Inverse design of topological photonic time crystals via deep learning

Photonic time crystals are a new kind of photonic system in modern optical physics, leading to devices with new properties in time. However, so far, it is still a challenge to design photonic time crystals with specific topological states due to the complex relations between time crystal structures and topological properties. Here, we propose a deep-learning-based approach to address this challenge. In a photonic time crystal with time inversion symmetry, each band separated by momentum gaps can have a non-zero quantized Berry phase. We show that the neural network can learn the relationship between time crystal structures and Berry phases, and then determine the crystal structures of photonic time crystals based on given Berry phase properties. Our work shows a new way of applying machine learning to the inverse design of time-varying optical systems and has potential extensions to other fields, such as time-varying phononic devices.