## 2 Design, Modeling, and STOP Simulation of an Optical Laser Head for LAAM
### Thermal Effect on Optical Performance with Sensitivity Analysis  
One design example of the laser head with a 1064-nm fiber laser beam at a designed 300-\(\upmu\)m spot radius size with 1.634 kW laser power output utilized for the STOP simulation. The cone-shaped laser beam was incident perpendicular to the center of the front surface of the collimating lens, as shown in Figure 2. In the original design, a 302-\(\upmu\)m root-mean-square (RMS) spot radius size at the focal plane position was obtained by using ray-tracing optical simulation only. The incident optical intensity was calculated at 4630 W/mm\({}^{2}\). Unlike ray tracing optical simulation, the STOP simulation model includes thermal effects due to high power laser heating and mechanical and thermal boundaries. The following thermal and mechanical boundary conditions of the STOP simulation were assumed:  
1. the ambient surrounding working condition at the temperature \(T_{0}\) = 293 K;
2. heat convective coefficients \(h_{n}\) = 5 (W/m\({}^{2}\)K) for all exposed surfaces of the housing and \(h_{c}\) = 1500-3500 (W/m\({}^{2}\)K) for cooling water channel plates;
3. surface emissivity set at 0.1 at the reflected mirrors due to the copper coating; and  
Figure 4: The flowchart of the STOP analysis for the optical laser head. (4) one side of the laser head mounted on the fixed plate via the screws. In the STOP simulation, thermal and optical properties of the lenses and mirrors were adopted as the temperature-dependency model. However, material properties of the housing metal components (stainless steel and copper) at room temperature were used due to smaller temperature changes in the range of 30-80 \({}^{\circ}\)C in this study. They are summarized in Table 1.  
The solution was converged in five iterative processes of the STOP simulation. The simulated temperature and thermal-induced deformation distributions are shown in Figure 5. The temperature rises to \(T_{max}\) = 179 K at the collimating lens, and the maximum thermal-induced deformations are 47.7 \(\upmu\)m and 47.2 \(\upmu\)m for the housing and the reflected mirrors, respectively. Figure 6 displays the temperature and deformation distributions of the focusing lens. It is observed that the temperature and deformation distributions are not placed centrally with small eccentric gaps. In the current design, the lenses are fully fitted into the ring structures. However, the mechanical components surrounding the rings may not be all cylinder shapes, as shown in Figure 1. It will generate unequal heat dissipation in the radial direction. In addition, one side of the laser head is mounted on the fixed plate via screws. Such a boundary condition may also result in temperature-induced radial gradient deformations with smaller eccentric gaps. Consequently, these thermal-induced deformations cause the lens to warp at 4-\(\upmu\)m differences in the radial direction, which will affect the laser beam focusing spot size and laser irradiation intensity. The calculated thermal-induced optical laser beam intensity and the root-mean-square (RMS) spot radius size at the focal plane position are presented in Figure 7. The optical performances at the same focal plane position computed by using ray-tracing simulation only are also given in the figure for comparison. The results indicate that the high-power laser beam generates a direct thermal influence on laser beam intensity and focal spot size in the operating condition. From Figure 7, it is shown that the RMS spot radius size with STOP is 16.5% less than one with ray-tracing simulation only while optical intensity is 2.6% more than the results by ray-tracing simulation. It is expected that thermal effects with higher than a 1.634 kW laser power level can generate significant impacts on the optical performance variations, such as laser beam irradiation quality. These optical performance variations will eventually affect laser intensity quality in manufacturing processing.