Rare-earth doped optical fiber, method of producing the same, and fiber laser

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A rare-earth doped optical fiber that includes a core and one or more clad layers surrounding the core, in which the core has a rare earth dopant, and a relationship of Equation (1) is satisfied : 0 < ∫ r 0 r c ⁢ D ⁡ ( r ) · P p 2 ⁡ ( r ) · P s 2 ⁡ ( r ) ⁢ r ⁢ ⁢ ⅆ r ∫ r 0 r c ⁢ D ⁡ ( r ) · P p 2 ⁡ ( r ) ⁢ r ⁢ ⁢ ⅆ r ≤ 0.35 ( 1 ) where Pp(r) represents an electric field distribution in an exciting wavelength, Ps(r) represents an electric field distribution in wavelengths of spontaneous emission and/or stimulated emission carried in the core, D(r) (mass %) represents a rare-earth dopant distribution, ro represents a core center, and rc represents a core radius.