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We designed and fabricated GaN-based light emitting diodes encompassed with self-aligned nanorod arrays of three different distribution densities. The radiation profiles show that the device with less dense nanorod distribution has the highest optical power enhancement factor. By regarding the nanorod arrays as sidewall reflectors, the enhancement is due to the light diffraction of the laterally guided mode to radiative modes in the surface normal direction. As for the densest nanorods in our experiment, the radiation profile shows a better emission directionality as the guided modes are phase matched to the radiation modes. However, they show less optical output enhancement since some of the laterally propagated light is diffracted back to p-mesa by the first several columns of nanorods.