By optimizing the refractive index profile, the absorption coefficient of a rare earth element doped optical fiber can be enlarged and nonlinear effect can be suppressed. Thus, according to the present invention, the optical fiber, which is suitable for wide band optical amplification, can be realized. Moreover, in the present invention, the optical fiber of W-shape profile comprising a core, the first cladding having a refractive index smaller than that of said core surrounding said core, and the second cladding having a refractive index smaller than that of said core and larger than that of said first cladding surrounding said first cladding is prepared and are suitable for the wide band optical amplification. That is, since in the rare earth element optical fiber of this W-shape profile, both the absorption coefficient of a rare earth element, and the absolute value of chromatic dispersion can be increased greatly as compared to the optical fiber of the conventional step index profile and nonlinear effect can be suppressed more efficiently, an optical fiber which is suitable for further wide band optical amplification, is realizable.