Non-spectral Field Representations in Dielectric Fibre Guides

Open waveguiding structures, such as acoustic, piezoelectric,gyrotropic and dielectric waveguides, are used for a varietyof applications. An example of such open waveguides is the dielectricfibre guide used in the construction of optical communicationsystems. An understanding of the modal properties of this guideis therefore of fundamental interest to the understanding ofthe modal properties of similar open structures. We analysein detail the transverse electric (TE) and transverse magnetic(TM) polarized electromagnetic fields within a circularly cylindricaldielectric waveguide with arbitrary non-vanishing analytic radialpermittivity variation. It is shown that the field can be representedas an infinite sum of functions, including the finite numberof spectral (surface wave) and an infinity of non-spectral (complex)eigenfunctions. Additional functions are also included. Boththe field polarization and the behaviour of the permittivityat the waveguide boundary are found to affect the form and thevalidity of the representation.