In working on optical specifications for Megajoule, CEA's laser for inertial confinement fusion (ICF), we came to look closely at optical beam propagation in non-linear material. All materials are non-linear, in that their refractive index at each point is a function of the intensity of the propagating beam at that point. However, only at the high intensities encountered, for example, in ICF lasers does this behavior become noticeable. We show in this paper the effect of non-linearity on beam propagation, in a basic and graphical manner, using easily understood first principles. To this effect, we look at plane waves modulated by sinusoidal ripples. It is possible, with this simplified model, to compute the spatial frequencies of ripples that suffer high amplitude amplification, leading to optical component damage, and those that do not suffer such large amplification. We also highlight the close analogy between a sequence of laser slabs in a laser amplifier, and a sequence of layers in an optical thin film coating. This analogy helps us understand the small ripple gain function of a Megajoule amplifier.