Wave propagation in nonlinear electromagnetic media

This brief tutorial review first discusses the physical origin of nonlinear electric and magnetic susceptibilities of electro-magnetic media, from the audio through the microwave to the visible range of the electromagnetic spectrum. Wave propagation in non-linear media can be described by a combination of Maxwell´s equations and the nonlinear constitutive equations. The Manley-Rowe relationships are verified for anisotropic lossless dielectrica. Microwave harmonic generation in ferrites and other materials, microwave modulation of light, light harmonic generation, light mixing and parametric conversion are all discussed from a general common viewpoint. The boundary conditions at the surface of a nonlinear medium lead to generalizations of the laws of reflection and refraction of light.