Surface plasmon modes in multi-layer thin-films

The surface plasmon modes in multi-layer thin-film structures of the metal–insulator–metal (MIM) type are modeled using a matrix method for the propagation of electromagnetic waves in stratified media. It is shown that the dispersion relation for the allowed surface plasmon modes is obtained from one of the matrix elements. The fundamental electromagnetic modes are the eigenfunctions of the differential equation for the magnetic field distribution and the eigenvalues are obtained from the dispersion relation. The expansion of an arbitrary wave profile in terms of the eigenfunctions is discussed and applied to the problem of surface plasmons propagating in a structure consisting of seven layers of alternating metal films and dielectrics.