## 2 Simulation Analysis of the Cubic FP Cavity with Reinforced Support
### Zero-Expansion Temperature Analysis  
According to the description of the literature [20], the reinforced-support FP cavity used silicone rubber to bond the screws to the FP cavity for enhanced fixing. When the FP cavity contacted the support screws and silicone rubber, a combined structure was formed. CTE (coefficient of thermal expansion) of the FP cavity could be affected by these contact materials. Therefore, zero-expansion temperature of the FP cavity needed to be analyzed.  
In the simulation, CTE of the ULE glass is shown in Figure 4a. The ULE glass has a zero-expansion temperature at 22 \({}^{\circ}\)C. Results of the zero-expansion temperature analysis of the FP cavity are shown in Figure 4b. It can be seen from the figure that the value of deformation in the center of the FP cavity varies with temperature. The zero-expansion temperature of the FP cavity is 12.8 \({}^{\circ}\)C. Compared to the ULE glass zero-expansion temperature of 22 \({}^{\circ}\)C, the zero-temperature of the FP cavity changed by 9.2 \({}^{\circ}\)C. This change is caused by fused silica mirrors, which has been reported in the literature [6]. After using the reinforced-support structure, the zero-expansion temperature of the FP cavity increased from 12.8 \({}^{\circ}\)C to 13.8 \({}^{\circ}\)C. This suggests that the FP cavity is affected by the reinforced-support structure about 1 \({}^{\circ}\)C.  
Zero-expansion temperature simulation results demonstrate that although the bracket, screws, and FP cavity formed a combined structure, the structure has limited effect on the zero-expansion temperature of the FP cavity. According to our analysis, for the FP cavity, the laser is transmitted between two fused silica mirrors to form a resonance. This means that the optical length of the FP cavity is equal to the distance between the two fused silica mirrors. The thermal deformation of the fused silica mirrors will directly affect the optical length of the FP cavity. Whereas the support bracket, screws, etc. do not directly contribute to optical length of the FP cavity. The thermal deformation of these structures affects the FP cavity through the action of forces. For example, when a temperature change causes the support structure and FP cavity to expand, if the expansion of the FP cavity is greater than that of the support structure, the support structure will produce a pressure on the FP cavity. This pressure applied to the FP cavity influences the optical length of the FP cavity. Since the FP cavity cube material is ULE glass, which has a Young's modulus of about 67.6 GPa, the effect of the pressure on the FP cavity needs to be divided by the Young's modulus.  
To verify the above analysis, the stress in the FP cavity at different temperatures was also analyzed during the simulation. The results of the analysis are shown in Figure 5. The stress on the FP cavity increases with the increase of temperature, which proves that the  
Figure 4: Zero-expansion temperature analysis: (**a**) CTE of ULE glass; (**b**) Deformation in the center of the FP cavity mirror.  
thermal deformation of the support structure affects the FP cavity by force. In addition, not all support structures have a limited effect on FP cavities. With the increase of contact surface between the FP cavity and the outer support structure, the thermal deformation of the outer support structure will also have an increased effect on the FP cavity.