An optical device having a surface in a silicon carbide or gallium nitride material is provided, the optical device having a non-periodic nano structure formed in the surface, the nano structure comprising a plurality of cone shaped structures wherein the cones are distributed non-periodically on the surface. The plurality of cone shaped structures have a random height distribution and at least a part of the cone shaped structures have a height of at least 100 nm. The nonperiodicity ensures a uniform spatial light distribution after light exits out of the chip. A method of manufacturing a non-periodic nano structured surface on an optical device is furthermore provided, the method comprising the steps of providing a silicon carbide or gallium nitride device,forming a thin film of a masking material on at least a part of the substrate, treating the thin film to form nano islands of the thin film material, etching the substrate in a mostly anisotropic etch and concurrently etching at least a part of the thin film masking material to form a non-periodical nano structure, the nano structure comprising a plurality of cone shaped surface structures. The optical device may comprise a white LED or a wavelength converter for a white light source.