## 4 Experiment
### Measurement Results and Discussions  
Measurement experiments are carried out on the volume holographic gratings prepared in Section 4.1. The angle of incidence \(\theta\) for the probing light was fixed at approximate 25\({}^{\circ}\). Since the manual manipulation cannot guarantee the exact value of angle of incidence, we set it as a measurand with an initial value of 25\({}^{\circ}\). The azimuthal angle \(\varphi\) was set as 0\({}^{\circ}\), which indicates the incident plane is perpendicular to the gratings. In this case, the off-diagonal elements in the measured Mueller matrices should be zeros, which can be applied to check the azimuthal angle settings in measurements. Same as angle of incidence, the azimuthal angle was set as a measurand with initial value of 0\({}^{\circ}\) to avoid the error introduced by manual manipulation. In analysis, the spectral range was from 400 to 1000 nm with an increment of 5 nm, and the distributed dielectric constant model based RCWA proposed in Section 2.1 was used to calculate the Mueller matrices. The distributed refractive index is assumed sinusoidal, which is defined as \(n(x)\) shown in Figure 1a. The number of retained orders in the truncated Fourier series was 12. Since the preliminary study [31] on the sample revealed that no significant refractive index variation along \(z\) direction had been observed because both the nanoparticles and the polymers are not absorbing materials, we set the layer number \(L\) to be 1 to improve the calculation  
Figure 5: Scheme of the experimental setup based on a dual rotating-compensator Mueller matrix ellipsometer (MME) in the transmission mode. efficiency and the measurement accuracy. In this case, the amplitude of refractive index curve \(n_{A}\), and the thickness of samples were measured simultaneously. Since the linear correlations between the refractive index and ZnS nanoparticles volume fraction have been achieved in our previous work [31], the distributed refractive indices can be directly converted into the volume fractions distributions. Figure 6 shows the comparison of calculated and measured Mueller matrix spectra when recording time \(t=5\) s, 10 s, and 40 s, as well as the achieved spatial volume fraction distributions corresponding to \(t=5\) s, 10 s, 25 s, and 40 s in the nanocomposite. More detailed measurement results including amplitude of concentration variation \(C_{A}\), thickness of samples \(H\), the angle of incidence \(\theta\), the angle of azimuth \(\varphi\), as well as the \(MSE\) of fitting are listed in Table 4. It is worth to point out that the pitch of the volume holographic grating is assumed 800 nm and the local nanoparticle concentration is ideally sinusoidally distributed. Figure 6: Results of calculated (red) and measured (blue) Mueller matrix spectra in the transmission mode when recording time (**a**) \(t=5\)s; (**b**) \(t=10\)s; (**c**) \(t=40\)s; and (**d**) measured spatial refractive index distribution curve of a volume grating at different exposure time. As shown in Figure 6a-c, the measured Mueller matrix fits well with the calculated matrix. All the Mueller matrices have similar characteristics, which indicates that the formed volume gratings are consistent. If some of the specific Mueller matrix elements such as \(m_{12}\) are selected for a further analysis, the depth of the dip become larger, which indicates that the characteristics of Bragg grating become more and more obvious. This is rational because with the increase of the recording time, the sinusoidal distribution of the refractive index is more obvious. Such a phenomenon is more intuitively shown in Figure 6d. It can be clearly observed in Figure 6d that the volume fractions in the dark regions are increasing, while the volume fractions in the bright regions are decreasing, with the process of holographic recording. Since the nominal azimuthal angle is selected as \(0^{\circ}\), the Mueller matrix elements observed in the off-diagonal blocks are close to 0.