# Numerical Estimation of Bending in Holographic Volume Gratings by Means of RCWA and Deep Learning
## 3 Results
### Suitability of the RCWA-Shooting Method
Figure 6a represents the variation in the amplitude of the maximum of the diffraction efficiency. Figure 6b shows the angle where the maximum value of the diffraction efficiency was located. Figure 6c,d represent the amplitude of the first lobes around the Bragg's angle. Following the same procedure, Figure 6d,f show the position of these lateral lobes as a function of the \(a_{1}\) parameter. The bottom graphs in Figure 6g,h represent the correlation coefficient of the diffraction efficiency compared to the response of the grating without bending and the deviation of the Bragg's angle compared to the ideal case (no bending), respectively. The analysis of Figure 6 implies that the amplitudes analysed remained constant for different values of \(a_{1}\). Figures 7 and 8 show the same analysis for \(a_{2}\) and \(a_{3}\), respectively. The linear dependence of the angular variations for \(a_{2}\) seems to be not as linear as the case shown in Figure 6. The variations in amplitude also became more significant. The performance of the SM-RCWA and Kubota seems to be consistent with the previous results. Figure 5: **(a) Absolute error between FDTD values and SM-RCWA, as well as FDTD vs. Kubota’s implementation (b) for the different simulations covered in Table 1. Blue bars represent the error for the transmitted order, and blue bar represents the error for the \(-1\)st-order. **  
Figure 6: Parametric analysis of the different methods as a function of the bending parameter \(a_{1}\). Here, \(a_{2}=a_{3}=0\). (**a**) Variation in the amplitude of the maximum of the diffraction efficiency of the \(-1\)st-order at the Bragg angle. (**b**) Position in degrees of the maximum of the diffraction efficiency. (**c**) Amplitude of the maximum of the right lobe of the \(-1\)st-order. (**d**) Position in degrees of the maximum of the right lobe of the \(-1\)st-order. (**e**) Amplitude of the maximum of the left lobe of the \(-1\)st-order. (**f**) Position in degrees of the maximum of the left lobe of the \(-1\)st-order. (**g**) Correlation parameter between the bending analysis and the response without bending. (**h**) Displacement of the position of the maximum correlation. Figure 8: Parametric analysis of the different methods as a function of the bending parameter \(a_{3}\). Here, \(a_{1}=a_{2}=0\). (**a**) Variation in the amplitude of the maximum of the diffraction efficiency of the \(-1\)st-order at the Bragg angle. (**b**) Position in degrees of the maximum of the diffraction efficiency of the \(-1\)st-order. (**d**) Position in degrees of the maximum of the right lobe of the \(-1\)st-order. (**e**) Amplitude of the maximum of the left lobe of the \(-1\)st-order. (**g**) Position in degrees of the maximum of the left lobe of the \(-1\)st-order. (**g**) Correlation parameter between the bending analysis and the response without bending. (**h**) Displacement of the position of the maximum correlation. \(-1\)st-order at the Bragg angle. (**b**) Position in degrees of the maximum of the diffraction efficiency. (**c**) Amplitude of the maximum of the right lobe of the \(-1\)st-order. (**d**) Position in degrees of the maximum of the right lobe of the \(-1\)st-order. (**e**) Amplitude of the maximum of the left lobe of the \(-1\)st-order. (**f**) Position in degrees of the maximum of the left lobe of the \(-1\)st-order. (**g**) Correlation parameter between the bending analysis and the response without bending. (**h**) Displacement of the position of the maximum correlation. Figure 8 shows the more extreme results due to the variation in \(a_{3}\). Regarding amplitude, it can be seen that as \(a_{3}\) rises, the diffraction efficiency significantly reduces. Figure 8g shows that the diffraction efficiency curve is progressively less correlated to the ideal response dealing with the disappearance of the lateral lobes of the curve, as it can be seen in the abrupt discontinuities on the tracking of the lateral lobes in Figure 8c-f.