# Chalcogenide Thin Films--Holographic Media for Augmented Reality Devices
## 2 Modeling Results  
### Efficiency-Thickness Modeling  
At first, modeling was provided in RSoft software (version 2018.12) in order to find the acceptable ChGs thickness range for achieving proper diffraction efficiency of HOEs recorded in ChGs films. Rigorous coupled-wave analysis method was used for the modeling [19]. A stack of three materials was modeled, namely air, a thin layer of a ChG film, and a glass substrate. The dimension of the ChG segment in the \(X\) direction was equal to one period of the simulated holographic grating (one period along \(X\) was modeled). The stack was assumed to be periodically infinite in the \(X\) direction, uniform in the \(Y\) direction, and had finite dimensions in the \(Z\) direction, which corresponded to the direction of incident light. The stack dimensions in the \(Z\) direction were limited by the plane on which the incident wave was specified and the plane on which the diffracted wave was measured. The incident wave with \(s\)-polarization propagated from the air towards the ChG film layer, while the diffraction response was measured in a glass substrate. When modeling, the thickness of the ChG film layer and its refractive index varied in the ranges shown in the figures below. A sinusoidal distribution of the refractive index was set inside the film with the refractive index modulation \(\Delta n\), which was also varied during the modeling in the ranges shown in the figures below. ChG film was considered optically isotropic and without absorption. Glass substrate was also considered without absorption; it had refractive index of 1.9, which was not changed during modeling. Figure 2: (**a**) RGB FOV provided through the system with high transparency, having good color balance; (**b**) RGB FOV provided through the system with high absorption in blue spectral region, having poor color balance. Single-exposure modeling of two key parameters (maximum diffraction efficiency and a full width at half maximum (FWHM) of angular selectivity contour) for materials with different parameters was made. The variable parameters were as follows:  
* thickness (\(d\)): from 0.1 to 4 \(\mu\)m;
* average refractive index (\(n_{0}\)): from 1.8 to 2.2;
* refractive index modulation (\(\Delta n\)): from 0.05 to 0.15. At single-exposure modeling, a sinusoidal refractive index distribution profile was set inside the ChG film for each taken film thickness, \(n_{0}\) and \(\Delta n\). The period of this profile along the \(X\) axis was chosen in such a way that a symmetrical FOV was introduced into the glass substrate from air; e.g., for 532-nm incident light and ChG refractive index \(n_{0}=1.8\), grating period along \(X\) axis was equal to 380 nm, and the TIR window was about 47 deg (from \(-23.5\) to \(+23.5\) deg). Here, it was assumed that the limitation on the FOV was set not by the refractive index of the glass but by ChG film refractive index. Then, the slant of the holographic planes of the grating relative to the \(Z\) axis was optimized to ensure location of the DE angular selectivity contour in the center of the FOV (symmetrically with respect to the center of the TIR window). This optimization was carried out numerically; a series of gratings with different slants of holographic planes was modeled, and finally, a specific slant was chosen at which the maximum of DE corresponded to normally incident light. Then this DE contour was processed by the in-house algorithm to obtain the values shown in the figures below. The modeling results are depicted in Figure 3.  
It is seen from Figure 3 that  
1. Maximum DE depends dramatically on \(d\) and \(\Delta n\) but not so much on \(n_{0}\). 2. FWHM depends mostly on \(d\), not much on \(n_{0}\), and does not depend on \(\Delta n\). 3. To reach the minimal possible DE for output HOE (1%), the least possible \(d\) should be 0.25 \(\mu\)m for \(\Delta n=0.15\) and 0.9 \(\mu\)m for \(\Delta n=0.05\).