# Second harmonic generation vs interference

## Main Question or Discussion Point

Hello,

I have a question about the mathematical expression of interference and second harmonic generation

If we have two waves $E_{1,2}(\Theta ,t) = E_{1,2}e^{j(\omega t + \Theta)} = \frac{1}{2}(E_{1,2}e^{j(\omega t + \Theta)} + c.c. )$

According to the Euler's formula. Now - both interference and second harmonic generation is connected to squaring the sum of the field and c.c. Interference is connected to the phase difference (I saw somewhere $\omega t$ being omitted when calculating the interference pattern) and if I square the $\omega t$ part, we have indeed second harmonic and some interference pattern because of that phase part.

Can anyone point to, or right down the second harmonic generation sort of equation also with phase information (interference) part ? I am a bit lost in this and would like that someone clear that for me.