A method of making an OLED device of the type shown in FIG. 2 is illustrated schematically in FIG. 7. In this method, the ink composition 400 for making the higher RI structures of the sub-domains and the ink composition 602 for making the first domain are designed such that they wet the surface of first inorganic barrier layer 108 similarly to form a planar coating on the surface, but do not substantially intermix within the coating. Droplets of the ink compositions 600 and 602 can be printed (either simultaneously or sequentially) onto first inorganic barrier layer 108 without curing in between the printing steps (panels (a) and (b)) and the coating can then be cured, whereby cylindrical sub-domain structures (or features resembling cones) 114 laterally encased in a polymeric layer of the first domain 110 are formed, followed by the deposition of second inorganic barrier layer 108A (panel (c)). In this method, some intermixing between the ink compositions is allowable, provided that the intermixing zones are relatively small and the RI contrast between the two domains is preserved.