# Chalcogenide Thin Films--Holographic Media for Augmented Reality Devices
## 2 Modeling Results
### Multi-Exposure Modeling  
Next, modeling was made for a uniform filling of so-called TIR waveguide window (54 deg for waveguide with \(n\) = 1.9) with two reflection exposures in one layer of chalcogenide material in order to find its appropriate parameters. Two exposures are two reflection holograms with the same surface periods but different slant angles of their holographic planes inside the material.  
We have chosen the following ranges of ChGs parameters for modeling:  
* average refractive index \(n_{0}\) from 1.9 to 2.2;
* refractive index modulation (for both the exposures) \(\Delta n\) from 0.5 to 0.15;
* thickness \(d\) from 0.8 to 3 \(\upmu\)m.  
Two exposures were modeled in a form of one gratings specified, in turn, as a function of two superimposed sines functions with the same period along the \(X\) axis but different slant angles (relative to \(Z\) axis). The modeling was carried out in the same way as the single exposure, but slant angles were optimized for two sub-gratings at the same time. Numerical optimization was carried out in order to have a symmetric FOV efficiency while having the best uniformity over the TIR window. For that, a series of gratings with different pairs of slant angles was modeled for each \(n_{0}\), \(\Delta n\), and \(d\) parameters combination. The average efficiencies of the gratings were calculated then, and the grating with the least deviation from the average efficiency along the angular plane was chosen as the optimal one for this parameters combination. The results are presented in Figure 4. The parameters of interest are diffraction efficiency and uniformity. The left graph illustrates the efficiency parameter by the value of maximal diffraction efficiency. The bunches of lines are distributed here by refractive index modulation, and within each bunch, different lines correspond to different average refractive index. The thing to point out is that efficiency depends more on the refractive index modulation. When we choose the minimal satisfying value of DE to be >10%, only thicknesses \(d\) > 1.65 \(\upmu\)m and refractive index modulation \(\Delta n\) > 0.13 fit this condition. The region where all these conditions are satisfied is highlighted by green rectangular in the left figure.  
The right graph shows the uniformity by the value of average diffraction efficiency in the TIR window divided by maximal diffraction efficiency. The bunches of lines are distributed here by average refractive index, and within each bunch, different lines correspond to different refractive index modulation. The thing to point out is that uniformity depends more on the average refractive index. Here, we choose the minimal satisfying value of uniformity being >50% (to ensure the comfort of visual perception of the image). This condition gives us the large, blue, rectangular area in the right figure. When we correlate it with the condition on the thickness from the left part of the figure, we get a final region of satisfying parameters, highlighted by the red rectangular in the right graph. Here, only the average refractive index > 2.1 fits.  
Thus, we can slightly correct ChG material parameters obtained in Section 2.1. The optimal parameters concluded from this calculation are as follows:  
* average refractive index \(n_{0}\) > 2.1;
* refractive index modulation (for both the exposures) \(\Delta n\) > 0.13;
* thickness \(d\) from 1.65 to 2 \(\upmu\)m.