An inhomogeneous theory for the analysis of an all-optical gain-stabilized multichannel erbium-doped fiber amplifier in the presence of ion pairs

In this paper the gain dynamics of an all-optical gain-clamped multichannel erbium-doped fiber amplifier (EDFA) with an inhomogeneous active medium in the presence of ion pairs is modeled. A two-level model for single ions and a three-level model for ion pairs are used to drive the propagation and rate equations of inhomogeneous laser medium. The governing equations are an uncountable system of partial differential equations (PDEs). Using the moment method, the system of PDEs is converted to a finite system of ordinary differential equations (ODEs). The solution of the system of ODEs is used to analyze the gain dynamics of all-optical gain-stabilized multi-wavelength heavy doped EDFA. Theoretical results are in good agreement with the published experimental results.