Beam quality management by periodic reproduction of wavefront aberrations in end-pumped Nd:YVO<sub>4</sub> laser amplifiers

Bin Liu; Chong Liu; Lifeng Shen; Chunhua Wang; Zhibin Ye; Dong Liu; Zhen Xiang

doi:10.1364/OE.24.008988

1. Introduction

Laser beam quality, which can be described by the beam propagation factor M ², is a critical parameter in applications such as nonlinear frequency conversion, laser remote sensing and laser material processing. Master oscillator power amplifier (MOPA) is a popular scheme to obtain high power high brightness laser output [1–3 ]. Unfortunately, the beam quality of the amplified laser beams deteriorates stage by stage in amplifier chains of MOPA laser systems. Yan et al. has made a brief summary in [4] about this point.

The mathematical expression of M ² factor is related to the beam intensity distributions and wavefront aberrations independently for a coherent laser source [5,6 ],

M^{2} = \sqrt{{(M_{d i f f}^{2})}^{2} + {(M_{a b}^{2})}^{2}},

where

M_{d i f f}^{2}

represents the amplitude term and

M_{a b}^{2}

represents the phase term. The minimum value of

M_{d i f f}^{2}

is 1 when the amplitude is Gaussian distribution. The minimum value of

M_{a b}^{2}

is 0 when the phase contains no high order aberrations. In traditional MOPA setups, expanding telescopes are inserted between the oscillators and power amplifiers for effective mode volume matching. These expanding telescopes are usually relay imaging optics, which image the near field of the seed beams with perfect Gaussian distributions from the oscillators to the amplifiers. This can retard the beam quality degradation due to the minimization of

M_{d i f f}^{2}

. The beam quality is still in the acceptable range if the pump power of the amplifiers is not so high, even this solution does nothing on

M_{a b}^{2}

. However, if the pump power is intensive enough, the thermally induced aberrations in the gain mediums of the amplifiers will be imposed onto the input beams. The aberrated beam wavefront results in the beam quality’s fast deterioration due to the increasing of

M_{a b}^{2}

, even if the beam intensity distribution is still Gaussian shaped. For high power laser amplifiers,

M_{a b}^{2}

grows to be the dominant item in Eq. (1) for beam quality deterioration.

Both active and passive compensations for wavefront aberrations to achieve beam quality improvements have been realized recently by using deformable mirrors (DMs) [7,8 ] or spherical aberration correctors (SACs) [9,10 ]. In this paper, a method is presented for beam quality management by periodic reproduction of wavefront aberrations in laser amplifier chains. The idea is from the mode self-consistency principle in a laser resonator. It is well known that the eigenmode of a laser resonator reproduces itself (both intensity and phase) after an intra-cavity round-trip propagation. The method we present for beam quality management in laser amplifiers is to perform such kind of behavior outside the cavity. Considering a MOPA with an oscillator operated with fundamental transverse mode, we could achieve extra-cavity periodic reproduction of wavefront by properly configuring the distances between the amplifiers, given the amplifiers have identical pump parameters as the oscillator. Even if the beam quality is deteriorated after the first amplifier, it could then be improved by the second amplifier. By periodically repeating this process in multi-stage amplifiers, one could manage beam quality in laser amplifier chains effectively. It should be noted that the concept of self-replication of a resonator to scale power was presented by Driedger for the first time [11]. The author scaled the resonator power by placing identical gain media inside a periodic resonator. The concept was then extended to MOPA systems where identical amplifiers were placed outside the resonator [12]. The oscillators in the previous work were operated in multi-transverse-mode with a symmetric plano-plano cavity configuration. The technique of self-replication was mainly used to reproduce the beam size in propagation in the amplifiers. The outputs from the MOPA were also multi-transverse-mode laser beams. The evolution of beam quality in the amplifiers was not mentioned.

The self-replication method we presented in MOPA system is to achieve outputs with fundamental transverse mode beams, in addition to power scaling. The basic principles for beam quality management are explained in the section 2. The wavefront aberration evolution of the intra-cavity beams is investigated in the section 3. Experiments are performed to prove the validity of evolution mechanism both in symmetrical and asymmetrical resonators. In the section 4, a high power end-pumped Nd:YVO₄ MOPA setup is built up. The experiment results verify the idea of beam quality management by the extra-cavity periodic reproduction of wavefront aberrations. Conclusions are given in the section 5.

2. Principles of beam quality management in laser amplifiers

In general, beam quality degrades when a laser beam passes through an aberrated gain medium. This viewpoint is not always correct, for example, when we consider an intra-cavity beam propagation, because the field could not be self-consistent if the beam quality of the eigenmode degrades in either trip of a round-trip propagation. This means there should be other kind of mechanism responsible for the intra-cavity beam quality evolution. There are only two possibilities considering the eigenmode self-consistency principle. The one is that the beam quality does not change when the beam passes through the gain medium. The other is that the beam quality is deteriorated in a single trip and is then improved in the return trip, or vice versa. We will show in the following paragraphs that the former is the situation for symmetrical resonators and the latter for asymmetrical ones. Experimental measurements will be shown in the section 3.

A symmetrical resonator with two flat mirrors are shown in the dashed box in Fig. 1(a) . It is a dynamically stable resonator (DSR) with fundamental transverse mode operation [13]. We define the direction from the high reflectivity mirror (HR) to the output coupler (OC) as the forward direction when the laser beam propagates inside the cavity. Then we have four beams inside the cavity, i.e., backward beam on the left of the medium (beam 1), forward beam on the left of the medium (beam 2), forward beam on the right of the medium (beam 3) and backward beam on the right of the medium (beam 4). We use two reference planes to represent the end surfaces of the gain medium, as RP1 and RP2. The labels A and B represent the left and right ends of the crystal, and the labels 1 and 2 represent the beams out of and into the crystal respectively. Then E_A1 and E_A2 represent the field of beam 1 and beam 2 on RP1 respectively, E_B1 and E_B2 represent the field of beam 3 and beam 4 on RP2 respectively.

Fig. 1 Schematics of the beam quality management in MOPA lasers for (a) the symmetrical oscillator and (b) the asymmetrical oscillator.

Download Full Size | PDF

The fields E_A1 and E_B1 are identical due to the symmetrical cavity configuration. The fields E_A2 and E_B2 are identical, too. Moreover, the fields E_A1 and E_A2 have the same beam quality because the M ² factor does not change when a beam propagates in a free space or is reflected by a flat mirror. So it can be concluded that the four intra-cavity beams have the same beam quality, that is, the beam quality does not change when the intra-cavity beam passes through the aberrated gain medium in a symmetrical DSR.

For the asymmetrical resonator shown in the dashed box in Fig. 1(b), studies have shown that the beam quality is different on different sides of the medium with a spherically aberrated thermal lens [14]. Without loss of generality, we assume that the beam in the right side of the medium has better beam quality than that in the left side. It means the beam quality is deteriorated when the backward beam passes the medium (beam 4 to beam 1) and it is improved when the forward beam passes the medium in the return trip (beam 2 to beam 3).

The laser fields and beam quality reproduce themselves after a round-trip propagation inside a resonator. Thus, if we use amplifiers with identical pumping parameters as the oscillator, the reproduction process can be realized outside the cavity, provided that the amplifiers are properly positioned. This is the principle of beam quality management in laser amplifiers. As shown in Fig. 1, the output beam from the OC propagates a distance of L ₂, and then enters the first laser amplifier. The front and the back surfaces of the amplifier are referred to as B2' and A1'. It is easy to understand that the field on the plane of B2' should be the same as that on the plane of B2 because the OC is a plane mirror. Thus, the field on the plane of A1' should be same as that on the plane of A1, given that the gain medium in the amplifier has the identical pumping parameters as the oscillator. Then the beam propagates twice of the distance L ₁ and enters the second amplifier, the front and the back surfaces of which are referred to as A2' and B1'. Similarly, the fields on the plane of A2' and B1' should be same as that on the plane of A2 and B1. The output beam from the second amplifier is expected to show the same beam quality as that from the oscillator. The beam propagation outside the oscillator from the OC to the second amplifier is equivalent to the intra-cavity round-trip beam propagation. Moreover, we can also use more amplifiers if we optimize every two amplifiers as a whole system. In this way, the laser fields are periodically reproduced outside the oscillator and the beam quality can be effectively managed in the amplifier chains.

3. Beam quality and wavefront aberration evolution of intra-cavity beams

Experiments are performed to achieve intra-cavity beam’s intensity and wavefront distributions with two different resonators, as shown in Fig. 2 . Both of them are diode-end-pumped solid-state lasers with plano-plano cavity configurations. One is a symmetrical DSR, and the other is an asymmetrical one. The schematic of the resonator is also shown in Fig. 3 . A 3 mm × 3 mm × 15 mm Nd:YVO₄ crystal with 0.3 at.% Nd³⁺-doped level is used as the gain medium. Two fiber coupled laser diodes with total power of 60 W and wavelength of 808 nm are used as pump sources. The output fibers have a fiber-core diameter of 400 μm and a numerical aperture of 0.22. The pump beams are focused into the crystal from the two ends through coupling lenses and dichroic mirrors. The waist diameter of the pump beam inside the crystal is 0.8 mm. The reflectivity of OC is 50%.

Fig. 2 Schematics of the beam quality and wavefront aberration measurements of intra-cavity beams. (a) A symmetrical cavity; (b) an asymmetrical cavity.

Download Full Size | PDF

Fig. 3 Setups of the beam quality management by extra-cavity reproduction of wavefront aberrations in MOPA lasers for (a) the symmetrical oscillator and (b) the asymmetrical oscillator.

Download Full Size | PDF

Two 1:1 imaging telescopes are used to image the intra-cavity fields outside the resonator as shown in Fig. 2. One telescope is for the beam in the left side of the medium. The other is for the beam in the right side of the medium. The CCD cameras and Hartmann-Shack wavefront sensors are used to measure the beam intensities and beam wavefront aberrations. More detailed and completed description about the measurement method can be found in [15]. The measured wavefront of an aberrated beam can be described by

φ (r) = k [C_{0} + C_{02} {(\frac{r}{r_{0}})}^{2} + C_{04} {(\frac{r}{r_{0}})}^{4} + (h i g h o r d e r s)],

where r ₀ is the normalized radius, C ₀₂ is the focusing coefficient, C ₀₄ is the spherical aberration (SA) coefficient, and k is the wavenumber. To demonstrate the robustness of the method for wavefront measurement with a Hartmann-Shack sensor, a comparison of M ² values is carried out in the experiments from a caustic measurement and a calculation from the wavefront measurement. The M ² factor can be measured using the ISO standardized methods [16] (also called caustic measurement). It mainly contains two steps. Firstly, the beam is coupled by a positive lens and a series of beam diameters are measured around the beam waist. Secondly, the M ² factor is calculated by hyperbolic fitting of the caustic. In the meanwhile, the M ² factor can also be calculated by the Eq. (1). The

M_{a b}^{2}

in Eq. (1) is proportional to the absolute value of SA coefficient C ₀₄, if other higher order aberrations are negligible [17],

M_{a b}^{2} = k | C_{04} | \sqrt{\frac{3}{2}},

where k is the wavenumber. In this way, we can compare the M ² values from the caustic measurement and the calculation from the wavefront measurement.

The symmetrical oscillator shown in Fig. 2(a) has the cavity length of L ₁ = L ₂ = 0.08 m. The value of the M ² factor is measured as 1.7 for all the four intra-cavity beams by the caustic measurements. The intensity distributions on end surfaces of the gain medium are shown in Fig. 2(a). All of them are nearly Gaussian distributions. The corresponding $M_{d i f f}^{2}$ is nearly 1. The aberration term $M_{a b}^{2}$ is the main factor for the beam quality deterioration for the four fields. With the measured values of C ₀₄ (shown in Table 1 ), the M ² factor can also be calculated by Eq. (3) and Eq. (1), which is also shown in Table 1. The calculated values of M ² factors agree well with the caustic measurements, which demonstrates that the wavefront aberration measurements are reliable.

Table 1. Results of $M_{d i f f}^{2}$ , C₀₄, $M_{a b}^{2}$ , the Calculated and Measured M² Factor, for the Symmetrical Resonator

View Table | View all tables in this article

Two results should be mentioned for the above experiment of symmetrical oscillator. The first is that the beam quality does not change when the intra-cavity beam passes through the aberrated gain medium in a symmetrical DSR, as explained in the section 2. The other is that wavefront spherical aberration of the intra-cavity beam can be positive or negative. The value of C ₀₄ reverses its sign when the beam propagates from plane A1 to A2, and also from plane B1 to B2. This is, intrinsically, an inevitable result of the mode self-consistency principle.

In the asymmetrical DSR, the cavity length is L ₁ = 0.1 m and L ₂ = 0.24 m. The beam 4 and beam 3 have the same beam quality with an M ² factor of 1.2. The beam1 and beam 2 have the same beam quality as well with an M ² factor of 3.0. It is also demonstrated that the beam quality is different on both sides of the medium. The measured C ₀₄ is nearly zero on planes B1 and B2, and |C ₀₄| is relatively large on planes A1 and A2, as shown in Table 2 . This is due to the different beam parameters in the two sides of the medium, i.e., different beam waists and different divergence angles, which hence influence the beam propagation and wavefront evolution. The value of C ₀₄ also reverses its sign when the beam propagates from plane A1 to A2. The beam intensities are still nearly Gaussian distributions for the four fields E_A1, E_A2, E_B1 and E_B2, which are shown in Fig. 2(b). The beam quality is still determined mainly by the aberration term $M_{a b}^{2}$ . The values of calculated M ² factor agree with the measured results.

Table 2. Results of $M_{d i f f}^{2}$ , C₀₄, $M_{a b}^{2}$ , the Calculated and Measured M² Factor, for Asymmetrical Resonators

View Table | View all tables in this article

4. Experiments for beam quality management in laser amplifiers

The wavefront SA coefficient C ₀₄ changes its value when a beam propagates inside a resonator. It reproduces itself after a round-trip propagation. In this section, we realize the reproduction of wavefront aberrations in the laser amplifier chains to achieve effective beam quality management by the principles presented in the section 2. Two MOPA systems are built up according to the schematic diagram shown in Fig. 1, with a symmetrical oscillator and an asymmetrical oscillator, respectively. Each MOPA contains one oscillator and four amplifiers and all mirrors are flat in the MOPA system. The oscillators are designed as dynamical stable resonators with large fundamental mode volume [18]. The focal length of the thermal lens is ~90 mm with the pump power of 60 W. The calculated Gaussian beam diameter in the laser crystal is 0.47 mm for the symmetrical oscillator and 0.78 mm for the asymmetrical oscillator.

The MOPA with symmetrical oscillator is shown in Fig. 3(a) and all the four amplifiers have identical pumping parameters as the oscillator mentioned in the section 2. Every two amplifiers work as a group to realize the reproduction of wavefront aberrations. The output power is 23 W from the oscillator. As shown in Fig. 4(a) , the laser power increases linearly and the beam quality hardly changes in the amplifiers. The beam intensities are nearly Gaussian distributions. The measured beam intensity distributions and SA coefficient C ₀₄ are also shown in Fig. 4(a). The C ₀₄ for the fields on the planes of B2', A1', A2' and B1' are −0.18 μm, 0.17 μm, −0.19 μm and 0.18 μm in the first two amplifiers, respectively. The evolution of beam quality and the evolution of wavefront aberrations during the beam propagation process on the planes of B2'→A1'→A2'→B1' is equivalent to that during the intra-cavity propagation on the planes of B2→A1→A2→B1. The beam propagation in the third and the fourth amplifiers is quite similar as that in the first two. This result is analogous to the previous aberration evolution inside the laser cavity.

Fig. 4 Power scaling up and beam quality evolution in MOPA systems with (a) a symmetrical oscillator and (b) an asymmetrical oscillator.

Download Full Size | PDF

The MOPA with the asymmetrical oscillator is shown in Fig. 3(b). The output power is 25 W from the oscillator and the beam quality factor M ² is 1.2. The output power from the first amplifier is 48 W and the deteriorated beam quality factor M ² is 3.2. The output power from the second amplifier is 72 W. The beam has an improved M ² factor of 1.3, i.e., the same level as that from the oscillator. The beam intensities are nearly Gaussian distributions as shown in Fig. 4(b). The C ₀₄ for the fields on the planes of B2', A1', A2' and B1' are −0.06 μm, 0.48 μm, −0.4 μm and 0.04 μm in the first two stages, respectively. It can be seen that the gain medium has little influences on the beam intensity distributions. It is also proved that the wavefront aberrations play the key role in M ² factor evolution in this system. The results in the last two amplifiers are similar as that in the first two. The power increases linearly from 72 W to 125 W, while the M ² factor is deteriorated to 3.3 and then is improved to 1.3 again. By this method of extra-cavity periodic reproduction of wavefront aberrations, we can achieve the power scaling and the effective beam quality management simultaneously in amplifier chains.

As a matter of fact, this beam quality management solution can also be valid for the laser amplifiers with different pumping parameters as the oscillator. The amplifiers usually have different pump diameters and different pump power with each other in actual MOPA systems. This results in different thermal effects and aberrations in the gain medium. The whole system must be carefully designed to achieve periodic reproduction of wavefront aberrations. The corresponding theoretical and experimental researches are ongoing and will be shown in the future.

5. Conclusion

In conclusion, a method for beam quality management is presented in MOPA systems by extra-cavity periodic reproduction of wavefront aberrations. The experimental results show that the value of SA coefficients C ₀₄ reverses its sign when the beam propagates inside the resonator. This is an inevitable result of the mode self-consistency principle. The wavefront aberration reproduction process has been successfully realized outside the cavity in four-stage amplifiers by properly positioning the amplifiers. This solution helps to achieve the effective beam quality management in laser amplifier chains.

Acknowledgments

This work is supported in part by the National Natural Science Foundation of China (NSFC) (No. 61575172), in part by Zhejiang Provincial Natural Science Foundation of China (No. LZ15F050001), in part by the foundation of the Key Laboratory of Science and Technology on High Energy Laser, CAEP (No. 2014HEL04), and in part by the Fundamental Research Funds for the Central Universities.

References and links

1. Z. Xiang, D. Wang, S. Pan, Y. Dong, Z. Zhao, T. Li, J. Ge, C. Liu, and J. Chen, “Beam quality improvement by gain guiding effect in end-pumped Nd:YVO₄ laser amplifiers,” Opt. Express 19(21), 21060–21073 (2011). [CrossRef] [PubMed]

2. M. Hu, Y. Zheng, J. Cai, G. Zhang, Q. Li, X. Zhou, Y. Wei, and Y. Lu, “CW dual-frequency MOPA laser with frequency separation of 45 GHz,” Opt. Express 23(8), 9881–9889 (2015). [CrossRef] [PubMed]

3. X. Yan, Q. Liu, X. Fu, Y. Wang, L. Huang, D. Wang, and M. Gong, “A 108 W, 500 kHz Q-switching Nd:YVO₄ laser with the MOPA configuration,” Opt. Express 16(5), 3356–3361 (2008). [CrossRef] [PubMed]

4. X. Yan, Q. Liu, X. Fu, D. Wang, and M. Gong, “Gain guiding effect in end-pumped Nd:YVO₄ MOPA lasers,” J. Opt. Soc. Am. B 27(6), 1286–1290 (2010). [CrossRef]

5. B. J. Neubert and B. Eppich, “Influences on the beam propagation ratio M²,” Opt. Commun. 250(4), 241–251 (2005). [CrossRef]

6. M. L. Gong, Y. Qiu, L. Huang, Q. Liu, P. Yan, and H. T. Zhang, “Beam quality improvement by joint compensation of amplitude and phase,” Opt. Lett. 38(7), 1101–1103 (2013). [CrossRef] [PubMed]

7. X. Lei, S. Wang, H. Yan, W. Liu, L. Dong, P. Yang, and B. Xu, “Double-deformable-mirror adaptive optics system for laser beam cleanup using blind optimization,” Opt. Express 20(20), 22143–22157 (2012). [CrossRef] [PubMed]

8. P. Yang, Y. Ning, X. Lei, B. Xu, X. Li, L. Dong, H. Yan, W. Liu, W. Jiang, L. Liu, C. Wang, X. Liang, and X. Tang, “Enhancement of the beam quality of non-uniform output slab laser amplifier with a 39-actuator rectangular piezoelectric deformable mirror,” Opt. Express 18(7), 7121–7130 (2010). [CrossRef] [PubMed]

9. I. Moshe, S. Jackel, A. Meir, Y. Lumer, and E. Leibush, “2 kW, M² < 10 radially polarized beams from aberration-compensated rod-based Nd:YAG lasers,” Opt. Lett. 32(1), 47–49 (2007). [CrossRef] [PubMed]

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]

11. K. P. Driedger, R. M. Iffländer, and H. Weber, “Multirod resonators for high-power solid-state lasers with improved beam quality,” IEEE J. Quantum Electron. 24(4), 665–674 (1988). [CrossRef]

12. N. Hodgson and H. Weber, Optical Resonators: Fundamentals, Advanced Concepts and Applications (Springer Science & Business Media, 2013), Section 13.3.

13. V. Magni, “Resonators for solid-state lasers with large-volume fundamental mode and high alignment stability,” Appl. Opt. 25(1), 107–117 (1986). [CrossRef] [PubMed]

14. R. Martinez-Herrero, P. M. Mejias, N. Hodgson, and H. Weber, “Beam-quality changes generated by thermally-induced spherical aberration in laser cavities,” IEEE J. Quantum Electron. 31(12), 2173–2176 (1995). [CrossRef]

15. Z. Ye, Z. Zhao, S. Pan, X. Zhang, C. Wang, Y. Qi, C. Liu, Z. Xiang, and J. Ge, “Beam Profile Evolution and Beam Quality Changes Inside a Diode-end-pumped Laser Oscillator,” IEEE J. Quantum Electron. 50(2), 62–67 (2014). [CrossRef]

16. Internation Organization for Standardization, “Lasers and Laser-Related Equipment-Test Methods for Laser Beam Parameters-Beam Widths, Divergence Angle and Beam Propagation Factor,” ISO 11146, (Geneva, 1999).

17. Y. Qi, Z. Zhao, C. Liu, and Z. Xiang, “Beam Quality Management in Multi-stage Side-Pumped Nd: YAG MOPA Laser Systems,” IEEE J. Sel. Top. Quantum Electron. 21(1), 1600506 (2015).

18. Z. Zhao, S. Pan, Z. Xiang, Y. Dong, J. Ge, C. Liu, and J. Chen, “Influences of spherical aberration on resonator’s stable zones and fundamental mode output power scaling of solid state laser oscillators,” Opt. Express 20(10), 10605–10616 (2012). [CrossRef] [PubMed]

	E_A1	E_A2	E_B1	E_B2
$M_{d i f f}^{2}$	1.0	1.0	1.0	1.0
C ₀₄(μm)	0.19	−0.17	0.17	−0.20
$M_{a b}^{2}$	1.37	1.23	1.23	1.45
M ² calculated	1.70	1.59	1.59	1.76
M ² measured	1.7	1.7	1.7	1.7

	E_A1	E_A2	E_B1	E_B2
$M_{d i f f}^{2}$	1.0	1.0	1.0	1.0
C ₀₄(μm)	0.40	−0.45	0.03	−0.05
$M_{a b}^{2}$	2.89	3.25	0.22	0.36
M ² calculated	3.06	3.40	1.02	1.06
M ² measured	3.0	3.0	1.2	1.2

	E_A1	E_A2	E_B1	E_B2
$M_{d i f f}^{2}$	1.0	1.0	1.0	1.0
C ₀₄(μm)	0.19	−0.17	0.17	−0.20
$M_{a b}^{2}$	1.37	1.23	1.23	1.45
M ² calculated	1.70	1.59	1.59	1.76
M ² measured	1.7	1.7	1.7	1.7

	E_A1	E_A2	E_B1	E_B2
$M_{d i f f}^{2}$	1.0	1.0	1.0	1.0
C ₀₄(μm)	0.40	−0.45	0.03	−0.05
$M_{a b}^{2}$	2.89	3.25	0.22	0.36
M ² calculated	3.06	3.40	1.02	1.06
M ² measured	3.0	3.0	1.2	1.2

Beam quality management by periodic reproduction of wavefront aberrations in end-pumped Nd:YVO₄ laser amplifiers

Abstract

1. Introduction

2. Principles of beam quality management in laser amplifiers

3. Beam quality and wavefront aberration evolution of intra-cavity beams

4. Experiments for beam quality management in laser amplifiers

5. Conclusion

Acknowledgments

References and links

Cited By

Figures (4)

Tables (2)

Equations (3)

Optics Express