# Polarization Transmission of Visible Light in Inhomogeneous Sea Fog Particle Environment
## 4 Results and Discussion  
### Simulation Results and Analysis  
To study the effect of wavelength, we input the following parameters to simulate DOP: three incident wavelengths (450, 532, and 671 nm), four polarization states (0\({}^{\circ}\), 45\({}^{\circ}\), and 90\({}^{\circ}\) linearly polarized lights and right-handed circularly polarized light), and particle radius 0.6 \(\upmu\)m. The values of the refractive index at different wavelengths are shown in Table 2, and the values of the optical thickness are shown in Table 4. The number of particles is 10\({}^{6}\). The curves are drawn according to the three groups of DOP values and optical thickness output by the simulation, as shown in Figure 7.  
Figure 7 shows the simulation results of the inhomogeneous particle scattering model. The three DOP curves overlap because of the DOP difference of less than 1% for 0\({}^{\circ}\), 45\({}^{\circ}\), and 90\({}^{\circ}\) linearly polarized lights. For the three wavelengths of the polarized lights, the DOP of both circularly polarized light and linearly polarized light decreases with the increase of optical thickness. In particular, the concentration of inhomogeneous sea fog particle environment increases, thereby increasing the number of collisions of photons in the transmission medium. That will decrease DOP. The DOP difference between the circularly polarized light and linearly polarized light is approximately 30%, which is different from the difference in the beginning. Because the overall scattering effect of the sea fog environment is forward scattering, circularly polarized light's polarization-maintaining ability is better than linearly polarized light. The linearly polarized light scatters to other states when the polarized light is transmitted in the forward scattering environment; however, this phenomenon does not occur with circularly polarized light [19]. The simulation data of 0\({}^{\circ}\), 45\({}^{\circ}\), and 90\({}^{\circ}\) linearly polarized lights and right-handed circularly polarized light of the three wavelengths are known. We use them to draw Figure 8 to compare the change of DOP under different wavelengths. In the visible band, the DOP decreases as the wavelength increases. DOP\({}_{450}\) is approximately 3% higher than DOP\({}_{532}\), and DOP\({}_{532}\) is approximately 5% higher than DOP\({}_{671}\). According to the scale parameter formula in Section 2.1, when the incident wavelength is smaller, the scale parameter is larger, and the equivalent refractive index of the particle is smaller. While the refractive index of the particles is smaller, the extinction effect of the particles is smaller. The photons carry more polarization information through the medium. Thus, DOP is inversely proportional to the wavelength at this time. Figure 7: Simulation curves of DOP and optical thickness under different wavelengths: (**a**) \(\lambda=450\) nm; (**b**) \(\lambda=532\) nm; (**c**) \(\lambda=671\) nm. To study the effect of relative humidity on DOP, we input parameters such as: wavelength 532 nm, four polarization states (0\({}^{\circ}\), 45\({}^{\circ}\), and 90\({}^{\circ}\) linearly polarized lights and right-handed circularly polarized light), and particle radius 0.6 \(\upmu\)m. The refractive index corresponding to relative humidity is shown in Table 3, and the optical thickness value is shown in Table 4. The number of particles is 10\({}^{6}\). The curve as shown in Figure 9 is drawn according to the DOP by the simulation. DOP shows an upward trend with an increase in relative humidity. The relative humidity increases from 45% to 85%, and DOP increases by approximately 10%. The relative humidity is defined as the ratio of the water content to the particle content of the medium; that is, when the relative humidity increases, the refractive index of inhomogeneous sea fog particles calculated from Equation (8) decreases. While the refractive index of the particles is smaller in the transmission medium, the extinction effect of the particles is smaller.