Introduction
In the Lorentz model we saw how we can study the interaction between and electro-magnetic wave and a medium considering only the linear effects of the interaction. While this case is the most common, it doesn’t allow to describe some phenomena that involve very high fields. In order to do this we need to introduce some non-linearity in the system.
One of the most intuitive effects of non linear media is that they can, for example, change the color of light, in the Lorentz model this was not possible, since the only changes that light could experience were a change in amplitude or velocity.
Anharmonic oscillator
A first way to introduce the non linear component is to modify the Lorentz model and add a quadratic dependence on the position: