@ 0:40 Once again, the E-field must be multiplied by the vacuum permittivity too. Source: en.wikipedia.org/wiki/Electric_susceptibility#Nonlinear_susceptibility
In this lecture: •Polarization in the material due to weak electric field is analogous to the harmonic oscillator. •Polarization in the material due to strong electric field have a much more general expression which can be obtained by expansion formula. •the electric susceptibility (degree of polarization of dielectric material in response to the applied electric field) is a tensor quantity. •Electric susceptibility is a complex number. Real part corresponds to the refractive index and the imaginary part corresponds to absorption coefficient. •Being in the linear optical regime means the superposition principle (electric field don't talk to each other) is being followed. If the superposition principle is not followed, then we are in nonlinear optical regime.