Second-order nonlinear disordered photonic media

The field of complex photonics has garnered significant interest due to its rich physics and myriad applications spanning physics, engineering, biology, and medicine. However, a substantial portion of research focuses primarily on the linear medium. Over the years, optical nonlinearity, particularly the second order denoted as $χ^{(2)}$, has been harnessed for diverse applications such as frequency conversions, three-wave mixing, material characterizations, and bio-imaging. When $χ^{(2)}$-nonlinearity combines with the disorder, a new realm of physics emerges, which in the last 30 years has witnessed substantial progress in fundamental studies and futuristic applications. This review aims to explore fundamental concepts concerning $χ^{(2)}$-nonlinear disordered media, chart the field's evolution, highlight current interests within the research community, and conclude with a future perspective.