An optical fiber includes a core region having a longitudinal axis. A cladding region surrounds the core region. The core region and cladding region are configured to support and guide the propagation of signal light in a fundamental transverse mode in the core region in the directions of the axis. The fiber has a bend-induced gradient of its equivalent index of refraction indicative of a loss in guidance of the mode. At least a portion of cladding region has a graded index of refraction opposite the bend-induced gradient. The cladding region is configured to have a substantially flat equivalent index in response to a bend of the optical fiber.