I'm refering here to Taflove's "computational electrodynamcis, 3rd ed."
Let us assume that the structure being modeled extends to infinity in the z-direction with no change in the shape or position in its transverse cross section. If the incident wave is also uniform in the z-direction, then all partial derivatives of the fields with respect to z must equal zero...
I don't quite understand why the wave should be uniform along z? How could you justify this assumption? Wave's have a finite wavelength, even within media which implies that they vary with respect to position.
BTW: It seems like this paragraph is also cited in another textbook: