Gallium nitride (GaN)-based light-emitting diodes (LEDs) with cylindrical nanostructures have been the subject of significant research interest in the past decade, due to the potential of such structures to increase light extraction efficiency and deliver highly directional light emission. Nanorod LEDs, where the light emission is within the nanocylinder, have the additional potential to increase internal quantum efficiency and emit in colours previously thought impractical with GaN-based LEDs. Optical modelling of nanostructured LEDs is usually carried out using finite-difference time-domain methods, which are computationally intensive and do not always provide sufficient insight into the physics underlying the simulation results. This thesis proposes an intuitive, quasi-analytic method based on modal expansion. It is found that it is possible to calculate the far field diffraction patterns of all guided modes supported by a single nanorod, with full consideration of Fabry-Perot effects, in minutes using a standard office desktop computer. Focus is placed on the case of a nanorod of radius 140 nm, for which angular photoluminescence measurements were available to provide a means of validating the model. Consideration of the guided modes alone provides a compelling explanation for gross features in the measured data where none previously existed. It is shown that, using a standard equation from a textbook, it is possible to calculate how much each of the guided and radiation modes of a single nanorod is excited by a Hertzian dipole of known position and orientation with respect to the nanorod geometry. When interference between these modes is considered, it is possible to calculate the total far field angular emission pattern due to that dipole. Comparing these patterns with photoluminescence measurements allows one to infer the locations and orientations of dipole current sources; the results are found to be consistent with those of cathodoluminescence studies.