# Inverse Design of Distributed Bragg Reflectors Using Deep Learning
## 3 Results and Discussion
### Colour Generation by Multilayers  
The model was further assessed through exploring the range of colours produced by each structure. From here, only the training data for the desired configuration need be generated. This allows for far sparser data sampling, and is perhaps a more intuitive way of demonstrating the versatility of each structure. Additionally, only by making very small changes to the model structure is it likely that (other than a small adjustment to the input vector size) the DL model architecture would not need to be altered.  
Using an adapted code by [PERSON] [24], the reflectance spectra data were converted into CIE chromaticity values of L\({}^{*}\), a\({}^{*}\), and b\({}^{*}\), which were then converted to the tristimulus values (\(XYZ\)) using Matlab. Finally, using the relations in Equation (11), the \(xy\) values were found, allowing the 2D chromaticity plot seen in Figure 8 to be constructed. The black data points represent a sample of the model predictions made for the test data, and therefore are an accurate indicator of the current model's true capabilities.  
Figure 7: An example of model performance when asked to design a structure to produce an arbitrary response within the material capabilities. The predicted (blue) curve shows good similarity to the target (red) curve, with the peaks and troughs in good agreement and a percentage accuracy of 88%. The predicted material depths were [61.4 49.4 65.3 46.5 52.6 12.1] nm.  
\[x=\frac{X}{X+Y+Z},\qquad y=\frac{Y}{X+Y+Z} \tag{2}\]  
The triangular plot represents the scope of the RGB colour space. It can be seen from this that the model was able to accurately produce colours across the yellow/orange and pink/purple ranges, as well as pale greens and turquoises. However, it struggles with vibrant greens and reds, and deep blue-purples, which lie at the corners of the RGB space. This is likely due to these colours being derived from narrow reflectance peaks, which are not producible using the tightly constrained model.  
Further work could focus on assessing small structural changes which could be made in order to improve the range of the model predictions. The white and blue data points show the additional breadth of responses which can be produced by a 10-layer SiO\({}_{2}\)-Si\({}_{3}\)N\({}_{4}\) structure and a six-layer MgO-ZrO\({}_{2}\) structure, respectively. It is apparent that the 10-layer structure extends further into the purple-blue and red colour spaces, but also covers the regions achieved with the original structure. Additionally, the MgO-ZrO\({}_{2}\) data are able to achieve the intense greens that were otherwise lacking, and extends even past the RGB colour space into the blue-turquoise regions. Green colour is a huge advantage of this multilayer system over conventional metamaterial-based structures [4]. The simplicity of this model and the smaller quantity of data needed to train it as compared to previous studies [15; 16] present the opportunity for the same model architecture to be used alongside a number of training datasets, each of which may be tuned to reflect the materials/structural constraints imposed by the user.  
Figure 8: A 2D chromaticity plot showing the RGB colour space (triangle plot). Black crosses represent the unique colours produced by each of the model predictions made using the test data for the SiO\({}_{2}\)-Si\({}_{3}\)N\({}_{4}\) system. White crosses show the breadth of a 10-layer system, and blue crosses show the results of the same 6-layer system using MgO-ZrO\({}_{2}\) as the material pair.