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When photoluminescence photons propagate in a planar luminescent waveguide, some are lost due to self-absorption and leakage from the top and bottom surfaces. The probability of the photon reaching a specified edge of the waveguide depends on the distance from the emission point. It is formulated by expressing the spectral intensities of the waveguided photons in cylindrical geometry first. Scattering and re-emission events are neglected for simplicity. Then, by specifying the perimeter of a waveguide and its photon-collecting region, the resultant radial distribution is converted to an Edge Collection Function. This is defined as the probability of collecting photons at a specified edge in case of single-spot excitation. It allows one to calculate optical efficiency for an arbitrary incident light pattern. This function is calculated for square and hexagonal waveguides which are suited for tiling. A figure of merit is defined as the product of the following factors: the probability of absorbing the incident light, Edge Collection Function averaged over the whole incident surface, and the geometric concentration factor. Its value for a hexagonal waveguide is slightly higher than that for a square one.
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