let's consider the so called dielectric slab waveguide (references for image and equations: here, page 53):
I do not know much about it, I know only that it is a planar guiding structure which is used in optics. It is made of two or more dielectrics, in these case there are two layers of different dielectrics, and then a layer of air with infinite height.
I have some questions about this kind of structure:
1) As you may see, the structure is semi-infinite along y axis. But what about the other axis? Is this structure, ideally, infinite along x and z, or are there some "walls"? It is important for me to know this because it determines different boundary conditions for EM field.
2) Now let's consider the following equations which describe the electric field inside each region:
You may see that all the fields depend on z and on y, but not on x. Can you explain me the reason of this?