## 5 Results and Discussion
### Experimental Results and Analysis of Laser Scribing Depth with Laser Incidence Angle
#### 5.3.3 Discussion of Laser Scribing Depth with Laser Incidence Angle  
According to the laser scribing depth of the forward angle and side slope angle under the same power density, and according to Figures 16b and 17b, the relation equation between the laser scribing depth and scribing angle can be established. According to the equation, the laser scribing depth at different angles can be predicted, which can be effectively applied to the laser secondary scribing. Meanwhile, there are two obvious phenomena: (1) the scribing depth at the forward angle (\(6^{\circ}\)) and side slope angle (\(7^{\circ}\)) are increased compared with the vertical incidence angle; (2) the scribing depth decreases linearly with the increase of incident angle. (1) Discussion of scribing depth improving by laser incident angle. According to Formula (5), the increase of laser scribing depth must be a change in the power absorbed by the material under the condition that other process parameters remain unchanged. In laser scribing, a large number of maskant particles, molecules and ions are splashed out from the surface of the matrix. Additionally, white fumes were observed during the experiment. As a kind of polymer material, chemical milling maskant inevitably produces fumes which leads to the loss of laser energy in the process of interaction with laser. The laser energy loss depends on the density of the particles in the fumes and the length of the fumes along the laser propagation direction. The loss of laser energy can be expressed as:  
\[P_{0}=P_{out}-P_{l}e^{-\alpha l}\]  
where,  
\(P_{0}\) is the laser power on the surface of the material;  
\(P_{out}\) is the laser output power;  
\(P_{l}\) is the laser power irradiating on the fumes;  
\(\alpha\) is the absorption coefficient of a laser incident to the fumes;  
\(l\) is the length of the fumes in the direction of the laser beam. The laser incident angle can change the fumes concentration in the direction of laser transmission and can also change the length of fumes in the direction of laser transmission. Figure 17: Relationship between side slope angle and scribing depth. (**a**) Relationship between side slope angle and scribing depth. (**b**) Relationship between side slope angle and scribing depth without vertical angle. In the process of laser scribing, the material will go through the whole process of material evaporation, plume formation and smoke formation. This phenomenon is quite complex, and a full computational fluid dynamics (CFD) simulation would be needed in order to really evaluate its effects. The evaluation of the plume needed advanced thermochemical non-equilibrium [36]. According to the literature, the reverse jet of laser ablation plume first occurs in the ablation plane and gradually diffuses around with time, but the density and temperature also gradually decrease [37]. This will cause relatively more fumes in the vertical direction. Considering that the flow speed of smoke is not enough to be completely blown away, it will have an impact on the energy actually irradiated on the material surface. The plume in the process of laser scribing is not the goal of this paper, and we only made a brief discussion and analysis. (2) Analysis of scribing depth decrease with increasing laser incidence angle. Aiming at the problem that the laser scribing depth decreases with the increase of angle, there are three kinds of influences jointly affecting this trend. Based on Formula (5), including the material reflectivity R, scribing width \(b_{c}\) and heat conduction loss \(P_{HL}\). The relationship between reflectivity R and inclination \(\theta\) of materials can be calculated by the Fresnel formula of the refraction law. When the incident angle is less than Brewster's angle, the reflectivity of materials to circularly polarized light stays roughly the same. When the incident angle is greater than Brewster's angle, the reflectivity of organic polymers to circularly polarized light increases rapidly until total reflection.