This is a brief introduction to the ideas and phenomena that occur in the nonlinear optics of photonic crystals and meta-materials. These are illustrated within the context of simple models that 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.