Theoretical analysis of spectral hole burning and relaxation oscillation in all-optical gain stabilized multichannel erbium-doped fiber amplifier (EDFA)

The spectral hole burning effects and gain dynamics of all-optical gain clamped multichannel erbium-doped fiber amplifiers (EDFAs) are modeled. The two-level laser model is used to write the propagation and rate equations of the inhomogeneous laser medium. The governing equations are an uncountable system of partial differential equations (PDEs). After some mathematical manipulations, averaging over the fiber length and introducing an approximation method, the system of PDEs is converted to a finite system of ordinary differential equations (ODEs). The gain dynamics and hole burning of an all-optical stabilized multiwavelength EDFA and the transient response of an optical fiber inverter are analyzed by the solution of the system of ODEs. Theoretical results are in good agreement with the published experimental result.