A fiber stub assembly is provided that has a cladding layer that is reduced in diameter near the end of the stub into which light is launched from a light source. The portion of the stub having the cladding layer with the reduced diameter is surrounded by a light-absorbing material that is in contact with the inner surface of the ferule and with the outer surface of the cladding layer. The light-absorbing material and the outer surface of the cladding layer have indices of refraction that are matched, or very close to one another, such that any modes of light that are propagating in the cladding layer that impinge on the interface propagate into the light-absorbing material and are absorbed thereby. The reduced diameter of the cladding layer and the surrounding light-absorbing material form a pin hole opening through which light is received. The pin hole opening makes it possible to use a simple ball lens to focus light from the light source into the end of the fiber stub to thereby reduce the number of modes that are dispersed into the cladding layer.