Itís very well know that Maxwell equations bring the solution for plane waves but as far as I know I cannot use them to detect how the field would evolve by only looking the E and B fields on the contour of the point under evaluation. Is that possible?
My question comes because on a plane wave, if we look at some point, all the points on the same plane of propagation that the point under study have the same phase, the same amplitude and they propagate on the same direction so this must be the reason the field doesnít decrease as it propagates.
On the other hand, on a spherical wave, the contour of a point in the plane parallel to the (local) direction of propagation will have the same amplitude but different direction. I suppose this difference between these two types of waves is what makes spherical waves to decrease whereas plane waves donít.
Does somebody know if there are some equations that can locally explain this?