Machine Learning offers the potential to revolutionize the inverse design of complex nanophotonic components. In addition to the celebrated numerical techniques, such as Finite-Element and Finite-Difference methods, Machine Learning can predict the scattering properties of complex optical components using artificial neural networks. A benefit of this neural network based approach is that it is especially suited for inverse design. The goal of inverse design is to obtain an optimal optical component that closely matches a desired optical response. The process consists of two steps. The first step trains a neural network to predict the response of an optical system based on its input parameters, such as material and geometric parameters. In the second step, the neural network is used to optimize these input parameters to obtain a desired optical response. An interesting problem can arise in this second step. In resonant systems, the optimization of the input parameters leads to gradient descent in a highly oscillatory loss landscape. The loss landscape contains a lot of local minima in which the gradient descent can get stuck, leading to a sub-optimal optical design. To address this problem, we propose a physics-inspired algorithm which adds the Fourier transform of the desired spectrum to the optimization procedure. The additional Fourier transform provides a way to differentiate between different minima such that the global minimum can be found. We investigate our approach on the transmission and reflection spectra of Fabry-Perot resonators and Bragg reflectors. We show that our method successfully finds optimal optical designs.
In addition to the celebrated numerical techniques, such as Finite-Element and Finite-Difference methods, it is also possible to predict the scattering properties of optical components using artificial neural networks. However, these machine-learning models typically suffer from a simplicity versus accuracy trade-off. In our work, we overcome this trade-off. We train several neural networks with an indirect goal. Instead of training the net to predict scattering, we try to train it the laws of Optics on a more fundamental level. In this way, we can increase the predictive power and robustness while maintaining a high degree of transparency in the system.
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