Light propagation in a cylindrical waveguide with a complex, metallic, dielectric function

Motivated by problems in scanning near-field optical microscopy, we discuss light propagation in circular dielectric waveguides with finite aluminum cladding. In order to understand the origin of the different solutions, optical modes are first investigated for the dielectric waveguide with infinite aluminum cladding and for the aluminum cylinder. For aluminum a plasma dispersion law is assumed, leading to complex dielectric constants with negative real parts and to generally complex propagation constants. The dependence of the dispersion on the geometry and on the frequency is discussed for the various kinds of modes. We find that the existence of most of the modes is limited to certain frequencies and geometries, i.e., the solutions have a cutoff in the complex propagation constant plane. Contrary to dielectric waveguide theory, where cutoff describes the abrupt transition from propagating to evanescent modes, no other solution is generated when cutoff of a mode is reached. Surface modes and other kinds of modes, such as guided or bulk modes, can either couple between each other or transform into each other.