Nonlinear topological photonics

The recent discovery of topological insulators had a remarkable impact on several fields of natural science, including condensed matter physics, optics, acoustics, and elastic waves. In the general context of optics, topological photonics is the discipline concerned with the investigation of the optical characteristics of topological insulators. Due to its remarkable, unusual features, including the robustness of wave dynamics against disorder and defects, topological photonics has attracted significant research efforts at fundamental science level and also spurred a broad range of important applications. Despite the fact that the main research efforts in this field were focused mostly on topics pertaining to linear topological photonic systems, in recent years we have witnessed a series of key advancements in nonlinear topological photonics. In this chapter, we survey these recent developments that have taken place in several areas of nonlinear topological photonics. Our review is divided into three main parts. In the first part, we briefly introduce the background knowledge and some basic concepts required to easily grasp the main ideas pertaining to linear and nonlinear topological photonics. In the second part, we introduce several ideas and phenomena specific to nonlinear optics, including frequency conversion, light-matter interaction in the nonlinear regime, and soliton propagation, and highlight how they manifest when the topological properties of a photonic system are considered. In the last part of the chapter, we present and discuss potential applications of nonlinear topological photonics.