## Enhancement of the beam quality of non-uniform output slab laser amplifier with a 39-actuator rectangular piezoelectric deformable mirror

Optics Express, Vol. 18, Issue 7, pp. 7121-7130 (2010)

http://dx.doi.org/10.1364/OE.18.007121

Acrobat PDF (256 KB)

### Abstract

We present a slab laser amplifier beam cleanup experimental system based on a 39-actuator rectangular piezoelectric deformable mirror. Rather than use a wave-front sensor to measure distortions in the wave-front and then apply a conjugation wave-front for compensating them, the system uses a Stochastic Parallel Gradient Descent algorithm to maximize the power contained within a far-field designated bucket. Experimental results demonstrate that at the output power of 335W, more than 30% energy concentrates in the 1x diffraction-limited area while the beam quality is enhanced greatly.

© 2010 OSA

## 1. Introduction

4. G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-Scaling Potential of Actively Phase-Locked Solid-State Laser Arrays,” IEEE J. Sel. Top. Quantum Electron. **13**(3), 460–472 (2007).

6. H. Zimer, K. Albers, and U. Wittrock, “Grazing-incidence YVO4-Nd:YVO4 composite thin slab laser with low thermo-optic aberrations,” Opt. Lett. **29**(23), 2761–2763 (2004). [PubMed]

9. G. D. Goodno, H. Komine, S. J. McNaught, S. B. Weiss, S. Redmond, W. Long, R. Simpson, E. C. Cheung, D. Howland, P. Epp, M. Weber, M. McClellan, J. Sollee, and H. Injeyan, “Coherent combination of high-power, zigzag slab lasers,” Opt. Lett. **31**(9), 1247–1249 (2006). [PubMed]

9. G. D. Goodno, H. Komine, S. J. McNaught, S. B. Weiss, S. Redmond, W. Long, R. Simpson, E. C. Cheung, D. Howland, P. Epp, M. Weber, M. McClellan, J. Sollee, and H. Injeyan, “Coherent combination of high-power, zigzag slab lasers,” Opt. Lett. **31**(9), 1247–1249 (2006). [PubMed]

12. W. Lubeigt, M. Griffith, L. Laycock, and D. Burns, “Reduction of the time-to-full-brightness in solid-state lasers using intra-cavity adaptive optics,” Opt. Express **17**(14), 12057–12069 (2009). [PubMed]

16. W. Lubeigt, S. P. Poland, G. J. Valentine, A. J. Wright, J. M. Girkin, and D. Burns, “Search-based active optic systems for aberration correction in time-independent applications,” Appl. Opt. **49**(3), 307–314 (2010). [PubMed]

## 2. Experimental setup and theory

_{00}mode output of 1.2W. The seed beam firstly passes through an expander which includes two cylinder lens and a slit, and then transforms into a 1.7 mm x10 mm rectangular beam. The beam then passes through a series of optical elements to achieve the goal that transmitting the slab laser amplifier back and forth two times which is represented by the blue arrow lines. M1 to M7 are seven reflectors all with high reflectivity (>99.9%) at 1064nm. Two lenses L1 and L2 (both with a focal length of 175 mm) are introduced to form a 4-f system. P1 and P2 are two quarter-wave plates which can convert the polarized orientation of seed beams to ensure that it passes through the slab laser amplifier 4 times. The seed beam will bounce 15 times for once passing through the slab amplifier. The diode end-pumped Nd:YAG slab amplifier has a dimension of 67 mm x 11 mm x 1.8 mm and can magnify the input beam power with a gain of 300. The slab amplifier is pumped by two 808 nm laser-diode (LD) arrays. The pump beams on both sides of the slab amplifier undergo total internal reflection at the slanted endface of the slab. This configuration ensures that the pump beams are absorbed along the entire length of the slab.

^{2}). The circles of Fig. 2 represent the actuators. The actuators are designed as trigonal arrangement and the distance between each actuator is 8mm. Figure 3 is the original DM surface shape measured by a WYKO interferometer which can measure the wave-front with a precision of ± 1/20 PV and ± 1/120 RMS. The peak to valley (PV) and root-mean-square (RMS) of the original DM surface are about 0.16μm and 0.03μm respectively which denote that the optical quality of original DM surface is rather good.

*φ(x,y)*relates to the mirror surface shape,

_{j}, y

_{j}) is the space position of the jth actuator, d is the distance between every two neighboring actuators and set at 8 mm, x and y represent respectively the value in x-coordinate and y-coordinate in the orthogonal coordinate plane.

18. M. A. Vorontsov, G. W. Carhart, and J. C. Ricklin, “Adaptive phase-distortion correction based on parallel gradient-descent optimization,” Opt. Lett. **22**(12), 907–909 (1997). [PubMed]

18. M. A. Vorontsov, G. W. Carhart, and J. C. Ricklin, “Adaptive phase-distortion correction based on parallel gradient-descent optimization,” Opt. Lett. **22**(12), 907–909 (1997). [PubMed]

^{(k)}= J (

*γ*is the gain coefficient,

*δ*is the metric perturbation. The choices of

*γ*and

*δ*depend on the actual experimental system, in our experiments, the

*γ*and

*δ*are set at 0.18 and 0.15 respectively. The iterative steps run continuously until they are ended manually or some promising results are achieved.

## 3. Experimental results

*P*and

*P*(

_{DL}*DL*is the abbreviation of diffraction-limited) are, respectively, the fractions of laser power contained within a far-field radius of λ/D (λ is the wavelength and D is the beam aperture before the focus lens) for the actual beam and for a hypothetical diffraction-limited beam with a spatially uniform intensity and wave-front profile [4

4. G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-Scaling Potential of Actively Phase-Locked Solid-State Laser Arrays,” IEEE J. Sel. Top. Quantum Electron. **13**(3), 460–472 (2007).

## 4. Conclusion and discussions

## Acknowledgements

## References and links

1. | F. D. Patel, D. G. Harris, and C. E. Turner, “Improving the beam quality of a high power Yb:YAG rod laser,” Proc. SPIE |

2. | H. Bruesselbach and D. S. Sumida, “A 2.65-kW Yb:YAG single rod laser,” IEEE J. Sel. Top. Quantum Electron. |

3. | A. Giesen, H. H¨ugel, A. Voss, K. Wittig, U. Brauch, and H. Opower, “Scalable concept for diode-pumped high-power solid-state-lasers,” Appl. Phys. B |

4. | G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-Scaling Potential of Actively Phase-Locked Solid-State Laser Arrays,” IEEE J. Sel. Top. Quantum Electron. |

5. | R. J. St. Pierre, D. W. Mordaunt, H. Injeyan, J. G. Berg, R. C. Hilyard, M. E. Weber, M. G. Wickham, G. M. Harpole, and R. Senn, “Diode array pumped kilowatt laser,” IEEE J. Sel. Top. Quantum Electron. |

6. | H. Zimer, K. Albers, and U. Wittrock, “Grazing-incidence YVO4-Nd:YVO4 composite thin slab laser with low thermo-optic aberrations,” Opt. Lett. |

7. | C. E. Max, D. T. Gavel, and S. S. Olivier, “Near infra-red astronomy with adaptive optics and laser guide stars at the keck observatory,” Proc. SPIE |

8. | K. N. LaFortune, R. L. Hurd, E. M. Johanssob, C. B. Dane, S. N. Fochs, and J. M. Brase, “Intracavity adaptive correction of a 10 kW, solid-state, heat-capacity laser,” Proc. SPIE |

9. | G. D. Goodno, H. Komine, S. J. McNaught, S. B. Weiss, S. Redmond, W. Long, R. Simpson, E. C. Cheung, D. Howland, P. Epp, M. Weber, M. McClellan, J. Sollee, and H. Injeyan, “Coherent combination of high-power, zigzag slab lasers,” Opt. Lett. |

10. | J. Notaras and C. Paterson, “Point-diffraction interferometer for atmospheric adaptive optics in strong scintillation,” Opt. Commun. |

11. | J. Sheldakova, A. Kudryashov, V. Samarkin, and V. Zavalova, “Problem of Shack-Hartmann wavefront sensor and Interferometer use while testing strongly distorted laser wavefront, ” Proc. SPIE |

12. | W. Lubeigt, M. Griffith, L. Laycock, and D. Burns, “Reduction of the time-to-full-brightness in solid-state lasers using intra-cavity adaptive optics,” Opt. Express |

13. | W. Lubeigt, G. J. Valentine, and D. Burns, “Enhancement of laser performance using an intracavity deformable membrane mirror,” Opt. Express |

14. | P. Yang, Y. Liu, W. Yang, M. W. Ao, S. J. Hu, B. Xu, and W. H. Jiang, “Adaptive mode optimization of a continuous wave solid-state laser using an intracavity piezoelectric deformable mirror,” Opt. Commun. |

15. | M. J. Booth, “Wave front sensor-less adaptive optics: a model-based approach using sphere packings,” Opt. Express |

16. | W. Lubeigt, S. P. Poland, G. J. Valentine, A. J. Wright, J. M. Girkin, and D. Burns, “Search-based active optic systems for aberration correction in time-independent applications,” Appl. Opt. |

17. | X. J. Rao, N. Ling, and W. H. Jiang, “Experimental of measuring influence function of deformable mirror using digital interferometer,” Acta Opt. Sin. |

18. | M. A. Vorontsov, G. W. Carhart, and J. C. Ricklin, “Adaptive phase-distortion correction based on parallel gradient-descent optimization,” Opt. Lett. |

19. | L. Liu, and M. A. Vorontsov, “Phase-Locking of Tiled Fiber Array using SPGD Feedback Controller,” Proc. of SPIE. |

**OCIS Codes**

(010.1080) Atmospheric and oceanic optics : Active or adaptive optics

**ToC Category:**

Adaptive Optics

**History**

Original Manuscript: January 12, 2010

Revised Manuscript: February 24, 2010

Manuscript Accepted: March 1, 2010

Published: March 23, 2010

**Citation**

Ping Yang, Yu Ning, Xiang Lei, Bing Xu, Xinyang Li, Lizhi Dong, Hu Yan, Wenjing Liu, Wenhan Jiang, Lei Liu, Chao Wang, Xingbo Liang, and Xiaojun Tang, "Enhancement of the beam quality of non-uniform output slab laser amplifier with a 39-actuator rectangular piezoelectric deformable mirror," Opt. Express **18**, 7121-7130 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-7-7121

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### References

- F. D. Patel, D. G. Harris, and C. E. Turner, “Improving the beam quality of a high power Yb:YAG rod laser,” Proc. SPIE 6100, 610018–610021 (2006).
- 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).
- A. Giesen, H. H¨ugel, A. Voss, K. Wittig, U. Brauch, and H. Opower, “Scalable concept for diode-pumped high-power solid-state-lasers,” Appl. Phys. B 58, 365–372 (1994).
- G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-Scaling Potential of Actively Phase-Locked Solid-State Laser Arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007).
- R. J. St. Pierre, D. W. Mordaunt, H. Injeyan, J. G. Berg, R. C. Hilyard, M. E. Weber, M. G. Wickham, G. M. Harpole, and R. Senn, “Diode array pumped kilowatt laser,” IEEE J. Sel. Top. Quantum Electron. 3(1), 53–58 (1997).
- H. Zimer, K. Albers, and U. Wittrock, “Grazing-incidence YVO4-Nd:YVO4 composite thin slab laser with low thermo-optic aberrations,” Opt. Lett. 29(23), 2761–2763 (2004). [PubMed]
- C. E. Max, D. T. Gavel, and S. S. Olivier, “Near infra-red astronomy with adaptive optics and laser guide stars at the keck observatory,” Proc. SPIE 2534, 412–422 (1995).
- K. N. LaFortune, R. L. Hurd, E. M. Johanssob, C. B. Dane, S. N. Fochs, and J. M. Brase, “Intracavity adaptive correction of a 10 kW, solid-state, heat-capacity laser,” Proc. SPIE 5333, 53–61 (2004).
- G. D. Goodno, H. Komine, S. J. McNaught, S. B. Weiss, S. Redmond, W. Long, R. Simpson, E. C. Cheung, D. Howland, P. Epp, M. Weber, M. McClellan, J. Sollee, and H. Injeyan, “Coherent combination of high-power, zigzag slab lasers,” Opt. Lett. 31(9), 1247–1249 (2006). [PubMed]
- J. Notaras and C. Paterson, “Point-diffraction interferometer for atmospheric adaptive optics in strong scintillation,” Opt. Commun. 281(3), 360–367 (2008).
- J. Sheldakova, A. Kudryashov, V. Samarkin, and V. Zavalova, “Problem of Shack-Hartmann wavefront sensor and Interferometer use while testing strongly distorted laser wavefront, ” Proc. SPIE 6872, 68720B–1-68720B–6(2008)
- W. Lubeigt, M. Griffith, L. Laycock, and D. Burns, “Reduction of the time-to-full-brightness in solid-state lasers using intra-cavity adaptive optics,” Opt. Express 17(14), 12057–12069 (2009). [PubMed]
- W. Lubeigt, G. J. Valentine, and D. Burns, “Enhancement of laser performance using an intracavity deformable membrane mirror,” Opt. Express 16(15), 10943–10955 (2008). [PubMed]
- P. Yang, Y. Liu, W. Yang, M. W. Ao, S. J. Hu, B. Xu, and W. H. Jiang, “Adaptive mode optimization of a continuous wave solid-state laser using an intracavity piezoelectric deformable mirror,” Opt. Commun. 278(2), 377–381 (2007).
- M. J. Booth, “Wave front sensor-less adaptive optics: a model-based approach using sphere packings,” Opt. Express 14(4), 1339–1352 (2006). [PubMed]
- W. Lubeigt, S. P. Poland, G. J. Valentine, A. J. Wright, J. M. Girkin, and D. Burns, “Search-based active optic systems for aberration correction in time-independent applications,” Appl. Opt. 49(3), 307–314 (2010). [PubMed]
- X. J. Rao, N. Ling, and W. H. Jiang, “Experimental of measuring influence function of deformable mirror using digital interferometer,” Acta Opt. Sin. 15, 1446–1451 (1995) (in Chinese).
- M. A. Vorontsov, G. W. Carhart, and J. C. Ricklin, “Adaptive phase-distortion correction based on parallel gradient-descent optimization,” Opt. Lett. 22(12), 907–909 (1997). [PubMed]
- L. Liu and M. A. Vorontsov, “Phase-Locking of Tiled Fiber Array using SPGD Feedback Controller,” Proc. SPIE 5895, 58950P–1-58950P–9 (2005).

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