In a linear optical system, the polarization of the material is directly proportional to the electric field of the light. However, in a nonlinear optical system, the polarization P can be expressed as: \[ P = P_0 + \chi^{(1)}E + \chi^{(2)}E^2 + \chi^{(3)}E^3 + \dots \] Here, \( \chi^{(1)} \) is the linear susceptibility, while \( \chi^{(2)} \) and \( \chi^{(3)} \) are the second- and third-order nonlinear susceptibilities, respectively. These higher-order terms lead to various nonlinear effects, including Second Harmonic Generation (SHG) and Third Harmonic Generation (THG).
