wave number role intuition about the direction of special electromagnetic mode

Thread Starter

yef smith

Joined Aug 2, 2020
364
Hello, I am starting to simulation periodic floquet mode structures.
There is a trick i cant understand which links floquet mode nm to its angle.

i have simulated a structure and as you can see bellow an incident wave which falls on a tructure reacts with it and created two modes.
floquet mode 4 TM (0 1) and floquet mode 6 TM (0 -1) as shown in the table bellow.

I am triying to understand the link between the mode K number in each direction and the direction of beam.

In the last two photo there is an equation 2.41 .
we only have general expression like 2.48 and Pnm expression for the direction of the mode in the end.
Pnm=^X*kx_mn+^Y*ky_mn+^Z*kz_mn

How did they get the expresson for Pnm?
its like taken from nowhere.
Thanks.

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