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Fiber optic amplifier (1) with a doped annulus comprises a monomode core (10) surrounded by a multimode core (20). The multimode core contains a doped layer, the doped annulus, (21) having a certain concentration of active rare earth ions (6), for an amplification by active rare earth ions of at least one optical signal injected into the fibre amplifier. The fiber is dimensioned such that the product of its length by its Raman efficiency may be greater than or equal to 0.5 W-1> and the fiber has an absorption defined by a coefficient of absorption expressed in dB/m which presents at a certain wave length a maximal absorption value, the cumulated absorption, that corresponds to the product of the length by the maximum absorption, that is greater than or equal to 100 dB. An independent claim is also included for an amplifier incorporating this fibre optic amplifier.