An optical fiber includes a core region having a longitudinal axis. At least a portion of the core region has a substantially helical shape about a helical axis. The longitudinal axis may be substantially tangential to a helical bend in the optical fiber. A cladding region surrounds the core region. The core region and cladding region may be configured to support and guide the propagation of signal light in a fundamental transverse mode in the core region in the direction of the longitudinal axis. The fiber has a bend-induced gradient in its equivalent index of refraction over the portion of the core region. The fiber has a bend-induced equivalent index of refraction. At least a portion of cladding region has a graded refractive index opposite that of the bend-induced gradient. The cladding region may be configured to have a substantially flat equivalent index in response to a helical bend of the optical fiber.