# Superposition of two electromagnetic waves and momentum

Electromagnetic waves follows superposition principle. So that we can simply add the fields of waves to calculate the final field. Then let's think there are two waves that are moving through x-axis and y-axis. If we control the phase difference well, we can make a situation like figure.

In the figure with some $$t=t_0$$, you can see that there is a poynting vector has a z-axis component. In initial condition, there was no z-axis component of momentum. This doesn't seem right.

What did I miss?(or miscalculated) Why there is a strange momentum out there?

edit: I thought that if two coherent lights have identical frequency, the direction of poynting vector will be always +z. So that the z-component doesn't vanish in average. Is there something wrong with my thoughts?

• Don't quite understand why it vanishes on average. Assuming the waves have the same frequency, when the phase changes by $\pi$ all the E and B arrows reverse. Doesn't that leave the direction of the Poynting vector unchanged? – Philip Wood Jul 31 at 21:01