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?
 A: Your observation is correct. For two coherent waves there is a z-component of momentum density. Note that it vanishes on average.
Extension:
Let me explain. We are superposing to plane waves. Your picture shows the situation only in one point and at one time. There are also points where ${\bf E}$ and ${\bf E'}$  are (anti-)parallel and the z momentum component vanishes. In other points ${\bf E}' \times {\bf B}$, or ${\bf E} \times {\bf B'}$, points in the -z direction. The average of $P_z$ over a square of sides $\lambda$ in the xy plane vanishes.
More generally, you should consider the full energy-momentum distribution. The contribution of the cross terms ${\bf E} \times {\bf B'}$ and ${\bf E}' \times {\bf B}$ to this energy-momentum distribution average to zero.
Note that at every point and time the energy-momentum is conserved. Specifically, the rate of change of momentum equals the divergency of the stress.
In conclusion, all things add up. Still your observation remains interesting as it point out a paradoxical, physically inconsequential, interaction between the two waves.
