Abstract: By heat treating a glass member containing at least one kind of cation to constitute a modifying oxide in contact with a source of another kind of cation to cause ion substitution, a light-conducting glass structure can be produced to have a refractive index distribution wherein the index varies progressively transversely to the intended light path, which is thereby bent toward the direction of increase of the index, such a light-conducting glass structure is not accompanied by differences or lagging of phase velocities of conducted light rays, spreading of the light flux width, and reflection losses.