Disclosed is an optical device for a display having a tapered waveguide and a method of fabricating such devices. In order to reduce light absorption inside the waveguide, a light-absorbing material is coated on the front surface only of the optical device Alternatively, a space adjacent to the waveguide is coated with a material having a refraction index different from the waveguide, preferably, lower than that of the waveguide and then filled with a light-absorbing material. In addition, a large- and uniform-sized light-absorbing material may be filled in the space. The optical device has an improved light efficiency, and thus exhibits an excellent luminance, as compared with the conventional ones, when using an identical light source. Furthermore, the fabrication method can produce such optical devices in a simplified manner, thus improving production efficiency.