Extending the concept of edge collection function to polygonal and curved planar luminescent waveguides

When a single spot in a planar luminescent waveguide is excited, some photoluminescence photons that are trapped inside reach its edge. Considering the photon losses due to leakage from its top and bottom surfaces and self-absorption during wave-guiding, the probability of collecting photons at its edge is expressed as a function of the coordinates of the excited spot for polygonal and curved waveguides. The emission is assumed to be isotropic, and scattering and re-emission events are neglected for simplicity. This model might be useful for predicting the performance of luminescent waveguides with various shapes under non-uniform illumination.