This is a brief introduction to the ideas and phenomena that occur in the nonlinear optics of photonic crystals and metamaterials. These are illustrated within the context of simple models which provide an easy understanding of the physical phenomena that are important in these two rapidly developing areas of nano-photonic technology.

An introduction and discussion of some of the basic principles of linear and nonlinear optical nano-systems are given. The focus is on engineered optical systems that have been of recent interest in physics, engineering, and applied mathematics for their opto-electronic applications. These include photonic crystals and meta-materials, and in the following discussions the operating principles of photonic crystals and meta-materials are outlined.