A multistage amplifier system based on high-power end-pumped two-segmented Nd:YVO4 is developed, which realizes the effective beam quality management in high-power lasers. Because of the severe thermal effect caused by high-power end pumping, both the appropriate crystal and beam filling factor (the ratio of the laser beam radius to the pump beam radius) are important in the amplifier. The multisegmented doped crystal is controlled in cooperation with the beam filling factor to realize high output power and maintain good beam quality. To study the thermal effect in the end-pumped crystal, the temperature distributions of end-pumped single-segmented and two-segmented Nd:YVO4 are theoretically calculated. In the experiment, a probe laser is employed to measure the spherical aberration coefficient and the beam quality of the laser at the rear end of the two end-pumped crystals, respectively, and the experimental results are in good agreement with the theoretical results. In the power amplification, a seed laser is employed in the experiment. The appropriate gain medium and beam filling factor are determined by considering the spherical aberration coefficient, beam quality, and power extraction efficiency. Based on the reasonable layout of the power amplification for each stage amplifier, the multistage amplifier system outputs a 280.2 W picosecond laser with the beam quality factors of Mx2 = 1.28 and My2 = 1.32.
【AIGC One Sentence Reading】:A 280 W picosecond laser system with good beam quality is developed using two-segmented Nd:YVO4 crystals and high-power end pumping.
【AIGC Short Abstract】:A 280 W picosecond amplifier system using two-segmented Nd:YVO4 crystals is developed, effectively managing beam quality in high-power lasers. Theoretical and experimental studies on thermal effects and beam quality show good agreement, achieving high output power with Mx2 = 1.28 and My2 = 1.32.
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High-power and high-beam-quality ultrafast lasers are essential for industrial processing applications such as high-precision glass processing, material cutting, and wafer slicing. Currently, rod lasers, slab lasers[1,2], and thin-disk lasers[3–5] are mainly used to generate high-power ultrafast lasers. The simplicity, reliability, and low cost make the conventional rod gain medium still widely used. A rod-shaped gain medium like crystal has attracted much attention because of its large stimulated emission cross section and high absorption coefficient. In 2022, Ouyang et al.[6] reported a picosecond laser based on end-pumped two-stage rod amplifiers. An output power of 148 W is achieved with the beam quality factors of and , respectively. In the same year, Yang et al.[7] used two stages of rod amplifier in the system, which produced a maximum average power of 122.3 W with a beam quality factor of . In 2023, Orii et al.[8] developed two-stage single-pass amplifiers using end-pumped rod-type crystals and high-power 914 nm LD modules. They achieved a 1064 nm light with an average power of 261 W, but the corresponding beam quality has not been reported.
Although the output power has improved in recent years, the beam quality will inevitably continue to deteriorate during power amplification. Laser thermal management has been proven to be an effective way to realize high output power, high efficiency, and good beam quality[9]. At high-power end pumping, a multisegmented crystal and an appropriate beam filling factor (, defined as the ratio of the laser beam radius to the pump beam radius) are two effective methods to realize thermal management[9,10]. In this study, we established a multistage amplifier system based on high-power end-pumped two-segmented crystals and an appropriate beam filling factor, realizing high power extraction efficiency and good beam quality. The temperature distributions of two types of crystals are presented theoretically. Using a probe laser, the spherical aberration coefficient and beam quality factor of the laser at the rear end of the end-pumped crystals are calculated and measured, respectively. The results indicate that the influence of the thermal effect is reduced in the two-segmented crystal for good laser beam quality. In the power amplification, an appropriate beam filling factor is found for both high power extraction efficiency and good beam quality experimentally. In the multistage amplifier system, a reasonable layout of power amplification is designed. Finally, the system realizes a picosecond laser output with an average power of 280.2 W and the beam quality factors of 1.28 and 1.32 on the and axes, respectively.
2. Temperature Distribution of End-Pumped Crystals
The inhomogeneous heat distribution in the crystal causes the thermal effect, which would be more serious, particularly at high-power end pumping[9]. Therefore, it is significant to analyze and manage the thermal effect in the crystal in order to achieve high power and high beam quality lasers. Figure 1 shows the thermal model of an end-pumped two-segmented rectangular-geometry crystal. The length of each side of the crystal is , , and , respectively. The front end of the crystal is bonded with an undoped endcap. According to the doping concentration, the pump absorption coefficient of the crystal is defined as and , respectively. Every transverse plane on the axis is denoted as , , , and , respectively, where and . For the edge-cooled crystal, the temperatures of each boundary on the sides can be assumed as room temperature , and the boundary convective heat transfer coefficients between the two ends of the crystal and air are too small to be regarded as 0. Therefore, the temperature distribution of the crystal can be expressed by a three-dimensional heat conduction equation. When the fiber-coupled LD end pumps the crystal, the temperature distribution can be expressed as[10]where is the coefficient to be determined, , , and are three orthogonal sets of eigenfunctions, , , and are the thermal conductivity coefficients on the , , and axes, respectively, is the intensity function of the pump following the super-Gaussian distribution, is the radius of the pump beam at the front end of the crystal, is the number of doped segments, is the fractional thermal loading, and is the pump power. The fractional thermal loading is given by , where and are the wavelengths of the pump beam and laser beam.
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The temperature distribution of an -cut 0.2+0.5% (atomic fraction) crystal with a 2 mm endcap end-pumped by 175 W power is presented, as shown in Fig. 2(a). Here, the parameters used in theoretical calculations are shown in Table 1. The maximum temperature rise and temperature distribution of the crystal directly affect the thermal effect. In this work, we use the wavelength of the pump beam at 878 nm rather than at the traditional 808 nm. The wavelength-locked 878.6 nm LD directly pumps from the ground state to the laser upper level , which reduces the quantum loss, heat generation, and thermal stress, to effectively improve the quantum efficiency[13]. Thus, under the in-band pumping at 878 nm, the heat generated in the laser crystal is diminished, so that the thermal effect of the crystal is reduced[14,15]. Additionally, it extends the power scaling of considerably and maintains excellent beam quality[14,15]. Another -cut single-segmented crystal with 0.3% (atomic fraction) -doped is used for comparison; the temperature distribution along the axis is shown in Fig. 2(b). The temperature rise of the two crystals on the axis is shown in Fig. 2(c). It can be seen that the maximum temperature rise of the two-segmented crystal is 78.1 K, which is 32.5 K lower than that of the single-segmented crystal (110.6 K). In addition, the temperature on the axis in the two-segmented crystal is smoother than that in the single-segmented crystal.
Table 1. Parameters Used in Theoretical Calculations
Table 1. Parameters Used in Theoretical Calculations
Parameter
Value
a
3 mm
b
3 mm
c1
2 mm
c2
17 mm
c3
25 mm
ωp
0.8 mm
λp
878 nm
λl
1064 nm
T0
293 K
Kx
9 W/mm·K[11,12]
Ky
9 W/mm·K[11,12]
Kz
12 W/mm·K[11,12]
N
2
Order of G( )
8
Figure 2.Cross-sectional temperature distributions of Nd:YVO4 with (a) 0.2 + 0.5% (atomic fraction) Nd3+-doped and (b) 0.3% (atomic fraction) Nd3+-doped on the x–z plane, and (c) the comparison of the temperature rise of the cross-section center along the z axis.
According to Refs. [16, 17], the increasing value of the spherical aberration coefficient will lead to the deterioration of beam quality, especially under high-power end pumping. A convenient mathematical expression of the aberration content is provided by a set of complete orthogonal polynomials which are defined on a unit circle, called Zernike polynomials. The Zernike coefficients could be obtained by direct matrix inversion[18]. The 11th of the Zernike polynomial is spherical aberration, which is given by [18,19]. Since contains the quartic term that makes a great contribution to the phase, the beam quality factor can be expressed as[16,17]where is the beam quality factor of the initial or unaberrated beam, and is the additional contribution to the beam quality factor caused by the quartic phase-aberration effects. could be given by , where is the lens focal length and is the radius of the laser beam. By the end pumping, the thermal effect of the crystal changes the laser phase, causing the deterioration of beam quality. Based on the numerical results of the crystal temperature distribution in Sec. 2, the phase distribution of the probe laser at the rear end of the crystal can be calculated[20]. Adopting the 974.5 nm probe laser with a beam filling factor , the Zernike coefficients of the laser beam at the rear end of the end-pumped single-segmented and two-segmented crystals are shown in Fig. 3. The 974.5 nm laser, which has excellent beam quality and no gain in the 878 nm-pumped crystal, can be employed as a probe laser to observe the phase distribution of the laser affected only by the refractive index of the crystal. Here, only the values of the 5th to 15th Zernike coefficients are presented because the Zernike coefficients of the 1st to 4th would not change the beam quality and those higher than the 15th are so small that they can be ignored.
Figure 3.In the case of the beam filling factor ωl/ωp = 1, the values of the 5th to 15th Zernike coefficients of the probe laser beam at the rear end of the end-pumped single-segmented and two-segmented crystals are calculated, respectively.
The initial probe laser has no aberration, whereas the phase distribution would change after passing through the end-pumped crystal. The numerical results show that the value of the 11th Zernike coefficient (spherical aberration coefficient) is always the largest with both crystals. With the two-segmented crystal, the calculated spherical aberration coefficient is 11.17 nm, and the corresponding beam quality factors on the and axes are and , respectively. With the single-segmented crystal, the calculated is 14.76 nm, and the corresponding beam quality factors on the and axes are and . This demonstrates that the spherical aberration is the primary cause of the deterioration in beam quality, and, for a given beam filling factor, the spherical aberration coefficient of the two-segmented crystal used as the gain medium is less than that of the single-segmented crystal. Thus, to achieve good beam quality in a high-power laser, it is essential to analyze the spherical aberration coefficient in the crystal. To further confirm the numerical model, a 974.5 nm probe laser is employed in the experiment to pass through the end-pumped single-segmented and two-segmented crystals, respectively.
3.2. Experimental setup for the phase measurement
Figure 4 depicts the experimental setup for measuring the phase of the probe laser beam at the rear end of the crystal. The pump beam (LD1) with the wavelength locked at 878 nm has the average power of 175 W. It passes through coupler 1 and goes into the crystal with a radius of 0.8 mm. Two types of crystals are employed as gain media, which are consistent with the theoretical condition in Sec. 2. A 974.5 nm probe laser (), without aberration passes through the coupler 2, is reflected by the dichroic mirror (DM), and goes into the crystal. Here, the DM is high reflectivity (HR)-coated at 974.5 nm and high transmittance (HT)-coated at 878 nm for the laser at the incidence angle of 45°. To obtain the spherical aberration coefficient of the probe laser at the rear end of the crystal, the beam is imaged by a system and measured by a wavefront sensor (Phasics, SID4).
Figure 4.Experimental setup for measuring the phase of the probe laser beam at the rear end of the crystal.
3.3. Analysis and discussion of experimental results
First, in order to verify the model of the spherical aberration coefficient caused by the crystal thermal effect on the Gaussian laser, a 0.01 W 974.5 nm laser is employed as the probe laser, and it enters the single-segmented and two-segmented crystals with different beam filling factors , respectively. The spherical aberration coefficient of the probe beam at the rear end of the crystal is measured by the wavefront sensor, and the beam quality factor is measured by a CCD. The experimental results are shown in Figs. 5(a) and 5(b). In addition, Figs. 5(a) and 5(b) also show the corresponding theoretical results.
Figure 5.In the cases of the single-segmented and two-segmented crystals as gain media, with the beam filling factors ωl/ωp from 0.5 to 1, the (a) spherical aberration coefficient c11 (theoretical and experimental) and (b) beam quality factor on x axis Mx2 (theoretical and experimental) are calculated and measured.
The results show that the values of spherical aberration coefficient and beam quality factor with the two-segmented crystal as the gain medium are smaller than those with the single-segmented crystal. This indicates that under the same pumping conditions, a lower maximum temperature rise and a smoother heat distribution along the axis are beneficial to reduce the spherical aberration of the laser caused by thermal effect and maintain good beam quality. Therefore, it is recommended to employ the two-segmented crystal as the gain medium for high-power end pumping.
Furthermore, it also shows that a small beam filling factor could control the beam quality well in the end-pumped crystal. With the single-segmented and two-segmented crystal as the gain medium, the influence of beam filling factor on spherical aberration coefficient and beam quality factor are analyzed, respectively. In the cases of the beam filling factor from 0.5 to 1 with the two-segmented crystal, the spherical aberration coefficient increases from 1.24 to 11.70 nm, and the beam quality factor on the axis increases from 1.11 to 1.85 experimentally. Compared with the single-segmented crystal, the value of the spherical aberration coefficient and the beam quality factor of the two-segmented crystal is smaller. In the experiment, the results of the beam quality factor on the axis are similar to that on the axis. The theoretical and experimental results are in good agreement. It also indicates that the larger the beam filling factor, the larger the spherical aberration coefficient, and the poorer the beam quality.
Second, to realize excellent beam quality and efficient power extraction efficiency in the amplifier at the same time, a suitable beam filling factor is determined by a 20 W 1064 nm laser () employed as the seed laser. It enters the single-segmented and two-segmented crystals with different beam filling factors , respectively, and the corresponding spherical aberration coefficient and the beam quality factor on the axis are calculated and measured, respectively, as shown in Figs. 6(a) and 6(b).
Figure 6.In the cases of the single-segmented and two-segmented crystals as gain media, with the beam filling factor ωl/ωp from 0.5 to 1, (a) the spherical aberration coefficient c11 (theoretical) and (b) the beam quality factors on x axis Mx2 (theoretical and experimental) of the amplified laser at the rear end of two crystals are calculated and measured.
With the increasing beam filling factor , the spherical aberration coefficient and beam quality factor of the amplified laser at the rear end of two crystals increase in theory. Generally, the performance of the laser amplified by the two-segmented crystal is better than that by the single-segmented crystal. In the cases of the beam filling factor from 0.5 to 1 with the two-segmented crystal as the gain medium, the spherical aberration coefficient increases from 2.19 to 10.89 nm theoretically, and the beam quality factor on the axis increases from 1.20 to 1.50 experimentally. In the experiment, the results of the beam quality factor on the axis is similar to that on the axis. The beam quality factor of theoretical and experimental results have good agreement, which proves the developed numerical model. In addition, compared with the 0.01 W, 974.5 nm probe laser, the values of and of 20 W, 1064 nm laser in the experiment are lower. This is because when the high-power 1064 nm laser enters the end-pumped , the pump power is extracted, and the heat and temperature rise are decreased in the crystal, which leads to weaker crystal thermal effect, smaller spherical aberration coefficient, and better beam quality.
Additionally, in the case of with the single-segmented crystal as the gain medium, the coefficient of 5.75 nm is calculated; the beam quality factors is 1.33 and is 1.34, which are larger than that of the two-segmented crystal. This shows that compared with the single-segmented crystal, the results of the two-segmented crystal as the gain medium are better. Therefore, in the power amplification, adopting the two-segmented crystal as the gain medium can reduce the thermal effect of the crystal more effectively than the single-segmented crystal. It is helpful to control the beam quality of the amplified laser and realize effective beam quality management.
The beam filling factor affects not only beam quality management but also the output power of the amplified laser. In the experiment, the output power is measured, and the corresponding extraction efficiency is calculated, as shown in Fig. 7.
Figure 7.In the cases of the beam filling factor ωl/ωp from 0.5 to 1 with the single-segmented and two-segmented crystals as gain media, the output power Pout is measured experimentally, and the corresponding extraction efficiency ηextr is calculated.
The experimental results show that both the output power and the extraction efficiency increase with the increasing beam filling factor . In the cases of the beam filling factor from 0.5 to 1, the output power increases from 54.6 to 119.1 W and the extraction efficiency increases from 20.9% to 59.7% with the two-segmented crystal as the gain medium, while increases from 52.6 to 116.4 W and increases from 21.2% to 62.8% with the single-segmented crystal. The results show that the extraction efficiency is close with two types of crystals as gain media, but the output power of the two-segmented crystal is slightly higher than that of the single-segmented crystal.
Generally speaking, the performance of the laser amplified by the two-segmented crystal is better than that amplified by the single-segmented crystal on beam quality and output power. In the case of , the beam quality hardly deteriorates, but the corresponding power extraction efficiency is too low. In the case of , the power extraction efficiency is high, but the corresponding beam quality deteriorates seriously. Therefore, adopting the two-segmented crystal as the gain medium and the beam filling factor of 0.75 is an appropriate decision for the high-power end-pumped amplifier. In this case, the beam quality of the amplified laser slightly deteriorates, which could be controlled well, and the power extraction efficiency is high, approaching 40%, which realizes efficient power amplification. More importantly, it lays a foundation for establishing a high-power multistage amplification system.
4. High-Power Multistage Amplifier System
4.1. Layout of power amplification
For high power and excellent beam quality in an end-pumped multistage amplifier system, it is necessary to arrange the power scaling of each amplifier. According to the above results, based on 0.2 + 0.5% (atomic fraction) -doped as gain medium with the beam filling factor of 0.75, the power extraction efficiency is around 40%, and the beam quality is maintained.
The power scaling of a high-power laser in the amplifier can be expressed as[21]where is the input power, is the output power, is the saturation power, is the gain coefficient, and is the doped length of the crystal. The gain coefficient is given by , where is the upper-level lifetime of the crystal, is the stimulated emission cross section, is the Planck constant, and is the speed of light. With the pump power of 115 W and the radius of 0.6 mm, is calculated. With the pump power of 175 W and the radius of 0.8 mm, is calculated. According to the power extraction efficiency of each stage amplifier, a reasonable multistage amplification system based on an end-pumped two-segmented crystal with a power exceeding 280 W is designed. With the pump radii of 0.6 and 0.8 mm, the corresponding saturation powers are 7.4 and 13.1 W, respectively.
The output power and extraction efficiency in two cases are shown in Figs. 8(a) and 8(b). In Case 1, the pump power is 115 W and the radius is 0.6 mm. In Case 2, the pump power is 175 W and the radius is 0.8 mm. The results show that the final output power is expected to be 283.6 W with high extraction efficiency by pumping the first-stage amplifier in Case 1 and the subsequent three-stage amplifiers in Case 2.
Figure 8.In Case 1 and Case 2, the (a) output power and (b) the corresponding extraction efficiency are calculated.
4.2. Experimental setup of high-power multistage amplifier system
The experimental setup of a high-power end-pumped multistage amplifier system is shown in Fig. 9. A homemade laser with a wavelength of 1064 nm is used as a seed laser, with an average output power of 20 W, a pulse repetition frequency of 1 MHz, and a pulse width of 10 ps. The beam quality factors on both the axis and axis are 1.14, and the beam ellipticity reaches 98%. The seed laser goes into the first-stage amplifier by the lens L1. Cr1 is an -cut, 0.2 + 0.5% (atomic fraction) -doped which has the dimension of , with a 2-mm-long thermal bonding endcap on the left end. The composite crystal is wrapped by 0.1 mm indium foil and is mounted in a water-cooled copper heat sink at 20°C. Both end faces are coated with antireflection (AR) films at 878 nm () and 1064 nm (). The 878 nm fiber-coupled pump diodes LD1 (BWT, K878BL9RN-120.0 W) can provide up to 120 W average power through a 200-μ-core diameter fiber with a 0.22 numerical aperture (NA). The pump beam is coupled into the laser crystal by the coupling lenses, with a pump radius of 0.6 mm. In Case 1, up to 113.7 W pump power can be absorbed by the Cr1. The seed laser is reflected by the M1 (DM), which is HR-coated at 1064 nm and HT-coated at 878 nm for light at the incidence angle of 45°. It goes through the Cr1 and is coupled into the second-stage amplifier by lens L2. The structures and pumping parameters of the second-stage amplifier are the same as the first one, except for the 0.8-mm-radius 175 W pump beam provided by LD2 (Everbright, EB-FCP-175-200-878.6-0.5). In Case 2, up to 165.9 W pump power can be absorbed by Cr2. The radius of the laser at the front end of the crystal is determined by the lens position and focal distance between adjacent amplifier stages so as to obtain a good spatial matching with the pump. The laser is reflected by M2 and M3 (DMs), then goes through Cr2. The amplified laser is coupled into the third-stage amplifier by lens L3 and the fourth-stage amplifier by lens L4 with the same structures and pumping parameters as the second-stage amplifier. The output power is close to 300 W after the four-stage amplifier.
Figure 9.Experimental setup of high-power end-pumped multistage amplifier system.
4.3. Experimental results and discussion of multistage amplifier system
With the beam filling factor close to 0.75, the output power and extraction efficiency of each stage are measured, as shown in Fig. 10. The seed laser with an average power of 20 W goes into the first-stage amplifier. The output power of the first-stage amplifier is 63.3 W, and the extraction efficiency is 38.1%. The output power of laser amplified by the second-, third-, and fourth-stage amplifiers are 132.3, 205.2, and 280.2 W, with an extraction efficiency of 41.6%, 43.9%, and 45.2%, respectively. Figures 8(a) and 8(b) also show the working points of the theoretical output power and extraction efficiency of each stage amplifier, indicating that the experimental results are in good agreement with the theoretical results.
Figure 10.Output power and extraction efficiency of experimental and theoretical results of the multistage amplifier system.
In addition, the beam quality of each stage amplifier is measured. Figures 11(a)–11(d) show the beam quality factors on the axis and axis of the first- to fourth-stage amplifiers, respectively. In the first-stage amplifier with the output power of 63.3 W, the beam quality factors are and . In the second- and third-stage amplifiers, the beam quality has deteriorated a little. Finally, in the fourth-stage amplifier with the output power of 280.2 W, the beam quality factors are and . This shows that although the end-pumped crystal has a serious thermal effect, the effective beam quality management is realized by adopting an appropriate beam filling factor. In addition, we also measured the power instability of the amplified laser. In 3 h, the RMS value is 0.92%, which is , and the ellipticity is 96%.
Figure 11.The beam quality of x and y axes is measured in the four-stage amplifier system. (a) First-stage amplifier with Pout = 63.3 W; (b) second-stage amplifier with Pout = 132.3 W; (c) third-stage amplifier with Pout = 205.2 W; and (d) fourth-stage amplifier with Pout = 280.2 W.
In summary, we developed a multistage amplifier system based on a high-power end-pumped two-segmented doped , with an output power over 280 W and a beam quality factor of , which realized the effective beam quality management under high-power end pumping. With the severe thermal effect, the appropriate gain medium and beam filling factor are critical for high extraction efficiency and good beam quality. Theoretically, the temperature distributions of end-pumped single-segmented and two-segmented are calculated, respectively. Experimentally, a probe laser is employed to measure the spherical aberration coefficient and beam quality of the laser at the rear end of the two end-pumped crystals, respectively, confirming the theoretical calculation. It was found that the thermal effect could be effectively reduced by employing the two-segmented crystal as the gain medium. In the power amplification, based on the calculated spherical aberration coefficient, the experimental beam quality factor and output power, an appropriate beam filling factor is found for good beam quality and high extraction efficiency. In the multistage amplifier system, by designing a reasonable layout of power amplification for each stage amplifier, the system outputs the picosecond laser with the power of 280.2 W and beam quality factors of and . The high-power picosecond multistage amplifier system has a wide range of potential industrial applications. It also provides the way for the development of future all-solid-state lasers with higher powers.