Eigenmodes for metal-dielectric light-transmitting nanostructures

We show that the concept of optical eigenmodes in lossless waveguide structures, which assumes the separation into propagating and evanescent modes, fails in the case of metal-dielectric structures. In addition to these modes, there is a sequence of new eigenstates with complex values of the propagation constant and nonvanishing lateral energy flows. The whole eigenmode problem ceases to be Hermitian because of changing sign of the optical dielectric constant. Particular examples of the waveguide structures include single slits, one-dimensional photonic crystals, and circular holes. The emphasis is made on the structures with nanoholes (whose sizes are considerably smaller than the light wavelength) possessing propagation modes and showing an extraordinary high light transmission. The results obtained form a necessary basis for modelling of this phenomenon.