Fresnel reflection coefficient for Second Harmonic Generation (SHG)

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Discussion Overview

The discussion centers on the Fresnel reflection coefficient in the context of Second Harmonic Generation (SHG) and its application in determining the thickness of a GaN crystal. Participants are exploring the theoretical underpinnings of a transmission coefficient defined in a specific article and seeking sources for its derivation.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant is investigating a Fresnel-like transmission coefficient for SHG as defined by J. Jerphagnon and S. K. Kurtz, questioning why it is not the absolute value squared.
  • Another participant requests a proper citation for the article referenced, indicating a need for clarity on the source material.
  • A third participant provides a link to the article, suggesting it may contain relevant information.
  • Some participants discuss the necessity of including both refractive indices at frequencies ω and 2ω in the coefficients, noting the complexity due to bound and free waves having different refractive indices.
  • One participant expresses difficulty in finding a source that deduces the result related to the transmission and reflection coefficients.
  • A later reply mentions that the derivation can be found in Appendix A of the referenced paper, indicating a potential resource for the original inquiry.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the derivation of the transmission coefficient, with multiple viewpoints and requests for clarification remaining unresolved.

Contextual Notes

Limitations include the lack of clarity on the derivation of the transmission coefficient and the dependence on specific definitions of refractive indices at different frequencies.

Jose Antonio
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Hello everyone, this is my first post so I don't know whether or not this is the right thread to be asking this question (if so I am sorry). I am currently working on my thesis where I am determining the thickness of a GaN crystal through second harmonic generation. However in a article published by J. Jerphagnon and S. K. Kurtz, they defined a Fresnel-like transmission coefficient for the second harmonic signal as:

Screenshot_from_2016_09_01_10_36_54.png


I was wondering if anyone knew a source of how to get this result. I am intrigued on why this transmission coefficient is not the absolute value squared (since it is a capital T) since one could be considering the complex form of the refractive indices. Thanks in advance for any response!
 
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Jose Antonio said:
However in a article published by J. Jerphagnon and S. K. Kurtz,

Could you please post a proper citation for the above? Thanks in advance.
 
I do understand that both transmission and reflection coefficients do somehow need to include both refractive indices at frequencies ω and 2ω, since the bound and free waves have different refractive indices and the solution of the inhomogeneous solution is the sum of the homogeneous solution (free wave) and particular solution (bound wave), however I can't seem to find any source where this result is deduced (and I certainly do can't find a way to find it myself).
 
Last edited:
Jose Antonio said:
I do understand that both transmission and reflection coefficients do somehow need to include both refractive indices at frequencies ω and 2ω, since the bound and free waves have different refractive indices and the solution of the inhomogeneous solution is the sum of the homogeneous solution (free wave) and particular solution (bound wave), however I can't seem to find any source where this result is deduced (and I certainly do can't find a way to find it myself).

Yeesh... rough paper. Looks like the derivation is in Appendix A.
 

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