International Journal of Optics and Photonic Engineering
Volume 7, Issue 1
Research on Evaluation Method of Coherent Combining Effect
Fei Lu1,2, Hong Yan1,2, Wei Zhang1,2, Yi Su1,2, Yidong Ye1,2, Xiaoyun Liu3, Nagendra Parasad Yadav4, Weize Wang3 and Maohua Jiang3*
Table of Content
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Fei Lu1,2, Hong Yan1,2, Wei Zhang1,2, Yi Su1,2, Yidong Ye1,2, Xiaoyun Liu3, Nagendra Parasad Yadav4, Weize Wang3 and Maohua Jiang3*
1Institute of Applied Electronics, China Academy of Engineering Physics, Mianyang, Sichuan, China
2Key Laboratory of Science and Technology on High Energy Laser, China Academy of Engineering Physics, Mianyang, Sichuan, China
3College of Physics and Electronic Engineering, Chongqing Normal University, Chongqing, China
4School of Electrical and Electronics Information Engineering, Hubei Polytechnic University N0.16 North Guilin Road, Huangshi, China
Maohua Jiang, College of Physics and Electronic Engineering, Chongqing Normal University, Chongqing 401331, China
Accepted: May 05, 2022 | Published Online: May 07, 2022
Citation: Lu F, Yan H, Zhang W, Su Y, Ye Y, et al. (2022) Research on Evaluation Method of Coherent Combining Effect. Int J Opt Photonic Eng 7:046
Copyright: © 2022 Lu F, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
The coherent combination of laser beams has attracted much attention in the field of high-energy laser research because it can significantly increase the power density of the focal spot. Traditional beam quality evaluation methods cannot well reflect the advantages of coherent combination over incoherent combination. According to the characteristics of a coherent combining, the concept of "dominant radius" is proposed, and a set of beam quality evaluation systems is constructed based on this, which can well define the boundary conditions of the coherent combining system better than incoherent combining system and can effectively reflect the improvement of the performance of the coherent combining system.
Coherent combination, Beam quality, Evaluation method, Dominant radius
The process of power calibration and amplification of a single laser beam will inevitably be restricted. With the increase of laser power, the problem of waste heat generated becomes more and more serious. The thermal effect of the laser medium caused by this will cause the beam quality to deteriorate sharply. The limitation of the damage threshold of each device may also damage the optical system. To further realize the output of high-energy and high-density laser beams, the laser beam combination technology must be adopted. Beam combination increases the total output power but does not increase the thermal effect of a single beam and aggravates various problems caused by the thermal effect, which maintains the beam quality while obtaining a high-power laser beam. At present, beam combination technology has been extensively researched [1-5], and more and more scientific researchers from all over the world pay attention to it. Foreign researchers have begun to implement various plans one after another, such as JHPSSL, APPLE, ADHELS, and so on . There is much literature on the theoretical analysis of the beam combination model and its effect [7-9]. Coherent combining and incoherent combining are distinguished from the far-field effect of the light field [10-13]. The coherent combination is not a simple superposition of intensity but has the effect of spatial energy modulation, that is, the effect of concentrating energy; Incoherent combination is just a direct superposition of light intensity, as shown in Figure 1, so the coherent combination has a higher energy density at the center of the target than the incoherent combination, this is why coherent combining is a common technical approach in beam combining. In 2009, Northrop Grumman used the multi-channel solid-state laser power amplification system (MOPA) and the technical solution of laser power coherent combination, which made it take the lead in realizing the coherent combination of 7-channel.
Solid-state lasers , getting a laser output of 105.5 kW, continuous working time of 300 s, and beam quality (BQ value) better than 3 times the diffraction limit. Its electro-optical conversion efficiency reaches 19.3%. However, the study found that, when the sub-beam is not an ideal beam near the diffraction limit, the traditional beam quality evaluation  index β value and BQ value cannot well reflect the advantages of coherent combination over incoherent combination. SR (Strehl Ratio) can well reflect the advantages of coherent combination, but it emphasizes the peak intensity which is of little significance in most laser orientations. This paper is based on the characteristics of the far-field light intensity distribution of the coherent combined beam. Compared with incoherent combined beam, the concept of "dominant radius" is first proposed a set of beam quality evaluation systems is constructed according to this, which well defines the boundary conditions of the coherent combined system better than the incoherent combined system.
Comparison of Coherent and Incoherent Combination under the Traditional Beam Quality Evaluation System
Taking the combination of four laser beams as an example, two major factors affect the combination effects: changes in the relationship between the duty cycle of research and sub-beam distortion and beam quality combination. The arrangement of sub-beams is shown in Figure 2. Which is an equal-large square beam, with side length a and edge spacing d.
When the sub-beam is an ideal beam and the sub-beams are seamlessly spliced (which is d/a = 0), the comparison of the far-field light intensity distribution between coherent and incoherent combination is shown in Figure 3a, while the comparison of the loop enclosing power is shown in Figure 3b. The essence of beam coherent combination is to suppress high-frequency components and increase low-frequency components. In the far-field, it shows the movement of energy from the periphery to the center, no new energy, just the energy redistribution. When the sub-beam is an ideal plane wave or is close to an ideal plane wave and the duty cycle is 100%, the tendency of energy moving to the center of the spot is very significant, and the advantage of the coherent combination is very obvious: β = 1, PIB = 81.5%, BQ = 1, while incoherent combination: β = 2, PIB = 60.5%, BQ = 1.16, and the peak power of the coherent combination is 4 times that of the incoherent combination. However, when the sub-beam beam quality is poor and the duty cycle is not high, the advantage of the combined beam energy moving from the periphery to the center is only reflected in a small area near the center of the far-field spot, so traditional beam evaluation methods, such as β value and BQ, cannot well reflect the advantages of coherent combination over incoherent. Here is how it works. Due to engineering limitations, sub-beam splicing cannot be achieved without gaps. After analysis, when the sub-beam is not deformed, only when d/a reaches 0.07, the coherently combined beam β value increases to 1.5, and the PIB (power in the bucket decreases to 73.1%. At the same time, the incoherent beam quality index is not affected. If considering the deformation of the sub-beam, with the beam quality of the sub-beams getting worse, the advantages of coherent combination over incoherent combination will continue to decrease.
Table 1 and Table 2 reflect the synthetic beam quality index comparison (Table 1 shows that the sub-beam deformation aberration is a low order aberration, and Table 2 shows that the sub-beam aberration is a high order aberration).
Although the data in Table 1 and Table 2 are obtained under specific simulation conditions, they are representative: From the perspective of β value, the coherent combination has no advantage over incoherent combination; from the perspective of PIB, the former has a slight advantage; from the perspective of SR, the former has obvious advantages, especially when high order aberrations account for a relatively large amount. We all know that the peak intensity of coherent combination is N2 times that of a single beam and N times that of incoherent combination (in an ideal situation). It does not change with the change of duty cycle, which means that the advantage of coherent combination lies in the central area of the spot, and the SR index can better reflect the advantage of coherent combination. However, from an application point of view, the SR evaluation is not objective.
Establishment of a New Beam Quality Evaluation System
According to the above analysis, the advantage of coherent combination over incoherent combination is mainly reflected in the central area of the focal spot. Therefore, establishing appropriate evaluation standards to define the area is an important means to achieve a scientific evaluation of the advantages of coherent combination. In the research, it is found that if the far-field angler radius determined by the maximum difference between the coherent and incoherent combined loop enclosing power curves is used as the reference standard, as shown in Figure 4a, then the far-field region where the coherent combination is dominant over the incoherent combination is determined, named as "dominant radius". The important physical meaning of the "dominant radius" is that, as shown in Figure 4b, the intensity of the coherent combination within this radius is greater than that of the incoherent combination, while outside this radius, the relationship between the two changes repeatedly. Therefore, the radius is the critical point where the coherently combined light intensity is exactly equal to the incoherent combination. The reason why the "dominant radius" is used as the reference standard is based on a good characteristic of the "dominant radius": In the case that the beam quality of the sub-beam is not particularly bad, as the wavefront deformation of the sub-beam increases, the "dominant radius" remains almost unchanged, which is consistent with the value when the sub-beam is combined with an ideal plane wave. However, as the deformation of the sub-beam increases, the loop enclosing power contained in the "dominant radius" in both coherent and incoherent combinations continues to decrease, and the difference between the two is also reduced. As shown in Table 3 and Table 4, as the RMS of the sub-beam wavefront changes, the change of the loop enclosing power ratio of coherent and incoherent combination within the "dominant radius". It can be seen that within this radius, the advantage of the coherent combination is very obvious, and the ratio of the power contained in the two is kept above 2.
The above discussion focuses on the horizontal comparison between coherent and incoherent combination, mainly the comparison of the loop enclosing power in the "dominant radius". If you want to evaluate the change in the coherent combination effect as the wavefront deformation of the sub-beam increases, the concept of "composite efficiency" (η) can be defined, which is equal to the ratio of the actual loop enclosing power to the ideal loop enclosing power (that is, the sub-beam without deformation) in the "dominant radius", which is
This definition is similar to SR, except that SR emphasizes the "peak" point of light intensity, while "synergistic efficiency" emphasizes the power in a "certain area" (that is, the "dominant radius"). The data in Table 5 shows the relationship between "synergistic efficiency" and the RMS of the sub-beam wavefront. It is seen that "synergistic efficiency" is more sensitive to sub-beam deformation, which can well reflect the influence of this factor on the combination effect.
Therefore, based on the characteristics of the far-field distribution of coherent combinations, we have constructed a new set of beam quality evaluation systems, which is mainly suitable for the evaluation of beam coherent combinations. It defines the region where the coherent combination is dominant over the incoherent combination. In specific applications, if the target area we care about exceeds this range, then the use of coherent combination is meaningless, on the contrary, the use of coherent combination technology will have great advantages. The system is mainly composed of "dominant radius", "dominant radius" inner loop enclosing power ratio, and "synergistic efficiency". Based on the "dominant radius", we get the definition of the "dominant radius" inner loop enclosing power ratio and "synergistic efficiency". The former can be used to horizontally compare the advantages of coherent combination and incoherent combination, and the latter can be used to compare longitudinally the influence of the corresponding changes incoherent combination efficiency when the beamlet deformation changes. The "dominant radius" only depends on the sub-bundle arrangement (which is the "duty cycle"). As shown in Figure 5, take the four-beam combination as an example, the obtained "dominant radius" and the relationship between the ratio of the inner loop enclosing power and the duty cycle. It can be seen in Figure 5 that the higher the duty cycle, the larger the "dominant radius" and the more internally contained power, which means that in directional energy applications, the coherent combination is more dominant.
As shown in Figure 6a-Figure 6b, it respectively reflects the far-field spot intensity distribution diagrams of the two sets of coherent combination systems with low duty cycle and high duty cycle after the closed-loop. It can be seen directly from the shape of the far-field spot: the small: dominant radius" of the coherent combination with low duty cycle is because the "side lobes" disperse more energy, while the high duty cycle "main lobe" accounts for the most energy. Therefore, incoherent combination, a combination system with a high duty cycle beamlet arrangement has a natural advantage.
Aiming at the characteristic that traditional beam quality evaluation indicators cannot well reflect the advantages of coherent combination, the concept of "dominant radius" is proposed, and on this basis, we know the power ratio of the inner loop enclosing of the "dominant radius" and the definition of "synergistic efficiency. While the "dominant radius" inner loop enclosing power ratio can well reflect the advantage of coherent combination over the incoherent combination, "synergistic efficiency" can sensitively show the influence of beamlet deformation and other factors on the effect of the coherent combination. Under this evaluation system, it is easy to see that the arrangement of beamlets with a high duty cycle will make the advantages of coherent combination over incoherent combination more significant.
Conflict of Interest
The authors declare that they have no conflict of interest.