Optical amplifying fiber, optical fiber amplifier, and optical communication system

An optical amplifying fiber, comprising:

• a plurality of core portions including a rare earth element added therein;
• an inner cladding portion surrounding at least one core portion of the plurality of core portions, the inner cladding portion having a refractive index lower than a maximum refractive index of the at least one core portion;
• and
• an outer cladding portion surrounding the inner cladding portion, the outer cladding portion having a refractive index lower than the refractive index of the inner cladding portion,
• the inner cladding portion including different refractive index regions each having a refractive index different from a refractive index of a region adjacent to that different refractive index region, wherein
• when a wavelength of pumping light is 976 nm±2 nm, and a cladding absorption rate=−10×log ((power of the pumping light transmitted through and output from the optical amplifying fiber including the plurality of core portions (W))/(power of the pumping light incident on the inner cladding portion of the optical amplifying fiber including the plurality of core portions (W)))/a length of the optical amplifying fiber (m),
• the cladding absorption rate is 0.05 dB/m or higher.