Recurrent Neural Network for Predicting Dielectric Mirror Reflectivity

Abstract

Optical devices often achieve their maximum effectiveness by using dielectric mirrors; however, their design techniques depend on expert knowledge in specifying the mirror properties. This expertise can also be achieved by machine learning, although it is not clear what kind of neural network would be effective for learning about dielectric mirrors. In this paper, we clarify that the recurrent neural network (RNN) is an effective approach to machine-learning for dielectric mirror properties. The relation between the thickness distribution of the mirror’s multiple film layers and the average reflectivity in the target wavelength region is used as the indicator in this study. Reflection from the dielectric multilayer film results from the sequence of interfering reflections from the boundaries between film layers. Therefore, the RNN, which is usually used for sequential data, is effective to learn the relationship between average reflectivity and the thickness of individual film layers in a dielectric mirror. We found that a RNN can predict its average reflectivity with a mean squared error (MSE) less than 10^-4 from representative thickness distribution data (10 layers with alternating refractive indexes 2.3 and 1.4). Furthermore, we clarified that training data sets generated randomly lead to over-learning. It is necessary to generate training data sets from larger data sets so that the histogram of reflectivity becomes a flat distribution. In the future, we plan to apply this knowledge to design dielectric mirrors using neural network approaches such as generative adversarial networks, which do not require the know-how of experts.