Nested deep transfer learning for modeling of multilayer thin films

Machine-learning techniques have gained popularity in nanophotonics research, being applied to predict optical properties, and inversely design structures. However, one limitation is the cost of acquiring training data, as complex structures require time-consuming simulations. To address this, researchers have explored using transfer learning, where pretrained networks can facilitate convergence with fewer data for related tasks, but application to more difficult tasks is still limited. In this work, a nested transfer learning approach is proposed, training models to predict structures of increasing complexity, with transfer between each model and few data used at each step. This allows modeling thin film stacks with higher optical complexity than previously reported. For the forward model, a bidirectional recurrent neural network is utilized, which excels in modeling sequential inputs. For the inverse model, a convolutional mixture density network is employed. In both cases, a relaxed choice of materials at each layer is introduced, making the approach more versatile. The final nested transfer models display high accuracy in retrieving complex arbitrary spectra and matching idealized spectra for specific application-focused cases, such as selective thermal emitters, while keeping data requirements modest. Our nested transfer learning approach represents a promising avenue for addressing data acquisition challenges.