Nonlinear waves and computational photonics

Since the time of Newton, physicists have often pictured the world as empty space populated by bodies that interact through forces. Waves, described around the same era by Huygens, do not fit easily into this view. An ideal wave is a periodic process: it is not localized, does not obey Newton's laws, and seems to be almost opposite to a particle. Yet in many physical situations, such as ripples on the surface of water or electromagnetic fields in laser devices, it is natural to think in terms of a medium filled with waves that propagate, interact with material objects, and even influence one another. In this talk, we explore several intriguing types of wave interactions in optical systems, introduce the physical phenomena they produce, and explain how physicists describe and calculate them.