Nonlinear refractive index in erbium-doped optical amplifiers

Influence of bidirectional pumping in high-power EDFA on single-channel, multichannel and pulsed signal amplification

“…n 2 , evaluated as the second-order term in the above expansion, for a fibre length of 5 m at a pump power of 50 mW at 980 nm and with signal at 1535 nm is 1.269 × 10 −17 m 2 W −1 , which is about three orders of magnitude larger than the nonlinear index coefficient of a conventional fibre [29]. n 2 is found to monotonously increase with the dopant concentration, till a maximum value is reached at a concentration of 1.05 × 10 25 ions m −3 , beyond which it is found to decrease [29]. It is also found to increase linearly with the signal and pump intensities.…”

“…where σ a (ω) and σ e (ω) represent the wavelength dependent absorption and emission cross-sections of the fibre, while N 1 and N 2 are the population densities of the ground and excited states [29]. Any change in α is accompanied by a change in the refractive index.…”

“…Any change in α is accompanied by a change in the refractive index. Nonlinear Kramer-Kronig relations [29][30][31] can be used to relate the change in refractive index ( n) to the change in the absorption coefficient ( α), caused due to some perturbation, ξ , as…”

“…Betts et al [32] and Montagna et al [29] propose a polynomial expansion for n in terms of the signal intensity, considering only the variation in the signal power as the source of perturbation. n 2 , evaluated as the second-order term in the above expansion, for a fibre length of 5 m at a pump power of 50 mW at 980 nm and with signal at 1535 nm is 1.269 × 10 −17 m 2 W −1 , which is about three orders of magnitude larger than the nonlinear index coefficient of a conventional fibre [29]. n 2 is found to monotonously increase with the dopant concentration, till a maximum value is reached at a concentration of 1.05 × 10 25 ions m −3 , beyond which it is found to decrease [29].…”

“…(1) is solved numerically with a GVD parameter of −20 ps 2 km −1 and n 2 of 3.2 × 10 −18 m 2 W −1 . The value of n 2 is chosen to be two orders of magnitude greater than an ordinary fibre from earlier work [29]. The longitudinal and transverse variation of n 2 is not considered since the motivation of this simulation is to emphasise the need to treat unidirectional and bidirectional pumping differently with regard to pulse propagation.…”