We present an analytic model to describe the existence of photonic energy gaps in the propagation of surface plasmon polaritons on corrugated surfaces. We concentrate on elucidating the physical origin of the band gap, and accordingly we place strong emphasis on the physical reasoning and assumptions that we use. Our model is designed to give direct access to expressions for the electromagnetic field and surface charge distributions associated with modes at the band edges, thus allowing their physical character to be easily appreciated. Having established why a band gap occurs we then find expressions for the central position and width of the gap. We compare the results of our model for the gap width with those already in the literature, and find excellent agreement. Our results for the central position of the gap, notably the prediction that it should fall as the corrugation amplitude rises, contradicts one prediction made in the literature. We also reexamine the comparisons made in the literature between experiment and theory for the gap width, and find them inadequate because the theories have been compared to inappropriate experimental data. Consequently we present our own recent experimental data, enabling us to validate our theoretical results, in particularmore » confirming our prediction that the central position of the gap falls as the corrugation amplitude is increased. The limitations of our model are discussed, as well as possible extensions and areas for future research. {copyright} {ital 1996 The American Physical Society.}« less