Integrating photonic microstructures into organic light-emitting diodes (OLEDs) has been a widely used strategy to improve their light out-coupling efficiency. However, there is still a need for optical modelling methods which quantitatively characterise the spatial emission pattern of microstructured OLEDs. In this paper, we demonstrate such rigorous calculation using the reciprocity theorem. The calculation of the emission intensity at each direction in the far field can be simplified into only two simple calculations of an incident plane wave propagating from the far field into a single cell of the periodic structure. The emission from microstructured OLED devices with three different grating periods was calculated as a test of the approach, and the calculated results were in good agreement with experiment. This optical modelling method is a useful calculation tool to investigate and control the spatial emission pattern of microstructured OLEDs.
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