PHYSICAL ORIGIN OF PHOTONIC ENERGY GAPS IN THE PROPAGATION OF SURFACE-PLASMONS ON GRATINGS

We present an analytic model to describe the existence of photonic ene rgy gaps in the propagation of surface plasmon polaritons on corrugate d surfaces. We concentrate on elucidating the physical origin of the b and gap, and accordingly we place strong emphasis on the physical reas oning and assumptions that we use. Our model is designed to give direc t access to expressions for the electromagnetic field and surface char ge distributions associated with modes at the band edges, thus allowin g their physical character to be easily appreciated. Having establishe d why a band gap occurs we then find expressions for the central posit ion 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 agr eement. Our results for the central position of the gap, notably the p rediction that it should fall as the corrugation amplitude rises, cont radicts one prediction made in the literature. We also reexamine the c omparisons made in the literature between experiment and theory for th e gap width, and find them inadequate because the theories have been c ompared to inappropriate experimental data. Consequently we present ou r own recent experimental data, enabling us to validate our theoretica l results, in particular confirming our prediction that the central po sition of the gap falls as the corrugation amplitude is increased. The limitations of our model are discussed, as well as possible extension s and areas for future research.