Why for arbitrary high input power the gain saturates in EDFA (erbium-doped fiber amplifer)?
For arbitrarily high input power? Seems like you've answered your own question.
Can you provide a pointer to information about the EDFA you are using, and be more specific about the power levels you want to run at?
I'm interested more in physical background. Why in saturated gain region gain is lower than in unsaturated (small signal) gain region. what happens with population inversion?
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