Efficient ray-optical scheme for radiation of incoherent sources in flexible layered formations

We present a ray-optical method for incorporating the spectral distribution of incoherent emitters into analytical electromagnetic models solving the radiation problem of sources embedded in arbitrarily shaped layered media. Such a configuration is typical to spontaneous emission at optical wavelengths, e.g. from flexible organic light-emitting diodes (FOLEDs). Geometrical ray-optics, highly applicable to such high-frequency asymptotic problems, is utilized for the derivation of a solution, resulting in an infinite ray-series. While in general this series may be truncated to a finite number of terms (M) by neglecting highorder reflections, further significant reduction can be achieved by integrating over the spectral distribution, thus establishing the main contribution of our work. The resultant closed-form expressions reveal a fundamental interplay between the ensemble spectral width and the layer dimensions, indicating that for typical devices, the number of terms in the radiation pattern series can be greatly reduced, generally from O(M²)to O(M). This results in both an efficient analytical scheme and clear physical interpretation, consistent with experimental results.