Analytically Supported Hybrid Photonic–plasmonic Crystal Design Using Artificial Neural Networks

An analytical and numerical study of hybrid photonic–plasmonic crystals is presented. The proposed theoretical model describes a system composed of a dielectric photonic crystal on a metallic thin film. To show the validity and usefulness of the model, four particular structures are analyzed: a one-dimensional crystal and three lattices of two-dimensional crystals. The model can calculate the photonic band structure of photonic–plasmonic crystals as a function of structural characteristics, showing two partial bandgaps for a square lattice, and complete bandgaps for triangular lattices. Furthermore, using a particular high-symmetry path, a full bandgap emerges in rectangular lattices, even with a small refractive index contrast. Using the analytical model, a dataset is generated to train an artificial neural network to predict the center and width of the bandgap, that is, the forward design. In addition, an artificial neural network is trained to tune the optical response, that is, to perform the inverse design. The analytical results are consistent with the physics of the system studied and are supported by numerical simulations. Moreover, the prediction accuracy of the artificial neural networks is better than 95%. Overall, this paper reports a useful tool for tuning the optical properties of hybrid photonic–plasmonic crystals with potential applications in waveguides, nanocavities, mirrors, etc.