In this paper, we study in detail the optical properties of the Er and silicon nanocrystal doped fiber amplifier system in steady state case. This analysis is based on energy coupling between each silicon nanocrystal and the neighboring Er(+3)ions. Also, we consider the interaction between pairs of Er ions such as cooperative up-conversion mechanism and concentration quenching effect. The proposed method is used the rate equation as fundamental basis for description of the light interaction with nanocrystals and Er ions. We show that with introducing Si-nanocrystals into Er doped fiber, amplification process strongly improves and the fiber length of the fiber amplifier for a given gain is reduced compared to traditional cases. In this paper, limiting factor Kexiton governing the maximum number of exitons that can coexist within a single silicon nanocrystal, has been introduced and it is shown that in the case of Kexiton=2, optical gain is considerably increased.
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