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We demonstrate a high-power laser system with a high-quality near-field beam by using a liquid-crystal spatial light modulator (SLM). An efficient spatial beam shaping algorithm is discussed which can improve the output nearfield beam quality effectively. Both small-signal and large-signal amplification situation of the laser are considered in the beam shaping algorithm. The experimental results show that the near field fluence modulation of output is improved from 1.99:1 to 1.26:1 by using the liquid-crystal SLM. Obvious uniform spatial fluence distribution and near-field beam quality improvement are observed.
© 2015 Optical Society of America
1. Introduction
Laser-induced thermonuclear fusion, one of the most popular research areas, motivates the development of large-aperture high-power laser systems such as National Ignition Facility (NIF) [1–3] of the Lawrence Livermore National Laboratory (LLNL) in the USA, OMEGA EP Laser Facility [4–6] at the Laboratory for Laser Energetics (LLE) in University of Rochester, LMJ facility in France [7–9] and SG-III Laser Facility [10–12] in China. The importance of controlling the laser-beam nearfield spatial fluence in high-power lasers plays an essential role in the gain precompensation [13] and laser induced damage in optics, both initiation [14] and growth [15] that cannot be overemphasized. In high-power lasers, the process of optics damage initiation and growth is strongly correlated with the local fluence [16–18]. For this reason, the over high local fluence must be suppressed. That is to say, the near field modulation must be minimized in the high power laser system.
Adaptive spatial beam shaping is an effective method to improve the near-field beam quality by using a programmable liquid-crystal spatial light modulator (SLM) [19,20]. Liquid-crystal spatial light modulator is an active and programmable spatial optical modulator with high contrast ratio and high resolution, which has important application prospect in the field of laser beam shaping [21,22], adaptive optics [23] and holographic measurement [24]. The transmittance of each pixel on SLM can be adjusted, which is designed for the compensation of the spatial beam non-uniformity resulted from the nonuniformity of the gain of the laser. To date, the beam-shaping system based on SLM has been deployed in several high-power laser systems [25–28,10]. The previous work only shows initial results of the output beam quality. However, an iterative algorithm of the spatial beam shaping has not been reported in detail in a high-power laser system. In this paper, we discuss a spatial beam shaping algorithm of the SLM that allows extremely fine control of the nearfield in a high-power laser system, which is mainly suited for a wide variety of high-energy density science experiments, including laser-induced damage mechanism for optics research, stimulated Brillouin scattering (SBS) and stimulated Raman scattering (SRS). The simple and effective algorithm of spatial beam shaping will be presented in Sec. 2. Experimental results in a high-power Nd:glass rod laser will be shown in Sec. 3. The output near filed modulation of 1.26:1 has been achieved. Sec. 3 is also devoted to the discussions of the output near-filed beam quality and Sec. 4 draws the conclusion.
2. Algorithm of spatial beam shaping
SLM has the capability to alter the near-field spatial fluence profile of a laser beam. As shown in Fig. 1, the initial laser beam with the near-field spatial fluence distribution IP(x,y) sequentially propagates through the SLM, the amplifiers of the high power laser system and the attenuation of the diagnostic unit. And finally the attenuated laser beam is injected into the CCD camera. The spatial fluence of the laser beam can be modified as following:
where TA(x,y) is spatial transmittance distribution and G(x,y) is the gain distribution of the amplifiers, TD(x,y) is the spatial attenuation coefficient distribution of the diagnostics unit, and IO(x,y) is the spatial fluence distribution of the laser measured by CCD. The SLM mainly consists of liquid crystal with two polarizers placed in the front and the back, respectively. The downstream polarizer functions as an intensity modulator. The phase change in each pixel of the SLM, which is related to the transmittance after the last polarizer, is controlled by 8-bit command. The dependency of the transmittance on the gray level of the SLM has been linearized. The formula is given by:where TSLM(x,y) is spatial transmittance distribution of the SLM, S(x,y) is the gray-scale pattern written into the SLM, and (x,y) represents the location of the pixel point. CSLM is the scaling coefficient. Provided the transfer function of the laser system is set as following:the transfer function indicates the whole spatial non-uniformity of the laser system. As a result, the spatial non-uniformity of the laser system is the product of input gray scale S and the system transfer function H as follows:Here, S(x,y) and IO(x,y) are all normalized. From Eq. (4), the laser system can be seen as a linear system. As shown in Fig. 2, the process of spatial beam shaping is designed. In the case of small-signal amplification, the laser output energy and the input energy into the amplifier obeys a linear relationship. On the first stage, an initial standard pattern S0(x,y) is written onto the SLM. The CCD obtains the output laser near-field fluence distribution IO0(x,y). From Eq. (4), the transfer function H(x,y) can be calculated. Based on the aimed image distribution IOf(x,y), H(x, y) and a coefficient GSLM of the SLM used for adjusting the output energy, the first compensation pattern S1(x,y) can be calculated. The formula is as followed:
Fig. 2 The process of spatial beam shaping. H(x,y) is the transfer function of the laser system and GSLM is a coefficient used for adjusting the whole transmission of the SLM and then the output energy.
When the calculated compensation pattern S1(x,y) is written into the SLM, IO1(x,y) will be achieved. If the laser system is a strictly small-signal amplification system, in principle, the aimed nearfield can be achieved by the first compensation pattern.
Under the condition of the large-signal amplification with the pump depletion, owing to the high output energy, the saturation amplification will appear in the laser system. Because of the non-linear relationship between the output and input energy, iteration algorithm is introduced into the calculation to make the near-field fluence distribution converge to the ideal one. The iterative process is shown in Fig. 3, which is a typical output intensity curve of the local beam in high-power lasers. The gray scale on the SLM can represent the input fluence. The process is divided into three stages. When the input gray scale is relatively low, the output fluence increases linearly with the input. When the input is relatively high, the relationship between the output and the input is nonlinear. The slope of the output fluence curve becomes lower with the increase of the input. When the input reaches to a certain level, the output will be saturated. Under the condition of large-signal amplification, the secant iteration method [29] is used to calculate the compensation pattern. As illustrated in Fig. 3, the initial input pattern, the corresponding output and the aimed output fluence distribution are S0, IO0 and IOf, respectively. At the first round of iteration, the line section through points of (S0, IO0) and (0,0) intersect the straight line described by the equation of IO = IOf, and the horizontal coordinate of the intersection is S1. The gray-scale pattern S1 is written onto the SLM, and the output fluence IO1 is going to be measured by CCD during the operation of the laser system. IO1 is closer to the aimed fluence IOf than IO0. Similarly, the second input pattern S2 and output fluence IO2 can be calculated and if the iteration is to be continued, the output fluence will converge to IOf in theory. The iteration process can be calculated by Eq. (6). The iteration stops when the quality of the near-field beam is not improved any more.
Fig. 3 The iteration process of the local beam shaping in the case of the large-signal amplification. Sj refers to various gray scale images, j = 0 initial, j = 1, 1st iteration, etc. Sf refers to the final gray scale image. IO0 and IOf refer to the initial and aimed fluence distribution, respectively.
3. Experimental results and discussion
The setup of the high power laser system is shown in Fig. 4. The laser pulse is generated in the front-end with all-fiber optic scheme which operates at 10 nJ in nanosecond duration with wavelength at 1053 nm. Then the laser pulse gets high gain in the preamplifier with the energy of millijoule level, and enters into the SLM (Holoeye LC2002). After spatial shaping in the SLM, the output laser energy is roughly 200 μJ with the beam diameter of D = 13 mm. And then the laser beam enters into the main amplifier system which consists of four Nd:glass rod amplifiers pumped by flash lamps and the output energy of 100 J can be achieved at the end of the laser system. There are six spatial filters in the main amplifier system, which are used to expand the beams and relay the high quality image plane. The original image plane is relayed from the SLM to the output port. The output nearfield can be measured in the diagnostic unit by a scientific-grade CCD camera which provides a 12-bit digital image. The sampling beam size is decreased 10 times by a 4f relaying telescope and the image plane is relayed on the CCD camera. The SLM, the spatial-filtered image relay system and the scientific-grade CCD camera make up the spatial beam shaping system, which ensures the output near-field beam quality is achieved by using the algorithm described in Sec. 2. The laser system is operated at 30 min per shot in regular, with the beam diameter of D = 60 mm and a super-Gaussian pulse shape with duration of 3 ns.
Fig. 4 High-power laser system schematic. The blue two-direction arrow real line refers to the image relay plane. P1-P9, polarizers; CSF (cavity spatial filter) and TSF (transport spatial filter).
The output nearfield profile is very poor without SLM working [see Fig. 5]. In this case, a round hard-edge aperture is placed in the beam path to shape the edge of the laser beam. The output fluence of the beam boundary edge is about five times higher than the fluence of the beam center due to the gain non-uniformity. In the high power Nd:glass lasers, more light from the flash lamp is absorbed at the edges than in the central parts of the rod. Correspondingly, the gain at the circular boundary edge is higher than that in the central part of the amplifier rod. Thus, the fluence at the boundary edge is larger than that of the central part. Without spatial beam shaping, the edge of the laser beam would be steeper after passing the rod amplifiers, and the center fluence would be lower than the edge. The calculated near field modulation, defined as M = Fmax/Favg, where Fmax is the maximum fluence and Favg is the average fluence, is 1.99:1. The near field contrast, defined as the standard deviation of fluence distribution divided by the mean, is 51.7%. Near field modulation shows the degree of the high fluence of the laser beam, which is related to the risk of laser-induced optical components damage.
Fig. 5 The laser beam near-field profile measured by CCD of the output without spatial beam shaping system. The original gray-scale image (a), the three-dimensional distribution (b) and the lineout gray distribution (c).
Since the gain at the edge of the rod amplifier is too high, it is required to suppress the edge of input laser beam. By the method of writing a pattern into the SLM with edge softened, the edge of the output laser beam can be reshaped. At the beginning of spatial shaping, the edge-softening factor of the pattern should be chosen suitably. The edge-softening factor is defined as the ratio of the width between 90% and 10% of the maximum laser fluence to the corresponding laser beam aperture size (at 1% fluence). It can be expressed by , where D0 and DF refers to the beam size at 10% and 90% value of the maximum respectively, and D is the beam diameter [see Fig. 6]. The edge-softening factor indicates the degree of softening the laser beam edge, which is related to the edge diffraction effects in the laser beam propagation. In the following amplification process, the soft edge of the input laser beam will be amplified more efficient than the center for the high gain factor. We will choose a pattern what will flatten the fluence field at the output. When the edge-softening factor of the initial pattern written into the SLM is 23%, the spatial fluence of the output laser beam is high in the center and low at the edge.
In the case of spatial beam shaping with the SLM working using the algorithm introduced in Sec. 2 in the high-power laser system, the output nearfield converges gradually to the aimed nearfield. An example of shaping a flat-top near-field laser beam is shown in Fig. 7. The aimed nearfield is a standard round flat-top image with the edge-softening factor of 8%. Before the SLM working, the local fluence at the edge is so high [Fig. 5(c)]. While after the SLM working, the initial output near-field lineout fluence distribution is high in the center and low at the edge, due to the initial pattern with high edge-softening factor (23%) shaping the edge. In the following compensation process, the output nearfield is more and more similar to the aimed nearfield. The iteration compensation does not stop until the output near-field beam quality cannot be improved further in the high-power laser system. In the end of spatial beam shaping, the output edge-softening factor is 8.1% and the overall spatial fluence distribution is relatively flat. In the process of shaping, the calculated near filed modulation is 1.66:1, 1.41:1, 1.29:1 and 1.26:1 of the initial and the following three compensated output laser beam.
Fig. 7 Results of the output near-field lineout fluence distribution (a) and the near field modulation factor (b) in the process of spatial beam shaping with SLM work.
Figure 8 shows the results in detail of the initial and the final output nearfield by spatial beam shaping with SLM. The two-dimensional and three-dimensional distribution near-field images [Figs. 8(a)-8(d)] are normalized. It is evident that the final output near-field beam quality (with the near field modulation of 1.26:1) is higher than the initial nearfield (1.66:1). The initial and final probability density function (PDF) of the output nearfield fluence distribution is shown in Fig. 9 giving a clear contrast of the beam quality between them over the 90% central patch of the laser beam aperture. Each PDF is normalized with the average value to be 1. The initial fluence distribution is relatively dispersive with the fluence contrast degree of 29%. After spatial beam shaping, the final fluence distribution is more centralized with the fluence contrast degree of 9%.
Fig. 8 Results of the initial and the final output nearfield by SLM adaptive spatial beam shaping. The original near-field profile of the output laser beam of the initial (a) and final (b) spatial beam shaping with SLM; the near-field three-dimensional distribution of the initial (c) and final (d) shaping.
Fig. 9 Initial and final probability density function (PDF) for near-field fluence data with the contrast of 29% and 9%, respectively.
First, let us discuss several factors that have effect on the output near-field beam quality in the high-power laser system. For example, more than 60 optical elements distributes in the beam path from the SLM to the CCD camera. Each optical element can contain a number of inner defects generated in the material growth process or surface defects generated as a result of the excitation conditions during its operation. These defects can cause high local diffraction effects and light intensity enhancements in the laser beam [30,31]. In addition, the 4 stage Nd:glass rod amplifiers in the complex laser system will increase the non-uniform degree of the gain distribution. The main task of the SLM is to pre-compensate the non-uniform of the gain distribution and any residual non-uniformity of the chain of optical elements. The more complex the high-power laser system, the more difficult to compensate the output nearfield to achieve high beam quality.
Secondly, as mentioned above in Sec. 1, the potential optics damage is strongly correlated with the local fluence in high-power lasers. Spatial beam shaping can reduce near-field fluence modulation to allow the laser to operate in a state of security, because the laser with same energy output but the pre-compensate beam and post-compensate beam would cause different potential damage. For example, for two laser beams with same energy of 100 J, 3 ns near square temporal profile and beam diameter of 60 mm, but with different near filed modulation of 1.99:1 and 1.26:1, respectively, the calculated maximum local fluence of them are roughly 7 J/cm2 and 4.5 J/cm2, respectively. Even though the laser-induced damage threshold of our optical elements is higher than 8 J/cm2 at 1053 nm, the form fluence is close to the threshold which leads higher risk to the laser system.
Last but not the least, the low transmittance of the SLM (e.g., Holoeye LC2002 T = 20%) in the beam path will reduce the output energy at the same pump power state. So, we improve the pump power state when using the SLM for compensation to achieve high energy and high near-field beam quality simultaneously. One way is to ensure the injecting into the main amplifier energy to be not less than 200 μJ by increasing the output of the front-end and preamplifier. Another way is, in addition, to improve the pump power of the 4 rod amplifiers of the main amplifier system. So, the laser can operate at 100 J level in the end with high near-field beam quality.
4. Conclusion
In this article, we discuss spatial beam shaping by using the liquid-crystal spatial light modulator for high-power lasers. The key elements of the spatial beam shaping system are a liquid-crystal spatial light modulator, a scientific-grade CCD camera as well as a spatial-filtered image relay system. After spatial beam shaping, results showed that the output near field modulation was 1.26: 1 and the fluence contrast was 9% after 4-stage amplification in the high-power laser system. This approach of spatial beam shaping is highly flexible and is able to produce flat-top beams with a high-quality near-field beam.
Acknowledgments
The authors would like to acknowledge the colleagues for their assistance in working for the high-power laser system. Sensen Li gratefully acknowledges much help from the team members for assistance in the execution of the experiments. This work is supported by the project of the National Natural Science Foundation of China (Grant No. 61378007 and No. 61138005). The support does not constitute an endorsement by the National Natural Science Foundation of China of the views expressed in this article.
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