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Three-dimensional ray tracing simulations show that a significant fraction of the phosphorescence emitted in high-power white light-emitting diode lamps with a remote phosphor is trapped as whispering-gallery modes propagating along the circumference of the encapsulant. The whispering-gallery modes, which are a significant optical loss mechanism and occur for multiple shapes of the encapsulation dome, are shown to be sensitively dependent on the diffusivity of the reflector cup employed in the lamp. By employing a diffuse reflector cup, up to 86% of the trapped modes is extracted out from the encapsulant. In addition, it is experimentally demonstrated that the phosphorescence efficiency is improved by up to 12.2% as the diffusivity of the reflector increases. The experimental results are consistent with theoretical ray tracing simulations.