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Interpretation of am and bm of Lumerical's Mode Expansion Monitors and relation witn S-Parameters in a dual port network

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peponas

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Hello,

According to Lumerical's help for the mode expansion monitor, am and bm coefficients represent complex transmission coefficient for mode m. However such and explanation is not clear to me enough. My first question is how these coefficients are related to the scattering matrix? Can we safely say that for mode m, in a structure where we excited mode n (above cutoff) the S11,m for example is |am|/|an|? What these coefficients exactly represent?
My second question is what happens if we choose to include in the mode analysis, modes below cutoff. Are these relations also hold?

Thank you in advance for your time!

The afforementioned page: https://support.lumerical.com/hc/en...ing-and-understanding-Mode-Expansion-Monitors
 
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