## Improving the output beam quality of multimode laser resonators

Optics Express, Vol. 13, Issue 7, pp. 2722-2730 (2005)

http://dx.doi.org/10.1364/OPEX.13.002722

Acrobat PDF (111 KB)

### Abstract

Multimode laser operation is usually characterized by high output power, yet its beam quality is inferior to that of a laser with single *TEM*_{00} mode operation. Here we present an efficient approach for improving the beam quality of multimode laser resonators. The approach is based on splitting the intra-cavity multimode beam into an array of smaller beams, each with a high quality beam distribution, which are coherently added within the resonator. The coupling between the beams in the array and their coherent addition is achieved with planar interferometric beam combiners. Experimental verification, where the intra-cavity multimode beam in a pulsed Nd:YAG laser resonator is split into four Gaussian beams that are then coherently added, provides a total increase in brightness of one order of magnitude. Additional spectral measurements indicate that scaling to larger coherent arrays is possible.

© 2005 Optical Society of America

## 1. Introduction

*TEM*

_{00}mode provide excellent output beam quality but typically with relatively low output power. Increasing the output power can be readily achieved by resorting to multimode operation, where several transverse modes oscillate simultaneously and exploit a larger volume of the laser gain medium. Unfortunately, the multimode beam does not have well defined phase and amplitude distributions, so the beam quality is relatively poor when compared to that of the

*TEM*

_{00}mode beam, and there is no increase of the optical brightness.

1. M. J. DiDomenico, “A single-frequency TEM00-mode gas laser with high output power,” Appl. Phys. Lett. **8**, 20–22 (1966). [CrossRef]

2. D. Sabourdy, V. Kermene, A. Desfarges-Berthelemot, M. Vampouille, and A. Barthelemy, “Coherent combining of two Nd:YAG lasers in a Vernier-Michelson-type cavity,” Appl. Phys. B **75**, 503–507 (2002). [CrossRef]

3. J. R. Leger, G. J. Swanson, and W. B. Veldkamp, “Coherent laser addition using binary phase gratings,” Appl. Opt. **26**, 4391–4399 (1987). [CrossRef] [PubMed]

4. J. R. Leger, M. L. Scott, and W. B. Veldkamp, “Coherent addition of AlGaAs lasers using microlenses and diffractive coupling,” Appl. Phys. Lett. **52**, 1771–1773 (1988). [CrossRef]

5. M. Tondusson, C. Froehly, V. Kermene, and M. Vampouille, “Coherent combination of four laser beams in a multi-axis Fourier cavity using a diffractive optical element,” J. Opt. A: Pure Appl. Opt. **3**, 521–526 (2001). [CrossRef]

6. D. Sabourdy et. al., “Efficient coherent combining of widely tunable fiber lasers,” Opt. Express **11**, 87–97 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-2-87. [CrossRef] [PubMed]

8. A. A. Ishaaya, N. Davidson, L. Shimshi, and A. A. Friesem, “Intra-cavity coherent addition of Gaussian beam distributions using a planar interferometric coupler,” Appl. Phys. Lett. **85**, 2187–2189 (2004). [CrossRef]

9. A. A. Ishaaya, L. Shimshi, N. Davidson, and A. A. Friesem, “Coherent addition of spatially incoherent light beams,” Opt. Express **12**, 4929–4934 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-20-4929. [CrossRef] [PubMed]

## 2. Basic principles

*P*from this type of resonator increases linearly with the aperture area, but in general, the one dimensional beam quality factor

10. A. E. Siegman, “New developments in laser resonators,” Optical Resonators: Proc. SPIE **1224**, 2–14 (1990). [CrossRef]

*TEM*

_{00}mode, so as to obtain four individual laser beam distributions with high quality. If these apertures are spaced sufficiently apart then each distribution will be independent and incoherent from the others. Since the relative phases of these distributions is random, the output beam quality of the total array will be poor. In order to improve the beam quality and thereby increase the brightness of the output beam, we now introduce two identical interferometric beam combiners [8

8. A. A. Ishaaya, N. Davidson, L. Shimshi, and A. A. Friesem, “Intra-cavity coherent addition of Gaussian beam distributions using a planar interferometric coupler,” Appl. Phys. Lett. **85**, 2187–2189 (2004). [CrossRef]

9. A. A. Ishaaya, L. Shimshi, N. Davidson, and A. A. Friesem, “Coherent addition of spatially incoherent light beams,” Opt. Express **12**, 4929–4934 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-20-4929. [CrossRef] [PubMed]

*θ*, and the second combiner is tilted horizontally at the same angle. The angle

*θ*and the thickness

*d*of the combiner, are designed to match the distance between the individual beams, so they optimally overlap and propagate collinear after exiting the combiner. For an angle

*θ, d*is determined by the simple relation

*d*=

*x*

_{o}/(2cos

*θ*tan(arcsin(

*θ/n*))), where

*x*

_{0}is the distance between adjacent two beams, and

*n*is the refractive index of the combiner material. When the beams in the array are phase locked such that destructive interference occurs at the beamsplitter layer, the losses introduced by the combiner may be completely suppressed, and all four beam distributions will be coherently added into a single output beam.

*e*

^{2}of its maximum value). This leads to an estimation of 43.2% for the fill factor. Assuming a combining efficiency of 95%, the expected output power, when replacing the square multimode beam with a tightly packed array of 2×2 Gaussian distributions, would thus be 41% of the original square multimode power. However, the beam quality would be significantly improved.

*M*

^{2}in each axis by a factor of 2, so that

*m,n*, such that

*m*+

*n*<2 (i.e.

*HG*

_{00},

*HG*

_{10},

*HG*

_{01},

*HG*

_{11},

*HG*

_{20},

*HG*

_{02}) [11], and the beam quality factors

9. A. A. Ishaaya, L. Shimshi, N. Davidson, and A. A. Friesem, “Coherent addition of spatially incoherent light beams,” Opt. Express **12**, 4929–4934 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-20-4929. [CrossRef] [PubMed]

*L*need only be greater than a certain value, so it is easy to control for a Nd:YAG laser [2

2. D. Sabourdy, V. Kermene, A. Desfarges-Berthelemot, M. Vampouille, and A. Barthelemy, “Coherent combining of two Nd:YAG lasers in a Vernier-Michelson-type cavity,” Appl. Phys. B **75**, 503–507 (2002). [CrossRef]

*L*

_{1}, L+Δ

*L*

_{2}, etc., the probability for having common frequencies within the gain bandwidth is drastically decreased. In our configuration, where the resonator channels end mirrors are common, the beam combiners introduce exact optical length differences, integer number of Δ

*L*, i.e Δ

*L*, 2Δ

*L*, 3Δ

*L*, etc., between the channels. For example, in our specific 2×2 array configuration, the resonator length of one channel is

*L*, of two channels

*L*+Δ

*L*, and of the remaining channel

*L*+2Δ

*L*. Thus, resorting to length differences of nΔ

*L*ensures that common frequency bands equally exist in coherent addition of two channels, four channels, and also of larger number of channels.

*L*, thereby ensuring the existence of common longitudinal modes. For example, a 4×4 array of Gaussian beam distributions can be obtained using a total of 4 beam combiners. In this case the thickness of the interferometric combiners in the second pair should be doubled in order to obtain a displacement twice that of the first pair. In general, the number of channels in the array will scale as 2

^{N}, where N is the number of beam combiners (N=2, 4, 6, …).

## 3. Experimental procedure and results

*R*=1.5 m) output coupler of 40% reflectivity at 1064 nm and a high-reflection flat rear mirror. A flash lamp pumped Nd:YAG rod of 5 mm diameter and 10 cm length (1.1% doping) served as a common gain medium for the four channels in the resonator. The rod was pumped with a pulse rate of 4 Hz at pump power levels between two to four times that of the threshold pump power. The maximum thermal lensing of the rod under these pumping conditions was measured to be

*f*=10 m. In order to establish the four separate channels, four apertures of 1.4 mm diameter, positioned 2.4 mm apart (between centers), were used. We confirmed that this distance between the channels was such that spontaneous phase locking, due to partial overlap of the beams [12

12. J. Xu, S. Li, K. K. Lee, and Y. C. Chen, “Phase locking in a two-element laser array: a test of the coupled-oscillator model,” Opt. Lett. **18**, 513–515 (1993). [CrossRef] [PubMed]

13. L. Fabiny, P. Colet, R. Roy, and D. Lenstra, “Coherence and phase dynamics of spatially coupled solid-state lasers,” Phys. Rev. A **47**, 4287–4296 (1993). [CrossRef] [PubMed]

*M*

^{2}values for the multimode beam distribution were

_{3}crystal and a

*λ*/4 retardation plate (see Fig. 3). The results in Q-switched operation reveal essentially the same behavior as for free running operation (with pulse duration of ~100

*µ*sec).

2. D. Sabourdy, V. Kermene, A. Desfarges-Berthelemot, M. Vampouille, and A. Barthelemy, “Coherent combining of two Nd:YAG lasers in a Vernier-Michelson-type cavity,” Appl. Phys. B **75**, 503–507 (2002). [CrossRef]

*c*/2|Δ

*L*|). When adding only two Gaussian distributions in the same configuration (using only one combiner and blocking half of the square aperture), we obtained essentially the same distribution of frequency bands.

*L*or 2Δ

*L*(see previous section), and that these length differences are stably maintained during lasing. These results indicate that up-scaling to larger arrays in our configuration, using additional interferometric beam combiners, is indeed possible. It is interesting to note that the side lobes in the spectrum, when coherently adding four channels, are not within the line width obtained with a single channel. This indicates that coherent addition influences the longitudinal mode competition dynamics.

## 4. Concluding remarks

*M*

^{2}>1), then our approach could be implemented with coherent arrays of multimode distributions instead of Gaussian distributions [9

**12**, 4929–4934 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-20-4929. [CrossRef] [PubMed]

## References and links

1. | M. J. DiDomenico, “A single-frequency TEM00-mode gas laser with high output power,” Appl. Phys. Lett. |

2. | D. Sabourdy, V. Kermene, A. Desfarges-Berthelemot, M. Vampouille, and A. Barthelemy, “Coherent combining of two Nd:YAG lasers in a Vernier-Michelson-type cavity,” Appl. Phys. B |

3. | J. R. Leger, G. J. Swanson, and W. B. Veldkamp, “Coherent laser addition using binary phase gratings,” Appl. Opt. |

4. | J. R. Leger, M. L. Scott, and W. B. Veldkamp, “Coherent addition of AlGaAs lasers using microlenses and diffractive coupling,” Appl. Phys. Lett. |

5. | M. Tondusson, C. Froehly, V. Kermene, and M. Vampouille, “Coherent combination of four laser beams in a multi-axis Fourier cavity using a diffractive optical element,” J. Opt. A: Pure Appl. Opt. |

6. | D. Sabourdy et. al., “Efficient coherent combining of widely tunable fiber lasers,” Opt. Express |

7. | A. Shirakawa, K. Matsuo, and K. Ueda, “Power summation and bandwidth narrowing in coherently coupled fiber laser array,” CThGG2, Conference on Lasers and Electro-Optics (CLEO), San Francisco, California, USA (2004). |

8. | A. A. Ishaaya, N. Davidson, L. Shimshi, and A. A. Friesem, “Intra-cavity coherent addition of Gaussian beam distributions using a planar interferometric coupler,” Appl. Phys. Lett. |

9. | A. A. Ishaaya, L. Shimshi, N. Davidson, and A. A. Friesem, “Coherent addition of spatially incoherent light beams,” Opt. Express |

10. | A. E. Siegman, “New developments in laser resonators,” Optical Resonators: Proc. SPIE |

11. | W. Koechner, |

12. | J. Xu, S. Li, K. K. Lee, and Y. C. Chen, “Phase locking in a two-element laser array: a test of the coupled-oscillator model,” Opt. Lett. |

13. | L. Fabiny, P. Colet, R. Roy, and D. Lenstra, “Coherence and phase dynamics of spatially coupled solid-state lasers,” Phys. Rev. A |

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

**OCIS Codes**

(140.3290) Lasers and laser optics : Laser arrays

(140.3410) Lasers and laser optics : Laser resonators

**ToC Category:**

Research Papers

**History**

Original Manuscript: December 1, 2004

Revised Manuscript: March 20, 2005

Published: April 4, 2005

**Citation**

Amiel Ishaaya, Vardit Eckhouse, Liran Shimshi, Nir Davidson, and Asher Friesem, "Improving the output beam quality of multimode laser resonators," Opt. Express **13**, 2722-2730 (2005)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-7-2722

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### References

- M. J. DiDomenico, �??A single-frequency TEM00-mode gas laser with high output power,�?? Appl. Phys. Lett. 8, 20�??22 (1966). [CrossRef]
- D. Sabourdy, V. Kermene, A. Desfarges-Berthelemot, M. Vampouille and A. Barthelemy, �??Coherent combining of two Nd:YAG lasers in a Vernier-Michelson-type cavity,�?? Appl. Phys. B 75, 503�??507 (2002). [CrossRef]
- J. R. Leger, G. J. Swanson and W. B. Veldkamp, �??Coherent laser addition using binary phase gratings,�?? Appl. Opt. 26, 4391�??4399 (1987). [CrossRef] [PubMed]
- J. R. Leger, M. L. Scott and W. B. Veldkamp, �??Coherent addition of AlGaAs lasers using microlenses and diffractive coupling,�?? Appl. Phys. Lett. 52, 1771�??1773 (1988). [CrossRef]
- M. Tondusson, C. Froehly, V. Kermene and M. Vampouille, �??Coherent combination of four laser beams in a multi-axis Fourier cavity using a diffractive optical element,�?? J. Opt. A: Pure Appl. Opt. 3, 521�??526 (2001). [CrossRef]
- D. Sabourdy et. al., �??Efficient coherent combining of widely tunable fiber lasers,�?? Opt. Express 11, 87�??97 (2003), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-2-87">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-2-87</a>. [CrossRef] [PubMed]
- A. Shirakawa, K. Matsuo and K. Ueda, �??Power summation and bandwidth narrowing in coherently coupled fiber laser array,�?? CThGG2, Conference on Lasers and Electro-Optics (CLEO), San Francisco, California, USA (2004).
- A. A. Ishaaya, N. Davidson, L. Shimshi and A. A. Friesem, �??Intra-cavity coherent addition of Gaussian beam distributions using a planar interferometric coupler,�?? Appl. Phys. Lett. 85, 2187�??2189 (2004). [CrossRef]
- A. A. Ishaaya, L. Shimshi, N. Davidson and A. A. Friesem, �??Coherent addition of spatially incoherent light beams,�?? Opt. Express 12, 4929�??4934 (2004), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-20-4929">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-20-4929</a>. [CrossRef] [PubMed]
- A. E. Siegman, �??New developments in laser resonators,�?? Optical Resonators: Proc. SPIE 1224, 2�??14 (1990). [CrossRef]
- W. Koechner, Solid-state laser engineering (Springer-Verlag, 5th ed., Germany, 1999, p. 209).
- J. Xu, S. Li, K. K. Lee and Y. C. Chen, �??Phase locking in a two-element laser array: a test of the coupled-oscillator model,�?? Opt. Lett. 18, 513-515 (1993). [CrossRef] [PubMed]
- L. Fabiny, P. Colet, R. Roy and D. Lenstra, �??Coherence and phase dynamics of spatially coupled solid-state lasers,�?? Phys. Rev. A 47, 4287�??4296 (1993). [CrossRef] [PubMed]
- N. Hodgson and H. Weber, Optical resonators, fundamentals, advanced concepts and applications (Springer-Verlag London, Great Britain, 1997, p. 319).

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