Abstract
Nonlinear effects in erbium-doped fibre amplifiers are analysed by a numerical approach based on the combined use of the finite element method and the Runge-Kutta algorithm. In particular, the variation of the refractive index due to the perturbation in the gain coefficient is evaluated through the nonlinear Kramers-Kronig relations. For the first time the nonlinear coefficients of the polynomial expansion of the refractive index variation have been calculated. Several kinds of perturbation, produced by signal and pump intensity, by amplifier length and by dopant concentration have been considered to investigate the refractive index change behaviour. The use of the finite element method allows the local evaluation of the pump and signal intensities without introducing any simplifying hypothesis on the electromagnetic field distribution.
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