Adv Search
Home | Accepted | Article In Press | Current Issue | Archive | Special Issues | Collections | Featured Articles | Statistics

2020,  2 (1):   28 - 42   Published Date:2020-2-20

DOI: 10.1016/j.vrih.2020.01.001
1 Introduction2 Laser frequency converter unit3 Methodology 3.1 Proposed virtual assembly framework (2) Assembly process modeling of large optics(3) Intelligent computation engine(4) Three-dimensional (3D) visualization engine 3.2 Mounting-induced surface distortion 3.3 Distortion-induced phase misma-tching 4 Case study, experiments, and result analysis5 Conclusions


A longstanding technological challenge exists regarding the precise assembly design and performance optimization of large optics in high power laser facilities, comprising a combination of many complex problems involving mechanical, material, and laser beam physics.
In this study, an augmented virtual assembly framework based on a multiphysics analysis and digital simulation is presented for the assembly optimization of large optics. This framework focuses on the fundamental impact of the structural and assembly parameters of a product on its optical performance; three-dimensional simulation technologies improve the accuracy and measurability of the impact. Intelligent iterative computation algorithms have been developed to optimize the assembly plan of large optics, which are significantly affected by a series of constraints including dynamic loads and nonlinear ambient excitations.
Finally, using a 410-mm-aperture frequency converter as the study case, we present a detailed illustration and discussion to validate the performance of the proposed system in large optics assembly and installation engineering.


1 Introduction
The Inertial Confinement Fusion (ICF) facilities, National Ignition Facility (NIF), and Laser MegaJoule or ShenGuang-III (SG-III), are the world’s largest high-energy laser facilities. They are designed to realize the nuclear fusion of a D-T target under extremely high temperatures and pressures generated by strong laser beams[1]. Such a facility that combines these extreme physical conditions and sophisticated engineering technologies is currently a super scientific project. For instance, NIF has 192 high-power laser beams, more than 40000 precision optical components of various sizes, and can output a peak power of 1.8-2.2 MJ. Each laser beam passes through complicated optical units, including a preamplifier/filter, main amplifier/filter, and frequency conversion, and, finally, precisely shoots at a 2-mm-diameter D-T target. The assembly of large optics is critical to the success of ICF, which requires the maintaining of rigorous cleanliness and precise alignment, not only during the initial installation, but also during the lifetime operation of the facility. As Hurst[2] pointed out, “this will be the first time that such large optics will be assembled in a Class 100 clean-room environment. Some of the assemblies will weigh 3000lb, negating the utility of existing equipment (which can handle up to 20lb for such tasks). In addition, the NIF Project’s severe time and cost requirements place great demands on the precision alignment and transport of these optics”. Generally, a large optical assembly will include a mechanical housing, laser optics (lenses and mirrors), utilities, and actuators. The optics require delicate handling to be tightened firmly into a frame-like mechanical structure using screws, and the mechanical parts to be cleaned vary considerably in size, geometry, surface finish, and material. The materials used are typically various grades of aluminum, steel, and stainless steel, each with a different surface finish. It is in this area that the engineering challenges truly begin. To improve the assembly and alignment performance of large optics, which is crucial to the design goal and reliability of a system, well-designed assembly processes should consider various factors such as the optimum assembly time and sequence, tooling and fixture requirements, ergonomics, operator safety, and accessibility, among others.
In theory, to solve the problems of precision assembly design and optical performance evaluation of large optics, there is a strong demand on the simulation and analysis methods of virtual assembly and multiphysics analyses to study the relationship between assembly structure imperfections and laser beam performance degradation. To realize this, sophisticated technologies that can empower the industry in terms of faster and more powerful decision-making processes are required. New virtual reality and visualization technology combine multiple human-computer interfaces to provide visual sensations, enabling users to become immersed in a computer-generated scene. As an ideal tool for the simulation of tasks of assembly prototyping and process visualization, virtual assembly has a powerful capability of assembling virtual representations of physical models through simulating realistic environment behavior and part interaction to reduce the need for physical assembly prototyping; thus, resulting in the ability to make more encompassing design/assembly decisions in an immersive computer-generated environment. Using virtual prototyping applications, design changes can be incorporated easily into the conceptual design stage; thus, optimizing the design process toward design for assembly. Virtual prototyping-based approaches[3] have been investigated in many manufacturing and process domains and emerging areas, such as biomedical/bioengineering. One primary benefit of adopting virtual prototyping approaches lies in being able to propose process design div in assembly and manufacturing contexts virtually and comparing the impacts of the design changes. In a virtual environment for a sophisticated assembly, it is easier and more beneficial to propose and compare assembly div virtually prior to the physical assembly owing to the high degree of complexity of the size and nature of the parts, fixtures, and the general assembly area. In 1999, Jayaram introduced the Virtual Assembly Design Environment that is used to evaluate, analyze, and plan the assembly of mechanical systems[4]. Later, Yang defined uniform representations of the assembly constraints, equivalent relations between constraints and the degrees of freedom (DOF), and movable DOF reduction in a virtual assembly system[5]. Based on real-virtual mapping of a basic motion sequence, Fan proposed an assembly process planning generation method, which was successfully used in an auto-engine assembly[6]. Brough presented the development of the Virtual Training Studio for mechanical assembly operations[7]. Previous research has allowed users and process engineers to gain a better understanding of the assembly constraints and div, which can then be compared, studied, and validated either individually or as a group[8].
In this study, with the aim of meeting the technical challenge by an assembly performance evaluation of the frequency conversion unit[9] in the final optical assembly (FOA) of China’s ICF facility[10], we investigated the influence of the assembly structure and process parameters of an anisotropic potassium-dihydrogen-phosphate (KDP) crystal on the second-harmonic generation (SHG) and wavefront quality of a laser beam. A computerized virtual environment is proposed to realize the virtual assembly and multiphysics analysis of large optics, which will allow an efficient evaluation and optimization of large optics assembly design.
2 Laser frequency converter unit
KDP and potassium-dideuterium-phosphate (dKDP) crystals are widely used in the FOA for the frequency conversion of high-power laser beams[11,12]. According to the theory of nonlinear optics, when a laser beam is incident on a KDP crystal for which the second-order susceptibility is nonzero, the created nonlinear second-order polarization has fundamental frequency ω1 and second-harmonic frequency ω2 contributions[13]. The latter contribution can lead to the generation of radiation at the second-harmonic frequency. Under proper experimental conditions, the process of SHG can be sufficiently efficient that nearly all the power in the incident beam at ω1 is converted to radiation at ω2, denoted as ω2 = ω1 + ω1 [14]. One common use of SHG is to convert the output of a 1053nm infrared laser beam into a 527nm double-frequency laser, as shown in Figure 2a. Table 1 shows some typical material parameters of the KDP crystal. As an important nonlinear optical material, its non-centrosymmetric crystal structure can efficiently generate second harmonics. Simultaneously, the rapid growth method can produce large and high-laser-damage-threshold KDP crystals, which provides a foundation for the development of ICF frequency converters (Figure 2b).
Basic material parameters of KDP crystal
Parameter Value
Laser damage threshold 5-10GW/cm2 for 10ns pulses @1064nm
Transmitting range 0.180-1.550μm (wavelength)
Density 2.332g/cm3
Nonlinear optical coefficient 0.4pm/V (d14 = d36)
For SHG, the intensity of the generated field at frequency ω2 = ω1 + ω1 varies with the wavevector mismatch:
m i n Δ k = m i n { k 2 - 2 k 1 } = m i n { 4 π λ ( n e ( θ , 2 ω , σ i j ) - ( ω , σ i j ) ) } 0
This expression predicts a dramatic decrease in the efficiency of the sum-frequency generation process when the phase matching condition Δk = 0 is not satisfied. Thus, the efficient generation of the output field requires that the condition Δk = 0 be maintained. For a KDP crystal, this angle, which enables a complete double-frequency conversion in theory, is called the phase matching angle. Barker[15] pointed out that the harmonic conversion efficiency in the frequency doubling process is very sensitive to the detuning angle (also called the phase mismatching angle) of a frequency converter. For example, as shown in Figure 3, a KDP doubler with a detuning of ±40 μrad internally reduces the third-harmonic generation (THG) efficiency from 90.8% to 85%. Therefore, the precise implementation and control of the crystal phase matching of frequency converters becomes a key condition that significantly impacts the physical performance of ICF laser beams. In the engineering practice of ICF, the actual state of the frequency converter does not always fit an ideal physical condition owing to the manufacturing errors of components, crystal material defects, surface contaminants, and ambient excitations, such as thermal effects and mechanical vibrations. To achieve better frequency conversion efficiency and beam quality, many stringent specifications exist regarding frequency converters, as shown in Table 2. These requirements pose a series of extremely sophisticated technical challenges on the design optimization of the assembly structure and process of the frequency doubler. The achievement of such high accuracy on a 410mm thin-walled crystal is a worldwide engineering problem in optical precision manufacturing. The manufacture and assembly deviations greatly limit the actual performance of the frequency doubler, thus reducing the THG efficiency and the laser beam wavefront quality. Therefore, there remains a strong demand for precise and reliable assembly technologies in the development of large optics in China’s SG-III facility. This is mainly because
Technical requirements for KDP crystal doubler
Parameter Value
Crystal size 420mm×420mm×11mm
Roughness <1.5nm RMS
Roughness PSD-2 <15v - 1.55, 2.5-0.12mm
Scratch/dig 40/15
Transmitted wavefront @ 633nm 5nm Rq, >33mm
PSD-1 <15v - 1.55, 33-2.5mm
Transmitted wavefront gradient 11nm/cm RMS, >33mm
Wedge 2±1s
Surface flatness 3.16μm
⊕ Owing to the soft and brittle material physical properties of the KDP crystal, most traditional precise grinding and polishing approaches cannot be used; thus, fine surface topography is more difficult to achieve;
⊕ The weak stiffness due to the thin-walled plate shape of the KDP crystal makes it extremely sensitive to external loads. Therefore, the KDP crystal easily deforms, leading to the problem of phase mismatching during the assembly process.
⊕ The gravity deformation and complex ambient excitations make it very difficult to maintain the stability of the frequency converter in service. Previous experiments and simulations have shown that the gravity effect and ambient excitations may lead to surface distortion 10-30 times more than offline measurements in the optical assembly building.
3 Methodology
3.1 Proposed virtual assembly framework
Based on the fundamental principles of assembly and mounting in large optics, a computerized framework for the flexible precise assembly design and analysis of large optics is proposed, currently with a specific focus on improving the optical performance of a KDP crystal. In addition, further development of this framework is expected to undertake a multiphysics simulation and analysis of a large optics assembly. Therefore, the concept of an integrated optomechanical analysis[16], particularly involving the coupling of the structural, thermal, and optical simulation tools in a multidisciplinary process, commonly referred to as a STOP analysis[17], is proposed as the foundation of this framework. The integrated system to support a virtual assembly of large optics comprises several important functional modules. In the interactive virtual assembly design environment, assembly personnel can experience and train a large optics assembly process. The multiphysics simulation and analysis system can visually support the establishment of an assembly process, solve problems with the assembly, and suggest improvements. The system architecture of the proposed framework, which has been layered based on the functional requirements, is shown in Figure 4. This framework mainly includes four modules, which are given below.
(1) Data input, processing, and output
This module can realize the information extraction of geometric models, assembly features, and assembly relationships from the inputted large optical assembly, and store structured data in the model’s assembly information base. Information related to the physical properties of large optics can also be mapped with the geometric features to generate complete virtual assembly models in the system. The generated technical data (documents) from the virtual assembly process can be saved, displayed, or exported. Then, the collected multiphysics simulation data can be timely transmitted to the developed virtual interactive user interface via calling of the interface from the sensor and camera.
(2) Assembly process modeling of large optics
This is a comprehensive module including many independent functional objects (toolbox) to process the calculations related to a large optics assembly. For instance, the preloads analysis and structural deformation analysis are related to the mechanical performance evaluation using finite element analysis (FEA). In addition, the surface analysis toolbox will link the structural deformation analysis and optical beam propagation modeling because surface distortion directly impacts the propagation of a laser beam. Hence, related algorithms can be used to calculate the initial assembly performance and determine a more feasible solution by interactive assembly design in the virtual assembly environment.
(3) Intelligent computation engine
This module is a mathematical toolbox for various assembly analysis processes. It includes many different mathematical functions to deal with the demands from the Assembly Process Modeling module of large optics. When a computation task is triggered, following the demand, it will read the imported data, call upon mathematical functions, and finally, return results to the module. However, the use of FEA only does not easily meet the requirement of a real-time analysis. To overcome this, the author established a database to store more than 10000 mounting strategies and related multiphysics results of the optical assembly. Basically, the built database can cover most mounting strategies of the KDP crystal doubler in practice. A search algorithm is an important tool to achieve the assembly error optimization. If the mounting plan of a given assembly and one stored mounting case have highly similar correlation coefficients, the algorithm can directly retrieve the case calculation results from the database by searching and comparing. According to the input information of the optical surface and mounting conditions, the search algorithm can determine the optimal assembly strategy and retrieve the multiphysics calculation results, and SHG and THG efficiencies. Only if the search process cannot determine a stored case from the database, the FEA tool will automatically start to implement the multiphysical simulation computation. Finally, the obtained results will also be stored in the database. This design can significantly improve the efficiency of real-time analysis.
(4) Three-dimensional (3D) visualization engine
The 3D visualization engine in the integrated framework is a tool that rapidly renders stunning graphics for the visualization of multiphysics simulations of large optics, including virtual assembly process simulation, mounting stress and deformation visualization, and optical performance visualization, which are implemented in accordance with the large optical assembly process modeling, and has a data interface with an external 3D solid modeling software.
In total, this integrated virtual assembly simulation and analysis framework has a triple-layered architecture. The interaction layer is the uppermost layer of the system, through which the human-computer interaction, system function display, scene control, display of data input, and result output are mainly achieved via the graphical interface. The core function layer, which is fundamental to achieve the functions of the multiphysics simulation and virtual assembly design, is the interlayer in the system. It includes a virtual assembly process analysis and optical performance simulation, assembly information/data visualization, and other functional toolboxes. Meanwhile, the data layer comprising the data conversion interface, assembly model information base, and assembly information modeling module, constitute the bottom of the system. This layer provides data support for the entire virtual assembly system. The function realization of the interaction and core function layers is based on the data layer. The data conversion interface can realize the large optics assembly information transformation from various external engineering software, for instance, CAD modeling or optical design software. Based on the proposed technical framework, an application for a KDP crystal doubler has also been developed and its user interface is shown in Figure 5. The simulation results are illustrated in Figure 6.
Next, we focus on introducing the core functional modules and technologies that determine the key performance of this system.
3.2 Mounting-induced surface distortion
To predict the performances of frequency converters under varying operational conditions, we apply the optomechanical numerical modeling method, which correlates the geometric, material, and mechanical factors with the nonlinear-optical properties of the frequency converter quantitatively. Thus, the first step is to develop an analysis model on the surface deformation under the mechanical effects for the frequency converter. The KDP crystal is an isotropic material whose stress and strain tensors relationship can be characterized by the generalized Hooke's law (Eqs. 2 and 3). The general constitutive equation for the KDP crystal is as follows:
σ = D ε
where σ is the stress tensor, D is the elasticity tensor, and ε is the strain tensor. The equation can be expressed in further detail as
σ X X σ Y Y σ Z Z σ Y Z σ Z X σ X Y = d 11 d 12 d 13 d 12 d 11 d 13 d 13 d 13 d 33 d 44 d 44 d 66 ε X X ε Y Y ε Z Z 2 ε Y Z 2 ε Z X 2 ε X Y
The specific parameters of the elasticity matrix of the KDP crystal in its elastic principal coordinate system are d11 = 71.2, d12 =-5.0, d13 = 14.1, d33 = 56.8, c44 = 12.6, and c66 = 6.22 (GPa). It can be seen that the material is relatively soft, which also explains why the KDP crystal is sensitive to external loads and is very prone to structural deformation or fragmentation[12,18,19]. Figure 7 shows the assembly structure of the frequency doubler. The 3D model of the frequency converter module, including the anisotropic crystal plate, metal frame, and other mechanical components, is established using Solid-works. Meanwhile, for the boundary conditions, the deformation of the rectan-gular metallic frame, which supports the KDP plate, is assumed to be negligible. The partial edges of the KDP crystal in contact with the frame are prevented from moving in all directions, other preload conditions are illustrated in Figure 8. Before the mechanical structural analysis through the ANSYS command line file, the discretization of the KDP plate comprises 200×200 elements in the transverse plane and 5 elements in the thickness. In this case, the crystal is constrained firmly by the support and clamping positions. Its load boundary condition is described as
F ( ω , x , y ) = G ( x , y ) + F p i / S p i             ( x , y S i )
where G(x,y) is the gravity that the crystal plate is subjected to, Fpi represents the clamping force on the edge, and Spi denotes the clamping contact area. As the low-stiffness crystal plate is very sensitive to external effects, the surface flatness error of the mechanical contacts between the frame and KDP crystal is also considered to accurately simulate the behavior of the crystal plate under actual operational conditions and to evaluate the error resistivity of different supporting schemes. Furthermore, the deflection of the mid-plane of the crystal plate ω is defined as the fundamental variable. The plate is well within the scope of Kirchhoff’s theory, and FEA is employed for the numerical solution. Our previous papers discussed and verified the FEA methods through real case studies[20]. Through the finite-element calculation, we obtain the displacement component in the Z-direction of each node, z(x,y), with which some general optical surface specifications like PV, RMS, and GRMS can be determined. Therefore, the mechanic analysis model provides an effective tool for a highly accurate evalua-tion of the frequency converter assembly process in this intergraded framework.
3.3 Distortion-induced phase misma-tching
Both the surface deformation and stress concentration will change the phase-matching condition of the KDP crystal, which may significantly decrease the frequency conversion efficiency. As previously mentioned, the KDP crystal is relatively soft and brittle, so it has a high stress sensitivity. Related experiments in the NIF frequency converter have shown the significant impact of mechanical preloads on the performance of phase-mismatching and wavefront distortion of KDP crystals[21,22]. Thus, there is a strong necessity for the development of a numerical computation approach to integrate the mechanical analysis and optical performance evaluation. When a high-power laser beam creates new physical conditions on the KDP crystal, the induced polarization field generated by the propagation of the strong laser beam in the medium will have nonlinear form. More specifically, the polarization depends nonlinearly on the electric field strength in a manner that can often be described by the following relationship:
P = ε 0 [ χ ( 1 ) E + χ ( 2 ) E 2 + χ ( 3 ) E 3 + . . . ]
where ε0 is the vacuum dielectric constant, χ(2) is the second-order nonlinear polarization rate, χ(3) is the third-order nonlinear polarization rate, and E is the electric field strength of the incident laser beam. We refer to the following:
P ( 2 ) = ε 0 χ ( 2 ) E 2
as the second-order nonlinear polarization. For a high-power laser beam passing through the KDP crystal, the nonlinear effects become sufficiently apparent that they cannot be ignored, as in a weak electric field[23]. However, for a 400-mm aperture KDP crystal, this also makes the transmission wavefront of the laser beam very difficult to control because the mounting preloads will intensify the inhomogeneity of the optical properties of the KDP crystal, leading to a performance degradation of the laser beam propagation. Thus, this drives us to develop a mathematical method to model the imperfections and the impact on the frequency conversion process. As shown in Figure 9, for a KDP surface, defined as w(x,y), we have Ecoefficiency of frequency conversion
η = I 2 ω I i ω
The wavevector mismatching
Δ k = k 3 - 2 k 1 = 2 ω c n e 2 ω - n o ω
Based on the refractive law of light
s i n α = n o s i n β
1 n e 2 ( θ 0 + β ) = c o s 2 ( θ 0 + β ) n o 2 + c o s 2 ( θ 0 + β ) n e 2
For a small surface area, defined as a neighborhood of point P (x,y), we know that the deviation of the incident angle (α) is directly linked with the gradient wP(x,y). A case of a KDP crystal surface slope is shown in Figure 10.
w p ( x , y ) = w ( x , y ) x i + ( x , y ) y j
Therefore, for the small neighborhood of point P (x,y), we can obtain the mathematical model to calculate the ecoefficiency of the frequency conversion, according to the theory of nonlinear optics,
d η = f ( x , y ) d x d y
and for a whole surface of w(x,y), we can calculate the integral:
η = w ( x , y ) f ( x , y ) d x d y
Based on the above discussions, the resulting numerical method can be used to calculate the total frequency conversion ecoefficiency of the doubler. According to the principle of using a Riemann sum to approximate the Riemann integral, we will obtain a computerized discrete method to evaluate the frequency conversion ecoefficiency of a mounted KDP crystal.
4 Case study, experiments, and result analysis
The proposed integrated simulation and analysis framework for large laser optics has been constructed. The computation framework provides an assembly analysis tool for engineers during the installation of the frequency conversion unit. Following the general principles in the presented system, a number of case studies on assembly tasks were completed, which demonstrate how the proposed framework investigates the influences of the support layout and clamping loads on the crystal physical performance. Furthermore, the general feasibility of the proposed methodology is established.
In terms of structural features, the KDP crystal component is an anisotropic thin plate of 410mm×410mm×12mm. The KDP crystal is precisely created by the diamond fly cutting process, whose surface form error is very small, approximately 0.5-1μm from peak to valley. Because the status of the surface form is directly related to the SHG efficiency, minimization of the surface distortion and phase mismatching will be a priority for the assembly process design of the KDP converter. Considering the assembly structure and surface contact conditions between the KDP plate and the frame, the tightening preload will be very a sensitive factor when mounting the KDP crystal. A prototype KDP frequency converter assembly measurement system and its experimental arrangement are schematically represented in Figure 11. First, small changes in the KDP crystal surface form and wavefront aberrations caused by the mounting preloads and gravity can be measured precisely using the ϕ600mm interferometer in the Optical Assembly Building. In Figure 12, the surface forms of the KDP crystal measured in the experiment are given respectively. Compared with the surface form before mounting (Figure 12a), the preloads on the crystal edges can lead to an evident change in the surface due to deformation (Figure 12b), suggesting the importance of controlling the preloads on the KDP crystal. Through a data exchange interface with the FEA tool (ANSYS APDL R19), the real-time results on the mechanical simulation of the mounting crystal component, shown in Figures 13a and 13b, respectively, can be imported into the assembly design module. As shown in Figure 13c, the mechanical analysis on the KDP crystal can provide the parameterized curves to represent the relationship between the clamping forces and surface deformation. More specifically, there is an efficient method of parameters matching in the deformation analysis and preload optimization in the assembly design module/virtual assembly environment of the framework. The results also suggest that a smaller installation orientation (the placement angle is commonly between 0° and 80°) can reduce the sensitivity of the total crystal surface deformation (PV).
The deformation of the KDP crystal surface can partially change the phase matching conditions and reduce the conversion efficiency. The surface slope (Gradient (x,y)) of the crystal surface (corresponding to the surface in Figure 12b) and the incident laser, a modulated Gaussian beam, are shown in Figure 14 and Figure 15, respectively. In the optical surface distortion analysis module, the phase-matching capacity of the frequency converter under given mounted conditions is calculated and predicted (Figure 16a). The surface gradient has a direct impact on the distribution of the angle of incidence, hence, an improvement on the surface slope (Gradient (x,y)) of the mounted KDP crystal, i.e., a more flat crystal surface, implies better uniformity of the crystal detuning angle. Thereby, the global phase-matching condition can be effectively improved by the optimization of the mounting design of the KDP crystal. This provides a significant motivation to minimize the crystal surface aberration by configuring the assembly layout and mounting loads. The SHG efficiencies corresponding to different installation orientations and preloads are presented in Figure 16b, which also indicates that the clamping loads on the crystal edges are more conducive to improving the frequency conversion efficiency of the crystals. Basically, this provides an approach to stabilize the effect of gravity sagging, hence, the mounting-induced surface distortion can be adjusted to improve the SHG efficiency. Thus, the combinations of the mechanical analysis and frequency generation modeling in the integrated framework can help us to determine the optimal clamping force at each installation attitude. During the surface control process, the nominal clamping force is supposed to be first exerted according to the online installation attitudes of the converter, and then the clamping force is slightly adjusted to mitigate the surface aberration generated by some imperfect factors, such as small problems in surface contacts. The proposed configuration of preloads on the crystal can be used not only to hold the frequency converter, but also to further modify its surface form. Following the above analysis, an improved KDP crystal assembly can be obtained, like the case described in this section.
⊕ When placed horizontally, the SHG efficiency will increase from 74.24% to 74.3%, with a preload increase at each clamping position from 1N to 8N, because the clamping pressure counterbalances the gravity effect.
⊕ While placed at an orientation of 45° or more, the SHG efficiency of the KDP crystal only indicates a moderate increase of preloads from 1N to 10N. This may be due to the lesser effect of gravity deformation on the crystal surface.
Based on the work, we finally determine the mounting scheme of the KDP crystal through numerical calculation and simulations in the virtual assembly framework. If we consider the real rough surface of a machined KDP crystal, further analyses and optimization can be conducted in this virtual assembly framework. For instance, assuming that the surface aberrations of KDP are presented in Figure 12, it is mounted horizontally and generates a deformed surface (Figure 12b) under 7 N of force per clamp. For a different position on the surface, the local detuning angle will change with the distribution of the clamping stress. An SHG efficiency of 73.98% will be obtained for this crystal, an evident reduction compared with that having a smooth surface. There are three important factors, the original surface topography of the crystal, the placement (orientation) of the crystal, and the clamping scheme, that contribute the most to crystal surface aberration. Therefore, we are planning an enhanced module of the virtual assembly analysis and multiphysics simulation that can reconfigure the clamping layout to realize a more favorable crystal performance. For example, first, the initial clamping scheme is determined through the method mentioned above. Then, to achieve a better SHG efficiency, each preload is adjusted in the clamping layout to obtain a total minimal distortion of the crystal surface. Thus, solving this problem is of great significance in strengthening the assembly process capability of the optomechanical system, improving the optical performance and its service stability, and hence, achieving a better SHG efficiency by minimizing the disorder of the phase matching condition. Therefore, this integrated framework provides a comprehensive computation platform for large optics assembly analysis and mounting design.
5 Conclusions
Through an in-depth study on the problems of “integration modeling and analysis on large optic assembly, mounting deformation, and wave-phase performance”, we developed a computerized simulation framework for the multiphysics performance analysis and assembly/mounting design for a crystal. The simulation framework involves the frontiers of anisotropic crystal material mechanics, precision assembly technology, and strong-laser nonlinear optics to establish a multi-objective analysis and optimization method for the assembly/mounting optimization of a large crystal component. The use of the virtual assembly framework assumes importance as it enables various assembly and process scenarios to be studied virtually prior to the physical assembly of large optics. This under-developing framework holds the potential to initiate a new era of manufacturing collaborations using distributed resources and tools. Further research activities are continuing, involving extending the capabilities of the virtual assembly framework to enable a greater degree of collaborations involving distributed teams of engineers.



Pfalzner S. An introduction to inertial confinement fusion. CRC Press. 2006


Hurst P, Grasz E, Wong H, Schmitt E, Simmons M. Optical assembly and alignment for the National Ignition Facility project. SPIE 3264, High-Power Lasers, 1998, 86–92


Cecil J, Kanchanapiboon A. Virtual engineering approaches in product and process design. The International Journal of Advanced Manufacturing Technology, 2007, 31(9/10): 846–856 DOI:10.1007/s00170-005-0267-7


Nee A Y C, Ong S K, Chryssolouris G, Mourtzis D. Augmented reality applications in design and manufacturing. CIRP Annals, 2012, 61(2): 657–679 DOI:10.1016/j.cirp.2012.05.010


Jayaram S, Jayaram U, Wang Y, Tirumali H, Lyons K, Hart P. VADE: a virtual assembly design environment. IEEE Computer Graphics and Applications, 1999, 19(6): 44–50 DOI:10.1109/38.799739


Yang R D, Fan X M, Wu D L, Yan J Q. Virtual assembly technologies based on constraint and DOF analysis. Robotics and Computer-Integrated Manufacturing, 2007, 23(4): 447–456 DOI:10.1016/j.rcim.2006.05.008


Fan X M, Gao F, Zhu H M, Wu D L, Yin Q. A real-virtual mapping method for mechanical product assembly process planning in virtual assembly environment//Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2009: 550–559DOI:10.1007/978-3-642-02771-0_61


Brough J E, Schwartz M, Gupta S K, Anand D K, Kavetsky R, Pettersen R. Towards the development of a virtual environment-based training system for mechanical assembly operations. Virtual Reality, 2007, 11(4): 189–206 DOI:10.1007/s10055-007-0076-4


Auerbach J M, Barker C E, Burkhart S C, Couture S A, DeYoreo J J, Hackel L A, Hibbard R L, Liou L W, Norton M A, Wegner P J, Whitman P A. Frequency converter development for the National Ignition Facility. Third International Conference on Solid State Lasers for Application to Inertial Confinement Fusion, 1999: 392–405


Zheng W G, Wei X F, Zhu Q H, Jing F, Hu D X, Yuan X D, Dai W J, Zhou W, Wang F, Xu D P, Xie X D, Feng B, Peng Z T, Guo L F, Chen Y B, Zhang X J, Liu L Q, Lin D H, Dang Z, Xiang Y, Zhang R, Wang F, Jia H T, Deng X W. Laser performance upgrade for precise ICF experiment in SG-Ⅲ laser facility. Matter and Radiation at Extremes, 2017, 2(5): 243–255 DOI:10.1016/j.mre.2017.07.004


Wegner P, Auerbach J, Biesiada T, Dixit S, Lawson J, Menapace J, Parham T, Swift D, Whitman P, Williams W. NIF final optics system: frequency conversion and beam conditioning. SPIE Photonics West, San Jose, California, 2004, 180–189


Lubin O, Gouedard C. Modeling of the effects of KDP crystal gravity sag on third-harmonic generation. Third International Conference on Solid State Lasers for Application to Inertial Confinement Fusion, 1999: 802–808


Boyd R W. Nonlinear Optics, 3rd Edition, Academic Press, 2008


New G. Introduction to nonlinear optics. Cambridge: Cambridge University Press, 2009 DOI:10.1017/cbo9780511975851


Barker C, Auerbach J, Adams C, Bumpas S, Hibbard R, Lee C, Roberts D, Campbell J, Wegner P, Van Wonterghem B, Caird J. National Ignition Facility frequency converter development. Solid State Lasers for Application to Inertial Confinement Fusion: Second Annual International Conference, 1997: 197–202


Yoder P, Vukobratovich D. Opto-mechanical systems design. CRC Press, 2015 DOI:10.1201/b18147


Doyle K B, Genberg V L, Michels G J. Integrated optomechanical analysis, second edition. SPIE, 2012 DOI:10.1117/3.974624


Liang Y C, Su R F, Liu H T, Lu L H. Analysis of torque mounting configuration for nonlinear optics with large aperture. Optics Laser Technology, 2014, 58: 185–193 DOI:10.1016/j.optlastec.2013.11.017


Qin T H, Quan X S, Pei G Q, Yan H, Xu, Ye L, Du W F, Xiong Z, Liu C C. Surface control apparatus and method of optical transmission with large aperture based on self-adaptive force-moment technology. Optics Express, 2017, 25(13): 15358 DOI:10.1364/oe.25.015358


Wang H, Liu T Y, Zhang Z, Pei G Q, Ye L, Xu X. An investigation on the precision mounting process of large-aperture potassium dihydrogen phosphate converters based on the accurate prediction model. Precision Engineering, 2019, 57: 73–82 DOI:10.1016/j.precisioneng.2019.03.009


Hibbard R, Norton M, Wegner P. Design of precision mounts for optimizing the conversion efficiency of KDP crystals for the National Ignition Facility. Lawrence Livermore National Lab. 1998


Summers M, Hibbard R, Michie R, Liou L, William M. CAVE: The design of a precision metrology instrument for studying performance of KDP crystal. In: Optical Society of America 1998 Summer Topical Meeting, 1998


Guha S. Laser beam propagation in nonlinear optical media. CRC Press, 2013