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let's consider the so called dielectric slab waveguide (references for image and equations: here, page 53):

enter image description here

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:

enter image description here

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?

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1) this is as an ideal structure to teach the basics of propagation inside a dielectric slab. The real guiding structure of course has walls if one wants to embed it in a photonic chip
2) This ideal structure is the same along the x axis. So there cannot be variations of the electric field along this axis. The same does not apply to the y axis

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  • \$\begingroup\$ About 2), why cannot be for instance a wave behaviour along x axis (like waves that propagate in a generic homogeneous medium)? \$\endgroup\$
    – Kinka-Byo
    Apr 14 '20 at 15:07
  • \$\begingroup\$ X and Z axis can be treated in the same way as they are both infinite in extent and so they can both serve the purpose of teaching the physics of propagation. And one wants to transfer a light signal in a straight line. Name this line x or z axis. \$\endgroup\$ Apr 14 '20 at 15:16
  • \$\begingroup\$ But why is there dependence on z and not on x, if x and z are equal? \$\endgroup\$
    – Kinka-Byo
    Apr 14 '20 at 15:37
  • \$\begingroup\$ Because one inserts a light signal in the slab in such a way so as to propagate along the z axis. It has to have sone resemblence to a real guide. \$\endgroup\$ Apr 14 '20 at 15:44

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