An organic light emitting diode (OLED) device having enhanced light extraction, comprising: an upper waveguide structure that supports first guided modes and comprising a cathode , an anode with a lower surface , and an organic light-emitting semiconductor material interposed between the cathode and the anode ; a lower waveguide structure interfaced with the upper waveguide structure and that supports second guided modes matched to the first guided modes , the lower waveguide structure comprising a substrate having an upper surface , a light-extraction waveguide distributed over the upper surface of the substrate , and a light-extraction matrix distributed over the light-extraction waveguide and the upper surface of the substrate ; wherein the light-extraction matrix includes a rough upper surface that interfaces with the lower surface of the anode and that facilitates mode coupling from the first guided modes of the upper waveguide structure to the second guided modes of the lower waveguide structure while avoiding coupling from the first guided modes to surface plasmon polaritons; wherein light traveling as second guided modes in the light-extraction waveguide of the lower waveguide structure is redirected to exit the lower surface of the substrate by light-redirecting features of the lower waveguide structure ; characterized in that the rough upper surface has a periodic component with a peak-to-valley amplitude A and a period P, wherein 0.5 μm ≤ P ≤ 2 μm, and wherein 20 nm ≤ A ≤ 60 nm; and the rough upper surface has a random component defined by a root-mean-square (RMS) surface roughness σ 33 , wherein 5 nm ≤ σ 33 ≤ 25 nm. an upper waveguide structure that supports first guided modes and comprising a cathode , an anode with a lower surface , and an organic light-emitting semiconductor material interposed between the cathode and the anode ; a lower waveguide structure interfaced with the upper waveguide structure and that supports second guided modes matched to the first guided modes , the lower waveguide structure comprising a substrate having an upper surface , a light-extraction waveguide distributed over the upper surface of the substrate , and a light-extraction matrix distributed over the light-extraction waveguide and the upper surface of the substrate ; wherein the light-extraction matrix includes a rough upper surface that interfaces with the lower surface of the anode and that facilitates mode coupling from the first guided modes of the upper waveguide structure to the second guided modes of the lower waveguide structure while avoiding coupling from the first guided modes to surface plasmon polaritons; wherein light traveling as second guided modes in the light-extraction waveguide of the lower waveguide structure is redirected to exit the lower surface of the substrate by light-redirecting features of the lower waveguide structure ; characterized in that the rough upper surface has a periodic component with a peak-to-valley amplitude A and a period P, wherein 0.5 μm ≤ P ≤ 2 μm, and wherein 20 nm ≤ A ≤ 60 nm; and the rough upper surface has a random component defined by a root-mean-square (RMS) surface roughness σ 33 , wherein 5 nm ≤ σ 33 ≤ 25 nm. <EOS>