Intro to Nonlinear Optics: (I) Classical Derivation of Susceptibility and Polarization

Here I introduce the concepts of electrical susceptibility and polarization. The Lorentz model assumes electrons behave as classical harmonic oscillators and will follow an electromagnetic field at the same frequency. I use this model to set up the driven damped harmonic oscillator equations with added anharmonic terms aka driven dampened anharmonic oscillator. The equation can be solved with the aid of perturbation theory to derive the classical susceptibility. Everything I say here is based on my understanding from Nonlinear Optics by Boyd and Molecular Spectroscopy by Mchale.

[janda]

isn't epsilon 0 the vacuum PERMITTIVITY?