Fig. 2: OLED and outcoupling structure design strategy.

a Cones of rays emanating with a polar angle of \({\theta }_{{{{\rm{sub}}}}}\) from different parts of the emission aperture. Here, \(S\) is the length of the overlap between the RA and the ray cone. b Cross-sectional view of the apertures, ray cones, and the OLED. c The ATW for systems with different aperture ratios. Here, \({t}_{{{{\rm{sub}}}}}/{r}_{{{{\rm{EA}}}}}\) is fixed to 1.4 and both emission and reception apertures are assumed to be circular with an overlapped centrosymmetric axis. d–f Global optimization of the OLED structure that maximizes, \(\int {I}_{{{{\rm{out}}}}}\left({\theta }_{{{{\rm{out}}}}}\right)\sin {\theta }_{{{{\rm{out}}}}}d{\theta }_{{{{\rm{out}}}}}\) (d), \(\int {I}_{{{{\rm{to}}}}-{{{\rm{sub}}}}}\left({\theta }_{{{{\rm{sub}}}}}\right)\sin {\theta }_{{{{\rm{sub}}}}}d{\theta }_{{{{\rm{sub}}}}}\) (e), and \({\gamma }_{{{{\rm{ATW}}}}}=\int {I}_{{{{\rm{to}}}}-{{{\rm{sub}}}}}\left({\theta }_{{{{\rm{sub}}}}}\right){{{\rm{ATW}}}}({\theta }_{{{{\rm{sub}}}}})d{\theta }_{{{{\rm{sub}}}}}\) (f), respectively. The stars indicate the (\({d}_{{{{\rm{ETL}}}}}\), \({d}_{{{{\rm{HTL}}}}}\)) that maximizes each integral. g To-substrate angular emission intensity of the OLEDs with their (\({d}_{{{{\rm{ETL}}}}}\), \({d}_{{{{\rm{HTL}}}}}\)) of (50 nm, 30 nm), (50 nm, 50 nm), and (70 nm, 140 nm), respectively. h The ratio of the power emitted from the EML to the radiant power received by the reception aperture in the geometry of \({r}_{{{{\rm{RA}}}}}/{r}_{{{{\rm{EA}}}}}=2\) and \({t}_{{{{\rm{sub}}}}}/{r}_{{{{\rm{EA}}}}}=1.4\). i Design rule of the optical structure cross-section comprised of C- and S-edges. j The cross-sections of optical structures designed with its weighting function of 30° lowpass (LP₃₀-LOS) and constant functions (UH-LOS), respectively and optimized for the OLED with its (\({d}_{{{{\rm{ETL}}}}}=50\,{{{\rm{nm}}}}\), \({d}_{{{{\rm{HTL}}}}}=50\,{{{\rm{nm}}}}\)).