The phase shift that the erbium-doped fiber amplifiers induce

The nonlinear Schroedinger equation in erbium-doped fiber and the more generalized form of the propagation equation in the erbium-doped fiber amplifiers are obtained which have included the phase shift that the erbium ions induce. An analytical expression is given to the erbium ions induced phase shift and frequency chirp. It was found that the frequency chirp dose not change much with the wavelength except at the neighboring wavelengths (around 1.531 mum)where the absorption and the emission cross-sections of the erbium ions reach their maximum, and the frequency chirp has opposite sign on the two sides around 1.531 mum.