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I really don't know if this is the right forum to ask the question...but please help me if you can!!

I was going through the Plane Wave Expansion Method Derivation...But to be honest I could not find any step by step proof of this method. (If you provide me one!! I would be thankful)

Next coming to the derivation given in the link below, while going through the derivation, I could not understand where come the components $G_i + G_{i'} \rightarrow G_{i'}$ could be written, and similarly the lines which follow it. Similarly ,how do we introduce $G_i,\ G_{i'},\ G_{ii}$...

It would be really helpful if anybody could help me out on this one...

Lastly I would also appreciate if anyone could just typeset the question properly as I am new here!!

PWM Manual

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  • $\begingroup$ As per the plane-wave expansion: please see the third section of this pdf and let me know if you have any questions about the derivation. I would be happy to clarify any specific questions, but do not want to type out what is already nicely done here. Also, in the second part, do you mean $G_i,\ G_{i'},\ G_{i''}$ ? $\endgroup$
    – codeAndStuff
    Commented Sep 30, 2013 at 17:47
  • $\begingroup$ Yes!! I mean $G_i,\ G_{i'},\ G_{ii}$ what does that actually mean?? Also i would like to know its physical interpretation of the $G_i,\ G_{i'},\ G_{ii}$ would really appreciate your help!! $\endgroup$
    – user93470
    Commented Oct 5, 2013 at 9:08

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The term $G_{i} + G_{i'} \rightarrow G_{i'}$ in the manual can be used because the structure which is under analysis is a periodic multi layered structure.Due to its periodicity the different indexes of summation can be grouped and coupled or reduced to a single summation index.

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