Nonlinear polarization ($P_i^{(2)}={ϵ}_0{\sum }_{jk}{\chi }_{ijk}^{(2)}{E}_j{E}_k$)

Nonlinear polarization is the part of an induced electric polarization nonlinear in the driving electric field. A quadratic response multiplies field components, creating sums and differences of their frequencies; second-harmonic generation is the equal-frequency sum case. Conversion strength also depends on phase matching and the material response.