Phase matching for a quadratic wave interaction
= Phase matching for a quadratic wave interaction
A resonant interaction requires matching both <wavenumber> and <angular frequency>: $k_3=k_1+k_2$ and $\omega_3=\omega_1+\omega_2$ for a sum interaction, with corresponding sign changes for differences. A common <phase velocity> alone does not guarantee that a generated harmonic lies on the <dispersion relation>.