| CPC G02B 27/0994 (2013.01) [C03B 37/02745 (2013.01); G02B 6/0286 (2013.01); G02B 6/4206 (2013.01); C03B 2203/26 (2013.01)] | 11 Claims |

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1. An optical fiber, comprising:
an input end;
an output end;
a core having a non-linear refractive index profile (RIP) that decreases from a first refractive index no at an axis of the fiber to a second refractive index at an outer circumference of the core according to a non-quadratic function
n(r)=n0−Arα
wherein n(r) is a refractive index at a radius r,
wherein the radius r is measured from the axis of the optical fiber,
wherein A is a positive scaling constant, and
wherein α is an exponent larger than 1, smaller than 3, and not equal to 2; and
a cladding surrounding the outer circumference of the core, the cladding having at least a third refractive index, smaller than the second index,
wherein, between the input end and the output end, the non-linear RIP rotationally and longitudinally homogenizes input light, input at the input end, to create output light, output at the output end, and
further wherein:
the core comprises a dopant,
the core is manufactured from a plurality of fibers,
the plurality of fibers comprise the dopant associated with a distribution of the exponent α characterized by a mean value μ and a standard deviation σ, and
the mean value μ of the exponent a deviates from two by more than two standard deviations σ.
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