Systems and methods are described for fabricating a varying-waveguide optical fiber. In one described method, a preform is fabricated having a core and at least one cladding region. The cladding region has a higher viscosity and the core region has a lower viscosity. The relative viscosities of the cladding region and core are chosen such that, when tension is applied to an optical fiber drawn from the preform, the applied tension is primarily borne by the cladding region thereby causing a viscoelastic strain to be frozen into the cladding region, while creating a minimal viscoelastic strain in the core. The method further includes drawing the preform into an optical fiber under an applied tension, such that a viscoelastic strain is frozen into the cladding region the frozen-in viscoelastic strain decreasing the cladding region refractive index. The cladding region refractive index is changed in a section of the optical fiber by heating the section so as to relax the viscoelastic strain frozen into the cladding region in the section of fiber, thereby increasing the cladding region refractive index in the section of fiber.