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Machine learning offers the potential to revolutionize the inverse design of complex nanophotonic components. Here, we propose a novel variant of this formalism specifically suited for the design of resonant nanophotonic components. Typically, the first step of an inverse design process based on machine learning is training a neural network to approximate the non-linear mapping from a set of input parameters to a given optical system’s features. The second step starts from the desired features, e.g. a transmission spectrum, and propagates back through the trained network to find the optimal input parameters. For resonant systems, this second step corresponds to a gradient descent in a highly oscillatory loss landscape. As a result, the algorithm often converges into a local minimum. We significantly improve this method’s efficiency by adding the Fourier transform of the desired spectrum to the optimization procedure. We demonstrate our method by retrieving the optimal design parameters for desired transmission and reflection spectra of Fabry–Pérot resonators and Bragg reflectors, two canonical optical components whose functionality is based on wave interference. Our results can be extended to the optimization of more complex nanophotonic components interacting with structured incident fields.

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.