## 3 Numerical Simulation and Results
\(N=2\), \(m=3\), \(\delta_{xx}=2\) μm, \(\delta_{yy}=4\) μm, \(P^{(0)}=0.5\), and \(C_{n}{}^{2}=10^{-4}\) μm\({}^{-1}\). Figure 4: Effect of the topological charge on the normalized average intensity distribution in the selected investigation plane of the turbulent biological tissue. \(w_{0}\) = 2 \(\upmu\)m, and the other parameters are the same as in Figure 2.  
Figure 5: Effect of the two transverse coherent lengths on the normalized average intensity distribution in the selected investigation plane of the turbulent biological tissue. \(w_{0}\) = 2 \(\upmu\)m, and the other parameters are the same as in Figure 2.  
The degree of polarization distribution of a partially coherent circular flattened Gaussian vortex beam in different study planes of the turbulent biological tissue is demonstrated in Figures 7-11. Except for different subjects, the parameters in Figures 7-11 are equivalent to those in Figures 2-6, respectively. Though the degree of polarization is the same in every point of the initial plane, the degree of polarization of a partially coherent circular flattened Gaussian vortex beam in the turbulent biological tissue is usually variable. Only when the two transverse coherent lengths are identical, the degree of polarization of the partially coherent circular flattened Gaussian vortex beam in the turbulent biological tissue is equal to \(P^{(0)}\) and remains unchanged, as shown in Figure 10. In Figure 7, as the value of radial coordinate \(\rho\) increases, the degree of polarization first decreases, then increases, and finally decreases again. In the investigation planes \(z=3\)\(\upmu\)m and \(z=5\)\(\upmu\)m, the edge of the degree of polarization may fluctuate, and the fluctuation increases with the increase of the waist size of the fundamental Gaussian part \(w_{0}\). The reason is as follows. Although \(W_{xx}(\rho,\rho,\theta,\theta,z)\) and \(W_{yy}(\rho,\rho,\theta,\theta,z)\) are very small for large \(\rho\) and \(w_{0}\), the variations of \(W_{xx}(\rho,\rho,\theta,\theta,z)\) and \(W_{yy}(\rho,\rho,\theta,\theta,z)\) are not synchronous, which results in a highly oscillating behavior of the degree of polarization for large \(\rho\) and \(w_{0}\). Upon propagation in the turbulent biological tissue, the range of change for the degree of polarization narrows. When the flat-topped average intensity is reproduced, the variation range of the degree of polarization is relatively small. When the waist size of the fundamental Gaussian part \(w_{0}\) increases, the range of change for the degree of polarization in the initial plane \(z=10\)\(\upmu\)m also increases. When the radial coordinate \(\rho\) is small, the degree of polarization is insensitive to the parameter \(N\). As the parameter \(N\) changes, the curve of the degree of polarization versus the radial coordinate \(\rho\) changes little, as shown in Figure 2.0 When the topological charge \(m\) increases, the degree of polarization in the points, except for the edge of the initial plane \(z=3\)\(\upmu\)m, augments, as shown in Figure 2.1 With the decrease of the turbulence level, the degree of polarization varies more widely and fluctuates more frequently, as shown in Figure 2.2 In this case, the flat-topped average intensity was been reproduced. Figure 2.3 Effect of the structural constant on the normalized average intensity distribution in the selected investigation plane of the turbulent biological tissue. \(w_{0}=2\)\(\upmu\)m, and the other parameters are the same as in Figure 2.4  
Figure 2.5 Effect of the parameter \(N\) on the degree of polarization distribution in the selected investigation plane of the turbulent biological tissue. All the parameters are the same as in Figure 2.6  
Figure 2.7 Effect of the waist size of the fundamental Gaussian part on the degree of polarization distribution in the selected investigation plane of the turbulent biological tissue.