, "Influences of spherical aberration on resonator’s stable zones and fundamental mode output power scaling of solid state laser oscillators," Opt. Express **20**, 10605-10616 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-10-10605

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### References

- N. Hodgson, K. Griswold, W. Jordan, S. L. Knapp, A. A. Peirce, C. C. Pohaiski, E. Cheng, J. Cole, D. R. Dudley, A. B. Petersen, and W. L. Nighanjr, “High power TEM00 mode operation of diode-pumped solid state lasers,” Proc. SPIE3611, 119–131 (1999). [CrossRef]
- N. Hodgson, M. Li, A. Held, and A. Krueger, “Diode-pumped TEM00 mode solid state lasers and their micromachining applications,” Proc. SPIE4977, 281–294 (2003). [CrossRef]
- C. X. Wang, G. Y. Wang, A. V. Hicks, D. R. Dudley, H. Y. Pang, and N. Hodgson, “High-power Q-switched TEM00 mode diode-pumped solid state lasers with 30 W output power at 355 nm,” Proc. SPIE6100, 610019, 610019-14 (2006). [CrossRef]
- A. Starodoumov and N. Hodgson, “Harmonic generation with fiber MOPAs and solid state lasers–technical challenges, state-of-the-art comparison and future developments,” Proc. SPIE7912, 79120H, 79120H-14 (2011). [CrossRef]
- Z. Zhao, Y. Dong, C. Liu, M. Hu, Z. Xiang, J. Ge, and J. Chen, “Diodes-double-end-pumped high efficiency continuous wave 36 W TEM00 mode Nd:GdVO4 laser,” Laser Phys.19(11), 2073–2076 (2009). [CrossRef]
- N. Hodgson and H. Weber, “Influence of spherical aberration of the active medium on the performance of Nd:YAG lasers,” IEEE J. Quantum Electron.29(9), 2497–2507 (1993). [CrossRef]
- Y. F. Chen, T. M. Huang, C. F. Kao, C. L. Wang, and S. C. Wang, “Optimization in scaling fiber-coupled laser-diode end-pumped lasers to higher power: influence of thermal effect,” IEEE J. Quantum Electron.33(8), 1424–1429 (1997). [CrossRef]
- I. Buske and U. Wittrock, “Diffraction analysis of aberrated laser resonators,” Appl. Phys. B83(2), 229–233 (2006). [CrossRef]
- E. Leibush, S. Jackel, S. Goldring, I. Moshe, Y. Tzuk, and A. Meir, “Elimination of spherical aberration in multi-kW, Nd:YAG, rod pump-chambers by pump distribution control,” in Advanced Solid-State Photonics, Technical Digest (Optical Society of America, 2005), paper MB45.
- Y. Lumer, I. Moshe, S. Jackel, and A. Meir, “Use of phase corrector plates to increase the power of radially polarized oscillators,” J. Opt. Soc. Am. B27(7), 1337–1342 (2010). [CrossRef]
- U. Wittrock, I. Buske, and H. Heuck, “Adaptive aberration control in laser amplifiers and laser resonators,” Proc. SPIE4969, 122–136 (2003). [CrossRef]
- C. Liu, T. Riesbeck, X. Wang, J. Ge, Z. Xiang, J. Chen, and H. J. Eichler, “Influence of spherical aberrations on the performance of dynamically stable resonators,” Opt. Commun.281(20), 5222–5228 (2008). [CrossRef]
- C. Liu, T. Riesbeck, X. Wang, Z. Xiang, J. Chen, and H. J. Eichler, “Asymmetric TEM00 mode cavity for birefringence compensated two-rod solid state lasers,” IEEE J. Quantum Electron.44(11), 1107–1115 (2008). [CrossRef]
- C. Liu, “A birefringence compensated two-rod Nd:YAG laser operating in TEM00 mode with a CW 61 W output power,” Laser Phys.19(12), 2155–2158 (2009). [CrossRef]
- C. Kennedy, “Improved brightness laser oscillator with spherical aberration,” in Advanced Solid-State Lasers, (Optical Society of America, 2002), paper WB13.
- A. M. Bonnefois, M. Gilbert, and P. Y. Thro, “Near-diffraction-limited high power cw Nd:YAG laser using the spherical aberration of laser rods,” in Conference on Lasers and Electro-Optics Europe (2005).
- R. B. Chesler and D. Maydan, “Convex-concave resonators for TEM00 operation of solid-state ion lasers,” J. Appl. Phys.43(5), 2254–2257 (1972). [CrossRef]
- J. Steffen, J. P. Lortscher, and G. Herziger, “Fundamental mode radiation with solid-state lasers,” IEEE J. Quantum Electron.8(2), 239–245 (1972). [CrossRef]
- S. Fan, X. Zhang, Q. Wang, S. Li, S. Ding, and F. Su, “More precise determination of thermal lens focal length for end-pumped solid-state lasers,” Opt. Commun.266(2), 620–626 (2006). [CrossRef]
- C. Mafusire and A. Forbes, “Mean focal length of an aberrated lens,” J. Opt. Soc. Am. A28(7), 1403–1409 (2011). [CrossRef] [PubMed]
- N. Hodgson and H. Weber, Laser Resonators and Beam Propagation: Fundamentals, Advanced Concepts and Applications (Springer Science + Business Media, 2005), Chap. 5.
- N. Hodgson and H. Weber, Laser Resonators and Beam Propagation: Fundamentals, Advanced Concepts and Applications (Springer Science + Business Media, 2005), Chap. 13.

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