RCWA derivation steps in Soifer diffraction grating analysis

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Krzysztow
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Hi,

Recently I'm trying to understand some explanation of RCWA, which introduces to computational analysis of diffraction grating efficiences. For explanation I use Soifer book, but cannot understand or don't agree with it. I tried to understand the derivation, not to write it straightforward into Matlab but understand as well. And I found that my derivation doesn't agreefully with the book. Can You explain to me:
1) how one can get from the set of equations 3.138 & 3.139 to the set 3.140 & 3.141. I got something for 3.140 like in equation (*).
2) where did He get set 3.150 from? It seems as if assumption (**) or (3.127) is not valid anymore. However then He shouldn't write 3.152.
If assumption (3.127) is valid for modulation zone, then result for coefficients is given by (***)

Please, help me. It's not I want anyone to do my work. I just dwell for too long on it. Thank in advance!
 
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7th, 8th and 9th pages
 
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10th and 11th and (*)
 
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(**) and (***)
 
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