Inverse design in photonic crystals

Photonic crystals are periodic dielectric structures that possess a wealth of physical characteristics. Owing to the unique way they interact with the light, they provide new degrees of freedom to precisely modulate the electromagnetic fields, and have received extensive research in both academia and industry. At the same time, fueled by the advances in computer science, inverse design strategies are gradually being used to efficiently produce on-demand devices in various domains. As a result, the interdisciplinary area combining photonic crystals and inverse design emerges and flourishes. Here, we review the recent progress for the application of inverse design in photonic crystals. We start with a brief introduction of the background, then mainly discuss the optimizations of various physical properties of photonic crystals, from eigenproperties to response-based properties, and end up with an outlook for the future directions. Throughout the paper, we emphasize some insightful works and their design algorithms, and aim to give a guidance for readers in this emerging field.