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What is the definition of the scattering matrix of a unit cell in CST, HFSS and FEKO?

Giuda

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Dear Sirs,
I’ve a question related to the Transmission/Reflection coefficients or scattering parameters evaluated by CST, HFSS and FEKO.
In particular in Reflectarray as well as Metasurfaces design it is of interest to evaluate the scattering matrix of the unit cell.
Regarding the polarization aspects, the scattering matrix can be written in different forms. For instance we can have the form in the first image 1_cartesian.PNG, so that the scattering matrix is defined with reference to the cartesian components of the incident and reflected/transmitted field. This is option 1.
Other possible definitions can involve:
- spherical components: option 2, such as in the second image 2_spherical.PNG
- co-polar and cross-polar components: option 3, such as in the third image 3_coPol-crossPol.

Please can you clarify me which option is used by the softwares?
Actually I’ve seen that for FEKO in the .tr file the CoPol and CrossPol are reported: does it mean CoPol and CrossPol defined as the Ludwig III definition?
Thank you.
Regards,

1_cartesian.PNG

2_spherical.PNG

3_coPol-crossPol.PNG
 

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