Rigorous Coupled Wave Analisys - help

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The discussion revolves around understanding the derivation of equations related to the Rigorous Coupled Wave Analysis (RCWA) for diffraction grating efficiencies, specifically from Soifer's book. The user seeks clarification on how to transition from equations 3.138 and 3.139 to 3.140 and 3.141, noting discrepancies in their own derivation. Additionally, there is confusion regarding the origin of equation 3.150 and the validity of assumption (3.127) in the context of modulation zones. The user emphasizes a desire for comprehension rather than simply seeking solutions, indicating a deep engagement with the material. Assistance is requested to resolve these specific mathematical concerns.
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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