The electromagnetic resonances of multilayer metal-dielectric stacks are investigated. These structures support periodic bandpass regions, whose band edges may be predicted by considering the character of the fields inside the different layers. It is shown that the response of the structure is largely independent of its overall length, and that only the geometry of the unit cell is important. In the metal layers, the fields may have either a cosh or a sinh distribution function and match to standing waves inside the adjacent dielectric cavities at the metal-dielectric interface. It is shown that the different boundary conditions, imposed by the evanescent fields, result in the dielectric layers having a different effective length for the two modes. The sinh fields result in an effective length being very close to that of the physical length, and adjacent cavities oscillating out of phase, while the cosh fields may result in a significantly larger effective dielectric length and adjacent cavities oscillating in phase. A bandpass region is opened, with its high frequency edge always being near the dielectric Fabry-Perot limit, while the low frequency band edge is significantly redshifted.

The dispersion diagrams of surface plasmon polaritons have been calculated for rectangular gratings, with very narrow wires, of varying depths. For gratings with a moderate height a family of vertical-standing-wave resonances may be excited, which consist of surface plasmons, oscillating on either vertical surface, coupling together through the metal wires. These modes evolve similarly to the manner in which shallow-grating surface-plasmon dispersion curves evolve into cavity modes in the grooves of the structure. However, on further increase in grating height these vertical standing waves evolve into a second resonant feature, which is independent of yet further increases in height. This new mode is shown to be equivalent to the resonances found on infinite multilayer metal/dielectric structures illuminated at normal incidence.

The optical response of sub-wavelength silver lamellar gratings has been theoretically investigated. Two distinct types of resonance have been predicted for incident radiation with E-field perpendicular to the long axis of the wires. The first resonance has been identified as a cavity mode resonance that is associated with transmission enhancement. The second resonance has been identified as an entirely new horizontal plasmon resonance on the incident (and transmission) surfaces of the wires of the grating. Normal surface plasmon modes are investigated on discontinuous gratings, and their relation to those found on continuous gratings is highlighted by focusing on the perturbation effect of the discontinuities. It is shown that the new horizontal plasmon mode is in no way related to the well known diffractively coupled surface plasmon, and is shown to have a particle plasmon-like nature. It is therefore termed a horizontal particle plasmon, and may be either an uncoupled horizontal particle plasmon resonance (a 1-dimensional particle plasmon) or a coupled horizontal particle plasmon resonance (a 2-dimensional particle plasmon) depending on the height of the grating. It is shown that this resonance may result in a reflection efficiency that is very high, even when the grating would be optically thin if it were a homogeneous film, therefore, it behaves as an inverse wire grid polariser as it reflects more TM than TE incident radiation.